U.S. patent application number 12/947585 was filed with the patent office on 2011-03-10 for defect-and-failure-tolerant demultiplexer using series replication and error-control encoding.
Invention is credited to Philip J. Kuekes, Warren Robinett, R. Stanley Williams.
Application Number | 20110057683 12/947585 |
Document ID | / |
Family ID | 38923884 |
Filed Date | 2011-03-10 |
United States Patent
Application |
20110057683 |
Kind Code |
A1 |
Robinett; Warren ; et
al. |
March 10, 2011 |
DEFECT-AND-FAILURE-TOLERANT DEMULTIPLEXER USING SERIES REPLICATION
AND ERROR-CONTROL ENCODING
Abstract
One embodiment of the present invention is a method for
constructing defect-and-failure-tolerant demultiplexers. This
method is applicable to nanoscale, microscale, or larger-scale
demultiplexer circuits. Demultiplexer circuits can be viewed as a
set of AND gates, each including a reversibly switchable
interconnection between a number of address lines, or
address-line-derived signal lines, and an output signal line. Each
reversibly switchable interconnection includes one or more
reversibly switchable elements. In certain demultiplexer
embodiments, NMOS and/or PMOS transistors are employed as
reversibly switchable elements. In the method that represents one
embodiment of the present invention, two or more serially connected
transistors are employed in each reversibly switchable
interconnection, so that short defects in up to one less than the
number of serially interconnected transistors does not lead to
failure of the reversibly switchable interconnection. In addition,
error-control-encoding techniques are used to introduce additional
address-line-derived signal lines and additional switchable
interconnections so that the demultiplexer may function even when a
number of individual, switchable interconnections are
open-defective.
Inventors: |
Robinett; Warren; (Chapel
Hill, NC) ; Kuekes; Philip J.; (Menlo Park, CA)
; Williams; R. Stanley; (Portola Valley, CA) |
Family ID: |
38923884 |
Appl. No.: |
12/947585 |
Filed: |
November 16, 2010 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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11484961 |
Jul 12, 2006 |
7872502 |
|
|
12947585 |
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Current U.S.
Class: |
326/9 |
Current CPC
Class: |
H03K 19/00315 20130101;
G06F 11/1076 20130101; H03K 19/007 20130101 |
Class at
Publication: |
326/9 |
International
Class: |
H03K 19/003 20060101
H03K019/003 |
Claims
1. A compound transistor comprising: m branches; and n serially
linked simple transistors in each of the m branches.
2. The compound transistor of claim 1 wherein n+m.gtoreq.1,
n.gtoreq.1, and m.gtoreq.0.
3. The compound transistor of claim 1 wherein the simple
transistors include: PMOS transistors; NMOS transistors; and
various additional types of field-effect transistors.
4. The compound transistor of claim 1 used within one of various
types of circuits and devices that include multiplexers,
demultiplexers, and logic gates.
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] The present application is a divisional application of
application Ser. No. 11/484,961, filed Jul. 12, 2006. the contents
of which are hereby incorporated herein in their entireties.
TECHNICAL FIELD
[0002] The present invention is related to
defect-and-failure-tolerant circuitry, integrated circuits, and
electronic devices and, in particular, to a method for employing
series replication of transistors and error-control-coding-based
signal-line redundancies to produce defect-and-failure-tolerant
demultiplexers.
BACKGROUND OF THE INVENTION
[0003] The spectacular decrease in the size of electronic circuits
and circuit components, including transistors, made possible by
continuous advances in photolithography and other
integrated-circuit fabrication technologies, and the ever
decreasing per-component cost of manufacturing transistors and
integrated circuits has lead to the development of increasingly
complex and densely patterned integrated circuits and electronic
devices. For example, the development of near-nanoscale
integrated-circuit manufacturing techniques has provided the basis
for development of the complex and extremely high-speed processors
that drive modern computers and processor-controlled electronic
devices, including personal computers, home-entertainment systems,
and a wide variety of processor-controlled machinery and electrical
systems used in airplanes, automobiles, machine tools, medical
instruments, scientific instruments, and a host of other products
and systems. The ability to economically and reliably manufacture
dense, large-scale arrays of transistors has led, for example, to
the development and commercialization of thin-film transistor LCD
monitors and TV screens.
[0004] However, as electrical circuitry grows increasingly smaller
and is more densely fabricated, manufacturing errors often become
more difficult to control. Even the presence of a tiny speck of
dust or a submicroscale misalignment of a photolithography mask
during manufacturing processes can lead to manufacturing defects in
many tens to hundreds of submicroscale electronic components,
including transistors and transistor-based logic gates. The
accumulation of such defects quickly leads to defective circuits
and devices and to precipitously decreasing yields of operational
devices produced by currently employed manufacturing processes. For
this reason, and because the scale at which electronic-circuit
components can be fabricated is being pushed increasingly smaller
by emerging technologies, further exacerbating problems associated
manufacturing defects, significant research and development efforts
are being applied to developing defect tolerance within electrical
circuits, integrated circuits, and electronic devices. Many of
these techniques are equally applicable to failures in
electronic-circuit components that arise after manufacture.
[0005] Many approaches to defect tolerance and failure tolerance
rely on incorporating redundant components in circuits, devices,
and systems, so that if a single component of a set of multiple,
redundant components fails, the remaining, operational components
within the set of multiple, redundant components may continue to
provide a desired functionality. Redundancies may be employed at
large-scale component levels, at the level of modules within
electronic circuits and integrated circuits, and at smaller levels.
However, incorporating redundancy within circuits and devices may
increase manufacturing costs, power consumption, and, at times,
increase the complexity of a system, thereby introducing
opportunities for new types of failures and manufacturing defects.
For example, while four-engine airplanes may intuitively seem to be
inherently more safe than two-engine airplanes, failure analysis
has shown, in certain cases, that the increased complexity of
control and monitoring systems in four-engine airplanes may
actually more than offset safety gains from the two redundant
engines. For this reason, designers and manufacturers of electrical
circuits, integrated circuits, and electronic devices are
continually seeking new methods and approaches for increasing
defect tolerance and failure tolerance of electrical circuits,
integrated circuits, and electronic devices without unnecessarily
increasing the complexity of the circuits and devices, without
unnecessarily increasing manufacturing costs and power consumption
of the circuits and devices, and without creating new modes and
opportunities for defects and failures that would offset gains
obtained by the defect-and-failure-tolerant methods and
approaches.
SUMMARY OF THE INVENTION
[0006] One embodiment of the present invention is a method for
constructing defect-and-failure-tolerant demultiplexers. This
method is applicable to nanoscale, microscale, or larger-scale
demultiplexer circuits. Demultiplexer circuits can be viewed as a
set of AND gates, each including a reversibly switchable
interconnection between a number of address lines, or
address-line-derived signal lines, and an output signal line. Each
reversibly switchable interconnection includes one or more
reversibly switchable elements. In certain demultiplexer
embodiments, NMOS and/or PMOS transistors are employed as
reversibly switchable elements. In a method that represents one
embodiment of the present invention, two or more serially connected
transistors are employed in each reversibly switchable
interconnection, so that short defects in up to one less than the
number of serially interconnected transistors do not lead to
failure of the reversibly switchable interconnection. In addition,
error-control-encoding techniques are used to introduce additional
address-line-derived signal lines and additional switchable
interconnections so that the demultiplexer may function even when a
number of individual, switchable interconnections are
open-defective. Additional embodiments of the present invention
include demultiplexers that incorporate both serial redundancy of
switchable elements within reversibly switchable interconnections
and parallel redundancy of address-line-derived signal lines and
reversibly switchable interconnections.
BRIEF DESCRIPTION OF THE DRAWINGS
[0007] FIGS. 1A-B illustrate operation of an NMOS transistor used
in a digital logic circuit.
[0008] FIG. 2 illustrates operational characteristics of NMOS and
PMOS transistors within digital logical circuits.
[0009] FIGS. 3A-C illustrate two types of defects that may occur in
an NMOS transistor.
[0010] FIGS. 4A-B illustrate one technique for incorporating
redundant transistors within circuits in order that the circuits
survive defects or failures of individual transistors according to
one embodiment of the present invention.
[0011] FIG. 5 illustrates certain combinations of working,
open-defective, and short-defective individual transistors within a
2S.times.2P compound transistor that lead to functional and
nonfunctional 2S.times.2P compound transistors according to one
embodiment of the present invention.
[0012] FIGS. 6 and 7 illustrate computation of the reliability of a
2S.times.2P compound transistor based on known rates of short
defects and open defects within the single transistors that
together compose the 2S.times.2P compound transistor according to
one embodiment of the present invention.
[0013] FIG. 8 shows a 12-transistor reversibly switchable element
comprising three parallel branches, each branch composed of four
serially linked simple transistors according to one embodiment of
the present invention.
[0014] FIGS. 9A-B show two different types of AND gates.
[0015] FIG. 10 shows a simple, two-address-line demultiplexer based
on parallel PMOS-transistor-based AND gates.
[0016] FIG. 11 illustrates operation of the PMOS-transistor-based
demultiplexer shown in FIG. 10.
[0017] FIGS. 12A-D illustrate the functional state of the
PMOS-transistor-based demultiplexer shown in FIGS. 10-11 when all
component PMOS transistors are functional and when certain of the
component PMOS transistors are defective.
[0018] FIGS. 13-14 illustrate one approach to creating a
defect-and-failure-tolerant demultiplexer that represents one
embodiment of the present invention.
[0019] FIGS. 15-16 illustrate a defect-and-failure-tolerant
demultiplexer, equivalent to the demultiplexers shown in FIGS.
10-11 and 14, which represents one embodiment of the present
invention.
[0020] FIGS. 17A-H illustrate, using the same illustration
conventions as employed in FIGS. 12A-D, various functional states
of the demultiplexer shown in FIG. 16 that represents one
embodiment of the present invention.
DETAILED DESCRIPTION OF THE INVENTION
[0021] The present invention is related to the design of circuits,
including demultiplexer circuits, at the nanoscale, microscale, and
larger-scale levels. An embodiment of the present invention
provides a method for designing defect-and-failure-tolerant
demultiplexers. Demultiplexers are used in many different
applications for address-based accessing of signal lines and
components. Additional embodiments of the present invention include
various types of demultiplexer circuits and demultiplexer-based
devices that incorporate serial switching-element redundancy and
parallel address-line-derived signal-line redundancies in order to
ameliorate short defects and open defects in reversibly switchable
elements within reversibly switchable interconnects. The parallel
redundancies are based on error-control-coding techniques developed
for a variety of information storage and information transmission
and reception applications. In a first subsection, below, an
overview of error-control-coding techniques is provided. In a
second subsection, embodiments of the present invention are
discussed.
Error-Control-Coding Techniques
[0022] Embodiments of the present invention employ concepts derived
from well-known techniques in error-control encoding. An excellent
reference for this field is the textbook "Error Control Coding: The
Fundamentals and Applications," Lin and Costello, Prentice-Hall,
Incorporated, New Jersey, 1983. In this subsection, a brief
description of the error-detection and error-correction techniques
used in error-control encoding is set forth. Additional details can
be obtained from the above-referenced textbook, or from many other
textbooks, papers, and journal articles in this field. The current
subsection represents a rather mathematically precise, but concise,
description of certain types of error-control encoding techniques.
The current invention employs concepts inherent in these
error-control encoding techniques for a different purpose.
Error-control encoding techniques systematically introduce
supplemental bits or symbols into plain-text messages, or encode
plain-text messages using a greater number of bits or symbols than
absolutely required, in order to provide information in encoded
messages to allow for errors arising in storage or transmission to
be detected and, in some cases, corrected. One effect of the
supplemental or more-than-absolutely-needed bits or symbols is to
increase the distance between valid codewords, when codewords are
viewed as vectors in a vector space and the distance between
codewords is a metric derived from the vector subtraction of the
codewords. The current invention employs concepts used in
error-control coding to add supplemental address-line-derived
signal lines to increase the distance between valid addresses in
order to correspondingly increase the signal separation, in the
number of reversibly switchable interconnections needed to be
properly set in order to address a signal line, and to thereby
provide open-defect tolerance in a demultiplexer. Thus, in the
current invention, the plain-text and encoded messages of
error-control encoding are analogous to input addresses and coded
addresses, and the additional or greater-number-than-needed symbols
or bits in error-control encoding are analogous to supplemental or
a greater-than-absolutely-needed number of address-line derived
signal lines.
[0023] In describing error detection and correction, it is useful
to describe the data to be transmitted, stored, and retrieved as
one or more messages, where a message .mu. comprises an ordered
sequence of symbols, .mu..sub.i, that are elements of a field F. A
message .mu. can be expressed as:
.mu.=(.mu..sub.0, .mu..sub.1, . . . .mu..sub.k-1)
where .mu..sub.i.epsilon.F. The field F is a set that is closed
under multiplication and addition, and that includes multiplicative
and additive inverses. It is common, in computational error
detection and correction, to employ fields comprising a subset of
integers with sizes equal to a prime number, with the addition and
multiplication operators defined as modulo addition and modulo
multiplication. In practice, the binary field is commonly employed.
Commonly, the original message is encoded into a message c that
also comprises an ordered sequence of elements of the field F,
expressed as follows:
c=(c.sub.0, c.sub.1, . . . c.sub.n-1)
where c.sub.i.epsilon.F.
[0024] Block encoding techniques encode data in blocks. In this
discussion, a block can be viewed as a message p comprising a fixed
number of symbols k that is encoded into a message c comprising an
ordered sequence of n symbols. The encoded message c generally
contains a greater number of symbols than the original message
.mu., and therefore n is greater than k. The r extra symbols in the
encoded message, where r equals n-k, are used to carry redundant
check information to allow for errors that arise during
transmission, storage, and retrieval to be detected with an
extremely high probability of detection and, in many cases,
corrected.
[0025] In a linear block code, the 2.sup.k codewords form a
k-dimensional subspace of the vector space of all n-tuples over the
field F. The Hamming weight of a codeword is the number of non-zero
elements in the codeword, and the Hamming distance between two
codewords is the number of elements in which the two codewords
differ. For example, consider the following two codewords a and b,
assuming elements from the binary field:
a=(1 0 0 1 1)
b=(1 0 0 0 1)
The codeword a has a Hamming weight of 3, the codeword b has a
Hamming weight of 2, and the Hamming distance between codewords a
and b is 1, since codewords a and b differ only in the fourth
element. Linear block codes are often designated by a three-element
tuple [n, k, d], where n is the codeword length, k is the message
length, or, equivalently, the base-2 logarithm of the number of
codewords, and d is the minimum Hamming distance between different
codewords, equal to the minimal-Hamming-weight, non-zero codeword
in the code.
[0026] The encoding of data for transmission, storage, and
retrieval, and subsequent decoding of the encoded data, can be
notationally described as follows, when no errors arise during the
transmission, storage, and retrieval of the data:
.mu..fwdarw.c(s).fwdarw.c(r).fwdarw..mu.
where c(s) is the encoded message prior to transmission, and c(r)
is the initially retrieved or received, message. Thus, an initial
message .mu. is encoded to produce encoded message c(s) which is
then transmitted, stored, or transmitted and stored, and is then
subsequently retrieved or received as initially received message
c(r). When not corrupted, the initially received message c(r) is
then decoded to produce the original message .mu.. As indicated
above, when no errors arise, the originally encoded message c(s) is
equal to the initially received message c(r), and the initially
received message c(r) is straightforwardly decoded, without error
correction, to the original message .mu..
[0027] When errors arise during the transmission, storage, or
retrieval of an encoded message, message encoding and decoding can
be expressed as follows:
.mu.(s).fwdarw.c(s).fwdarw.c(r).fwdarw..mu.(r)
Thus, as stated above, the final message .mu..sub.r may or may not
be equal to the initial message .mu.(s), depending on the fidelity
of the error detection and error correction techniques employed to
encode the original message .mu.(s) and decode or reconstruct the
initially received message c(r) to produce the final received
message .mu.(r). Error detection is the process of determining
that:
c(r).noteq.c(s)
while error correction is a process that reconstructs the initial,
encoded message from a corrupted initially received message:
c(r).fwdarw.c(s)
[0028] The encoding process transforms messages, symbolized as
.mu., into encoded messages .mu.. Alternatively, a messages .mu.
can be considered to be a word comprising an ordered set of symbols
from the alphabet consisting of elements of F, and the encoded
messages c can be considered to be a codeword also comprising an
ordered set of symbols from the alphabet of elements of F. A word
.mu. can be any ordered combination of k symbols selected from the
elements of F, while a codeword c is defined as an ordered sequence
of n symbols selected from elements of F via the encoding
process:
{c:.mu..fwdarw.c}
[0029] Linear block encoding techniques encode words of length k by
considering the word .mu. to be a vector in a k-dimensional vector
space, and multiplying the vector .mu. by a generator matrix, as
follows:
c=.mu.G
Notationally expanding the symbols in the above equation produces
either of the following alternative expressions:
( c 0 , c 1 , , c n - 1 ) = ( .mu. 0 , .mu. 1 , , .mu. k - 1 ) ( g
00 g 01 g 02 g 0 , n - 1 g k - 1 , 0 g k - 1 , 1 g k - 1 , 2 g k -
1 , n - 1 ) ##EQU00001## ( c 0 , c 1 , , c n - 1 ) = ( .mu. 0 ,
.mu. 1 , , .mu. k - 1 ) ( g 0 g 1 g k - 1 ) ##EQU00001.2##
where g.sub.i=(g.sub.i,0, g.sub.i,1, g.sub.i,2 . . .
g.sub.i,n-1).
[0030] The generator matrix G for a linear block code can have the
form:
G k , n = ( p 0 , 0 p 0 , 1 p 0 , r - 1 1 0 0 0 p 1 , 0 p 1 , 1 p 1
, r - 1 0 1 0 0 0 0 1 0 p k - 1 , 0 p k - 1 , 1 p k - 1 , r - 1 0 0
0 1 ) ##EQU00002##
or, alternatively:
G.sub.k,n=[P.sub.k,r|I.sub.k,k].
Thus, the generator matrix G can be placed into a form of a matrix
P augmented with a k-by-k identity matrix I.sub.k,k. A code
generated by a generator in this form is referred to as a
"systematic code." When this generator matrix is applied to a word
.mu., the resulting codeword c has the form:
c=(c.sub.0, c.sub.1, . . . , c.sub.r-1, .mu..sub.0, .mu..sub.1, . .
. , .mu..sub.k-1)
where
c.sub.i=.mu..sub.0p.sub.0,i+.mu..sub.1p.sub.1.1, . . . ,
.mu..sub.k-1p.sub.k-1.1).
Note that, in this discussion, a convention is employed in which
the check symbols precede the message symbols. An alternate
convention, in which the check symbols follow the message symbols,
may also be used, with the parity-check and identity submatrices
within the generator matrix interposed to generate codewords
conforming to the alternate convention. Thus, in a systematic
linear block code, the codewords comprise r parity-check symbols
c.sub.i followed by the symbols comprising the original word .mu..
When no errors arise, the original word, or message .mu., occurs in
clear-text form within, and is easily extracted from, the
corresponding codeword. The parity-check symbols turn out to be
linear combinations of the symbols of the original message, or word
.mu..
[0031] One form of a second, useful matrix is the parity-check
matrix H.sub.r,n, defined as:
H.sub.r,n=[I.sub.r,r|-P.sup.T]
or, equivalently,
H r , n = ( 1 0 0 0 - p 0 , 0 - p 1 , 0 - p 2 , 0 - p k - 1 , 0 0 1
0 0 - p 0 , 1 - p 1 , 1 - p 2 , 1 - p k - 1 , 1 0 0 1 0 - p 0 , 2 -
p 1 , 2 - p 2 , 2 - p k - 1 , 2 0 0 0 1 - p 0 , r - 1 - p 1 , r - 1
- p 0 , r - 1 - p k - 1 , r - 1 ) . ##EQU00003##
The parity-check matrix can be used for systematic error detection
and error correction. Error detection and correction involves
computing a syndrome S from an initially received or retrieved
message c(r) as follows:
S=(s.sub.0, s.sub.1, . . . , s.sub.r-1)=c(r)H.sup.T
where H.sup.T is the transpose of the parity-check matrix H.sub.r,n
expressed as:
H T = ( 1 0 0 0 0 1 0 0 0 0 1 0 . . . 1 - p 0 , 0 - p 0 , 1 - p 0 ,
2 - p 0 , r - 1 - p 1 , 0 - p 0 , 1 - p 0 , 2 - p 0 , r - 1 - p 2 ,
0 - p 0 , 1 - p 0 , 2 - p 0 , r - 1 . . . . - p k - 1 , 0 - p k - 1
, 1 - p k - 1 , 2 - p k - 1 , r - 1 ) . ##EQU00004##
Note that, when a binary field is employed, x=-x, so the minus
signs shown above in H.sup.T are generally not shown.
[0032] Hamming codes are linear codes created for error-correction
purposes. For any positive integer in greater than or equal to 3,
there exists a Hamming code having a codeword length n, a message
length k, number of parity-check symbols r, and minimum Hamming
distance d.sub.min as follows:
n=2.sup.m-1
k=2.sup.m-m-1
r=n-k=m
d.sub.min=3
The parity-check matrix H for a Hamming Code can be expressed
as:
H=[I.sub.m|Q]
where I.sub.m is an m.times.m in identity matrix and the submatrix
Q comprises all 2.sup.m-m-1 distinct columns which are m-tuples
each having 2 or more non-zero elements. For example, for in m=3, a
parity-check matrix for a [7,4,3] linear block Hamming code is
H = ( 1 0 0 0 1 1 1 0 1 0 1 1 1 0 0 0 1 1 0 1 1 ) ##EQU00005##
A generator matrix for a Hamming code is given by:
G=[Q.sup.TI.sub.2.sub.m.sub.-m-1].
where Q.sup.T is the transpose of the submartix Q, and
I.sub.2.sub.m.sub.-m-1 is a (2.sup.m-m-1).times.(2.sup.m-m-1)
identity matrix. By systematically deleting l columns from the
parity-check matrix H, a parity-check matrix H' for a shortened
Hamming code can generally be obtained, with:
n=2.sup.m-l-1
k=2.sup.m-m-l-1
r=n-k=m
d.sub.min.gtoreq.3
[0033] As will be discussed, below, one embodiment of the present
invention involves employing the above-described error-control
coding techniques to a very different problem space, in which,
rather than generating codewords of length k+r from messages of
length k, interconnections between 2(k+r) address lines and
address-line-derived signal lines and 2.sup.k output signal lines
within a demultiplexer are generated using a [n, k, d] linear-block
code so that each of the 2.sup.k output signal lines can be
uniquely addressed by a k-bit input address despite as many as d-1
open-defective interconnections to each output signal line. In
other words, one embodiment of the present invention involves
applying error-control coding techniques to demultiplexer design so
that the demultiplexer is defect-and-failure tolerant to
open-defective reversibly switchable interconnections.
[0034] Other types of codes are employed to increase the Hamming
distance between codewords in various applications. Many of these
alternative codes do not have the convenient properties of linear
block codes, including easy generation using generator matrices,
and the transparent, pass-through feature of linear block codes
allowing for the encoded value to be directly read from the code
word. For linear block codes, a plain-text message transfers
directly to a codeword containing, in addition, parity-check
symbols or bits. In other types of codes, the plain-text message is
not directly readable in a corresponding codeword. In both cases,
codewords contain a greater number of symbols or bits than
absolutely needed to enumerate all valid messages to be encoded. In
the case of linear block codes, the additional symbols or bits are
parity-check symbols or bits that supplement the plain-text symbols
or bits, while in the other types of codes, valid messages are
distributed throughout a vector space of dimension equal to the
codeword size. It should be noted that, in the following
descriptions of the present invention, the term "supplemental
address lines" refers to either parity-check address lines,
analogous to parity-check symbols or bits in linear block codes, or
to the greater-number-than-absolutely-needed address lines,
analogous to the greater-number-than-needed symbols or bits in
these other types of codes. However, these other codes may have
different advantages that provide utility in different
applications.
[0035] Combinatoric codes provide a straightforward approach to
increasing the Hamming distance between codewords. To create a
combinatoric code (also known as a "constant-weight code" or an
"r-hot code"), one may select combinations of r bits having a fixed
number of 1's from a total codeword space of n-bits to produce
C r n = n ! r ! ( n - r ) ! ##EQU00006##
codewords of length n. Of course, one can produce a symmetrical
code with an identical number of codewords by choosing combinations
of r bits having a fixed number of 0's from a total codeword space
of n bits. For example, a combinatoric code including
C r n = n ! r ! ( n - r ) ! = 165 ##EQU00007##
codewords can be obtained by choosing all possible 11-bit codewords
with exactly three bits having the value "1," the codewords
provided in the following table:
TABLE-US-00001 TABLE 1 11100000000 11010000000 11001000000
11000100000 11000010000 11000001000 11000000100 11000000010
11000000001 10110000000 10101000000 10100100000 10100010000
10100001000 10100000100 10100000010 10100000001 10011000000
10010100000 10010010000 10010001000 10010000100 10010000010
10010000001 10001100000 10001010000 10001001000 10001000100
10001000010 10001000001 10000110000 10000101000 10000100100
10000100010 10000100001 10000011000 10000010100 10000010010
10000010001 10000001100 10000001010 10000001001 10000000110
10000000101 10000000011 01110000000 01101000000 01100100000
01100010000 01100001000 01100000100 01100000010 01100000001
01011000000 01010100000 01010010000 01010001000 01010000100
01010000010 01010000001 01001100000 01001010000 01001001000
01001000100 01001000010 01001000001 01000110000 01000101000
01000100100 01000100010 01000100001 01000011000 01000010100
01000010010 01000010001 01000001100 01000001010 01000001001
01000000110 01000000101 01000000011 00111000000 00110100000
00110010000 00110001000 00110000100 00110000010 00110000001
00101100000 00101010000 00101001000 00101000100 00101000010
00101000001 00100110000 00100101000 00100100100 00100100010
00100100001 00100011000 00100010100 00100010010 00100010001
00100001100 00100001010 00100001001 00100000110 00100000101
00100000011 00011100000 00011010000 00011001000 00011000100
00011000010 00011000001 00010110000 00010101000 00010100100
00010100010 00010100001 00010011000 00010010100 00010010010
00010010001 00010001100 00010001010 00010001001 00010000110
00010000101 00010000011 00001110000 00001101000 00001100100
00001100010 00001100001 00001011000 00001010100 00001010010
00001010001 00001001100 00001001010 00001001001 00001000110
00001000101 00001000011 00000111000 00000110100 00000110010
00000110001 00000101100 00000101010 00000101001 00000100110
00000100101 00000100011 00000011100 00000011010 00000011001
00000010110 00000010101 00000010011 00000001110 00000001101
00000001011 00000000111
It is somewhat more complex to encode messages into combinatoric
codes, but the logic to do so may be straightforwardly constructed
at the logic-circuit level. Combinatoric codes have a guaranteed
minimum Hamming distance of 2, and may have significantly better
average Hamming distance separations between codewords. For
example, in the above
( 11 3 ) ##EQU00008##
code, the average Hamming distance between codewords is 4.39.
Combinatoric codes also have an advantage in producing total signal
distinguishability within relatively narrow ranges, since these
codes have constant weights, where the weight is defined as the
number of bits having the value "1."
[0036] Another, similar type of code, referred to as a "random"
code, is obtained by choosing random codewords of fixed length. For
example, one can choose a fixed-length, binary, n-bit codeword
size, and select a sufficient number of random n-bit binary numbers
in order to obtain a desired number of binary codewords 2.sup.k,
where n>Ak. The greater the value of A, the greater the expected
minimum Hamming distance between the codewords. When creating
random codes, distance checking can be carried out to reject new
codewords that have a Hamming distance less than a minimum value
with respect to those codewords already selected, and random
codewords having approximately equal numbers of "1" and "0" bits
can be used in order to obtain an increased average Hamming
distance and increased expected minimum Hamming distance.
[0037] Yet another type of code that may be employed in the methods
and systems of the present invention is a random linear code. In a
random linear code, the generator matrix is randomly generated,
under linearity constraints, rather than generated as the
combination of a parity-check matrix generated from linear sums of
information elements that represent parity-check sums, and an
identity matrix. A random linear block code is generally not
systematic, but linear.
[0038] In general, codes that may be employed in the methods and
systems of the present invention may be systematic and linear,
systematic and non-linear, non-systematic and linear, or
non-systematic and non-linear. For example, if C is a code, and u
is an arbitrary n-vector, then the coset C'=u+C={u+c:c.epsilon.C}
is another code with the same distance properties, and hence with
the same error correction and defect tolerance capabilities. If C
is linear, and u is non-zero, then C' is non-linear, technically,
an affine space. The random codes are generally neither systematic
nor linear. Although linear block codes have properties that are
attractive in the applications to be discussed below, linear codes,
systematic codes, and non-linear, non-systematic codes may also be
employed in various embodiments of the present invention.
Embodiments of the Present Invention
[0039] FIGS. 1A-B illustrate operation of an NMOS transistor used
in a digital logic circuit. A transistor is used, in digital logic
circuits, as a voltage-controlled or current-controlled switch that
allows or prevents transmission of a voltage or current signal from
a source input to a drain output. In FIG. 1A, the NMOS transistor
102 is schematically shown in cross section. The NMOS transistor
comprises a p-doped silicon substrate 104 in which two highly
n-doped channels 106 and 108 are fabricated. A conductive
polysilicon gate 110 overlies a region of the p-doped silicon
substrate between the two n-doped channels 106 and 108, separated
from the p-doped silicon substrate by a thin, silicon-dioxide
insulator layer 112. In FIG. 1A, a voltage V.sub.DD is applied 114
through a resistor 116 to the source and drain, with the source
channel 106 held at the same voltage as the gate 110. Under these
conditions, no current flows through the NMOS transistor. The
circuit shown in the top portion of FIG. 1A, including the NMOS
transistor 102, is shown as an electrical schematic diagram 118 in
the lower portion of FIG. 1A. The NMOS transistor operates as an
open switch 120 with a small internal resistance r.sub.on 122.
[0040] FIG. 1B illustrates application of a voltage to the gate of
the NMOS transistor so that the NMOS transistor conducts current.
FIG. 1B uses the same illustration conventions as used in FIG. 1A.
When a voltage 124 is applied to the gate 110, as shown in FIG. 1B,
electrons are withdrawn from the gate, leaving the gate with a
cumulative positive charge. The cumulative positive charge within
the gate attracts negative charges from the p-doped silicon
substrate 104, which accumulate in a layer, or channel, 126
interconnecting the n-doped source channel 106 with the n-doped
drain channel 108. This negatively charged channel 126 can carry
current, thus completing the circuit and allowing current to flow
from the source to the drain. An electrical schematic, in the lower
portion of FIG. 1B, illustrates the circuit obtained when the NMOS
transistor switch 120 is closed.
[0041] A variety of different types of transistors are employed in
modern circuits and electronic devices, including the class of
transistors referred to as metal-oxide-semiconductor field-effect
transistors ("MOSFET"), which includes both NMOS and PMOS
transistors. FIG. 2 illustrates operational characteristics of NMOS
and PMOS transistors within digital logical circuits. An NMOS
transistor, diagrammatically represented by schematic 202 in FIG.
2, is open when a "0" logic signal is applied to the gate, and
closed when a "1" logic signal is applied to the gate, as indicated
in the first row of the table 204 provided in FIG. 2. The logic
signal "1" is often electronically represented by a positive
voltage, and the logic signal "0" is often electronically
represented as a ground or reference voltage, although alternative
conventions may be used. A PMOS transistor, diagrammatically
represented by the schematic 206 in FIG. 2, has an opposite
switching convention, shown in the second row of the table 204
provided in FIG. 2.
[0042] Two types of defects frequently occur during manufacture of
transistors, and subsequently arise as failures, during operation
of transistors within circuits and devices. FIGS. 3A-C illustrate
two types of defects that may occur in an NMOS transistor. As shown
in FIG. 3A, a functional NMOS transistor 302 acts as an open switch
when the logic signal "0" is applied to the gate 304, and as a
closed switch when the logic signal "1" is applied to the gate 306.
A stuck-open defect, or open defect, as illustrated in FIG. 3B,
results in the NMOS transistor remaining in the open-switch state,
regardless of the logic signal input to the gate. A short defect,
as illustrated in FIG. 3C, results in the NMOS transistor remaining
in the closed, conductive state regardless of the logic signal
input to the gate. Open and short defects also occur in PMOS
transistors and in other types of transistors.
[0043] Absent defect-and-failure tolerant provisions, open defects
and short defects generally result in non-functional devices in
which the defective transistors are incorporated. Even though the
probability of an open defect or short defect occurring, during
manufacture, can be controlled to be relatively low, the vast
number of transistors employed in modern circuits, integrated
circuits, and electronic devices result in significant
probabilities of defectively manufactured circuits, integrated
circuits, and electronic devices despite relatively low
probabilities of defects in individual transistors. For this
reason, a variety of techniques are employed to allow circuits,
integrated circuits, and electronic devices to tolerate a certain
number of defectively manufactured transistors and still operate in
a desired fashion. As discussed above, many of these techniques
rely on incorporating redundant modules, circuits, or larger
components within devices and systems, so that a defect or failure
in one of multiple redundant circuits, modules, or components, does
not lead to overall device or system failure.
[0044] FIGS. 4A-B illustrate one technique for incorporating
redundant transistors within circuits in order that the circuits
survive defects or failures of individual transistors according to
one embodiment of the present invention. FIG. 4A shows a compound
NMOS transistor 402 with a gate 404, source 406, and drain 408. The
compound transistor includes four simple NMOS transistors 410-413.
The gates of the four simple transistors 410-413 are electronically
connected to the gate 404 for the compound transistor, with two
pairs of simple NMOS transistors (410, 412) and (411, 413),
serially connected within two parallel circuit branches connecting
the source 406 to the drain 408. FIG. 4B shows a schematic
representation of the compound transistor. The compound transistor
shown in FIGS. 4A-B is representative of a larger class of compound
transistors, discussed below. Compound transistors of this larger
class of compound transistors are referred to as "nS.times.mP
compound transistors," "nS.times.mP transistors," or simply as
"compound transistors." In the notation "nS.times.mP", n refers to
the number of simple transistors connected in series in each
parallel branch of the nS.times.mP transistor, and m refers to the
number of parallel branches within the nS.times.mP transistor. The
compound transistor shown in FIGS. 4A-B is, according to the
above-described notation for compound transistors, a 2S.times.2P
transistor.
[0045] A compound transistor can survive various combinations of
short and open defects. FIG. 5 illustrates certain combinations of
working, open-defective, and short-defective individual transistors
within a 2S.times.2P compound transistor that lead to functional
and nonfunctional 2S.times.2P compound transistors according to one
embodiment of the present invention. In FIG. 5, two vertical
columns 502 and 504 show functional 2S.times.2P compound
transistors, and a third vertical column 506 shows examples of
nonfunctional, 2S.times.2P compound transistors. Each
compound-transistor functional state is represented, in FIG. 5, by
a diagram, such as diagram 508, in which each simple transistor is
represented by a circle 510-513 and in which the gate 514, source
515, and drain 516 are positioned corresponding to the positions of
the gate, source, and drain in the schematic shown in FIG. 4A. The
label "W" indicates a working, or functional, simple transistor,
the label "O" indicates an open-defective simple transistor, and
the label "S" indicates a short-defective simple transistor. When
all four simple transistors are working, as shown in the
functional-state diagram 508 in the first column 502 of FIG. 5, the
2S.times.2P compound transistor is functional. When a single simple
transistor is short-defective, as shown in diagram 520, the
compound transistor remains functional. The short-defective
transistor 522 is compensated for by the working transistor 524 in
the same branch as the short-defective simple transistor. When the
working transistor 524 is open, no signal is transmitted through
the branch, despite the short-defective transistor. As shown in the
diagram 526, two short-defective simple transistors, one in each of
the two parallel branches of the 2S.times.2P compound transistor,
result in a functional 2S.times.2P compound transistor. In certain
cases, as, for example, in the case represented by diagram 528 in
FIG. 5, a 2S.times.2P compound transistor remains functional even
when three of the four simple transistors are defective. However,
in other cases, two or more defective simple transistors lead to
nonfunctional 2S.times.2P compound transistors, examples of which
are shown in the third column 506 in FIG. 5. For example, as shown
in diagram 530, an open-defective transistor in each of the two
branches of the compound transistor leads to a nonfunctional,
open-defective 2S.times.2P compound transistor. As shown in diagram
532, two short-defective simple transistors within a single branch
of the 2S.times.2P compound transistor lead to a short-defective
compound transistor.
[0046] Using nS.times.mP compound transistors, rather than simple
transistors, can lead to substantially increased defect-and-failure
tolerance within a circuit. A compound transistor, by itself, has a
reliability greater than the reliability of the individual, simple
transistors of which it is composed. FIGS. 6 and 7 illustrate
computation of the reliability of a 2S.times.2P compound transistor
based on known rates of short defects and open defects within the
single transistors that together compose the 2S.times.2P compound
transistor according to one embodiment of the present invention.
The functional state of a 2S.times.2P compound transistor 602 can
be viewed as one of a number of different two-dimensional binary
patterns. Each binary pattern 604 representing a functional state
of the 2S.times.2P compound transistor includes 12 cells, such as
cell 606. Each cell is indexed by a transistor number, such as the
number "1" 608 representing the first simple transistor 610 in the
2S.times.2P compound transistor, and a functional state selected
from among the above-described functional states "W," "S," and "O."
The binary-digit contents of a cell indicate whether or not the
simple transistor corresponding to the cell currently has the state
corresponding to the cell. In subsequent diagrams, the symbol "X"
indicates that the corresponding transistor has the corresponding
state, and no symbol shown in a cell indicates that the
corresponding transistor does not have the corresponding stats.
Since each of the four transistors can occupy one of three states,
there are 81 different binary patterns that describe all of the
possible functional states of the 2S.times.2P compound
transistor.
[0047] Two types of patterns within a functional-state-representing
binary pattern represent defective 2S.times.2P compound
transistors. The first type of pattern 612 includes two
short-defective transistors within the same branch of the
2S.times.2P compound transistor, with the first two rows of the
binary pattern representing a first branch and the second two rows
in the binary pattern representing a second branch. These patterns
include two adjacent "X" symbols in the short-defective column 614,
either in the first two rows of the pattern or the second two rows
of the pattern. The other two transistors may have any of the three
states, "W," "S," and "O." Thus, there are 18 different states, or
binary patterns, that represent short-defective 2S.times.2P
compound transistors. A second type of binary pattern 616
represents an open-defective 2S.times.2P compound transistor. In
these patterns, at least one "X" symbol occurs in the
open-defective column 618 in each branch. In other words, the
2S.times.2P compound transistor is open defective when at least the
following pairs of transistors are open-defective: (1,3), (1,4),
(2,3), and (2,4). There are 36 binary patterns, or functional
states, that represent open-defective 2S.times.2P compound
transistors. By computing the probabilities of each of the
different, 81 functional states, or binary patterns, for a
2S.times.2P compound transistor based on the known defect rates of
the single, simple transistors incorporated within the compound
transistor, assuming transistor failures to be independent events,
the statistical failure or defect rate for a compound transistor
can be computed.
[0048] FIG. 7 shows a table showing the defect rate for a single
transistor and for a 2S.times.2P compound transistor that
incorporates four single transistors according to one embodiment of
the present invention. The working and defect probabilities of a
single transistor are shown in the first row 702 of the table, and
the computed probabilities for 2S.times.2P compound transistor
defects are shown in the second row 704 of the table. When the
single transistor has an overall 95% probability of being
functional, a 3% probability of being short-defective, and a 2%
probability of being open-defective, the 2S.times.2P compound
transistor has an overall 99.7% probability of being functional.
The difference between a defect-free probability of 95% and 99.7%
can lead to an enormous difference in yield of functional circuits
made up of multiple single transistors and 2S.times.2P compound
transistors. For example, in a 10-transistor circuit using simple
transistors, a 95% probability for each transistor being defect
free yields a 60% probability of the circuit being defect free,
while the same device fabricated from 10 compound-transistors, each
with a 99.7% probability of being defect free, yields a 97%
probability for the circuit being defect free. In actual devices
manufactured by current fabrication techniques, transistors are
fabricated with much higher defect-free probabilities.
[0049] Even greater defect tolerance can be achieved by
higher-order multi-transistor reversibly switchable elements, such
as nS.times.mP compound transistors with n>2 and m>2. For
example, FIG. 8 shows a 12-transistor reversibly switchable element
comprising three parallel branches, each composed of four serially
connected simple transistors, or, in other words, a 4S.times.3P
transistor, according to one embodiment of the present invention.
This 12-transistor reversibly switchable element, or 4S.times.3P
transistor, can tolerate three short-defective transistors within a
single branch, and can tolerate two open-defective parallel
branches. A higher-order reversibly switchable element, such as an
nS.times.mP compound transistor, can be composed of arbitrarily
many branches m, each composed of an arbitrary number of serially
linked simple transistors n. However, as the number of simple
transistors included within an nS.times.mP compound transistor
increases, the number of simple transistors within a
failure-tolerant circuit or device rapidly increases,
correspondingly rapidly increasing both the manufacturing cost and,
in certain cases, the power consumption.
[0050] FIGS. 9A-B show two different types of AND gates. FIG. 9
shows a serial AND gate with a voltage source V.sub.DD 902 and a
pull-down resistor 904. Three NMOS transistors 906-908 are serially
linked together. Three address lines A.sub.1, A.sub.2, and A.sub.3
910-912 are input to the gates of transistors 906-908,
respectively. The output signal line 914 of the AND gate carries a
voltage signal representing the three-way AND of the logic states
of the three address lines A.sub.1, A.sub.2, and A.sub.3. When all
three address lines have logic state "1," then, as shown in FIG. 2,
all three NMOS transistors 906-908 are closed, connecting the
output signal line 914 with the voltage source 902. Otherwise, when
even a single of the address lines has logic state "0," the output
signal line 914 is disconnected from the voltage source 902, and
has 0 voltage, being connected to ground through the pull-down
resistor 904. FIG. 9B shows a parallel AND gate employing PMOS
transistors. As in the serial AND gate, the gates of PMOS
transistors 916-918 are connected to address lines A.sub.1 920,
A.sub.2 921, and A.sub.3 922, respectively. When all of the address
lines are in logic state "1," all of the PMOS transistors are open,
as shown in FIG. 2, so that the output signal line 924 is not
connected to ground, but only to the voltage source 926 through
pull-up resistor 928. If even one of the address lines is in logic
state "0," then the output signal line 924 is connected to ground,
and has logic state "0."
[0051] FIG. 10 shows a simple, two-address-line demultiplexer based
on parallel PMOS-transistor-based AND gates. A two-bit address
input to address lines A.sub.0 1002 and A.sub.1 1004 sets one of
the four output signal lines 1006-1009 to logic state "1," while
the remaining output signal lines are set to logic state "0." Thus,
the demultiplexer allows each output signal line to be addressed,
or set to logic state "1," by a unique 2-bit address. In
alternative implementations, the addressed output signal line may
be set to logic state "0," while all other output signal lines are
set to logic state "1." In general, a demultiplexer selects the
output signal line corresponding to, or associated with, an input
address, where selection generally means that the selected output
signal line is set to desired logic state. Note that each address
line is divided into an internal signal line carrying the same
logic states as the address line and an internal signal line
carrying a logic state complementary to that of the address line,
the logic state of the complementary internal signal line set via a
NOT gate, such as NOT gate 1010. Each output signal line is
connected to a voltage source 1012 through a pull-up resistor
1004-1017.
[0052] FIG. 11 illustrates operation of the PMOS-transistor-based
demultiplexer shown in FIG. 10. In FIG. 11, the address "01" is
input to address lines 1002 and 1004. This input address results in
the pattern of open and closed transistors shown in FIG. 11. For
example, the "0" logic state of address line A.sub.0 results in a
logic state "1" on complementary signal line 1102 which, in turn,
opens PMOS transistors 1104 and 1106. Conversely, logic state "1"
input to address line A.sub.1 1004 results in a logic state "0" on
complementary signal line 1108, which in turn closes PMOS
transistors 1110 and 1112. Output signal line 1007, corresponding
to the input address "01," is not connected to ground, and
therefore essentially reflects the voltage of voltage source 1012.
All of the other output signal lines 1006 and 1008-1009 are
connected to ground through one PMOS transistor, and therefore have
logic state "0."
[0053] FIGS. 12A-D illustrate the functional state of the
PMOS-transistor-based demultiplexer shown in FIGS. 10-11 when all
component PMOS transistors are functional and when certain of the
component PMOS transistors are defective. In FIGS. 12A-D, and in
subsequent, similar figures. each transistor is represented by a
circle. such as circle 1202, within a two-dimensional matrix, each
cell of which represents each possible interconnection between
address lines, and complementary signal lines derived from the
address lines, and output signal lines. A filled circle indicates
an open transistor, and an unfilled circle represents a closed
transistor. An open circle labeled with the character "S" indicates
a short-defective transistor, and a matrix cell completely
darkened, such as matrix cell 1204, indicates an open-defective
transistor. FIG. 12A shows a fully functional demultiplexer with
input address "01," as in FIG. 11. Four PMOS transistors are open
1206-1209 and four PMOS transistors are closed 1202 and 1210-1212.
The output signal line with address "01" has logic state "1" 1214,
and the remaining output signal lines have logic state "0." FIG.
12B shows the demultiplexer with an open-defective PMOS transistor
1204. Address "01" is input to the demultiplexer in FIG. 12B.
Because of the open-defective transistor 1204, two output signal
lines 1214 and 1216 have logic state "1." Thus, the demultiplexer
is defective, since only a single output signal line corresponding
to the input address has logic state "1" in a properly functioning
demultiplexer. Similarly, FIG. 12C shows the functional state of
the demultiplexer when a PMOS transistor 1218 is short-defective.
In this case, when address "01" is input to the demultiplexer, no
output signal line has logic state "1." Thus, the demultiplexer
shown in FIG. 12C is defective. As shown in FIG. 12D, a defective
demultiplexer may still provide correct output for certain input
signals. In FIG. 12D, the address "00" is input to the defective
demultiplexer first shown in FIG. 12C, leading to the correct logic
state of the output signal lines. The PMOS-transistor-based
demultiplexer shown in FIG. 10 cannot therefore tolerate even a
single defective transistor. The PMOS-transistor-based
demultiplexer of FIGS. 10-11 is not defect-and-failure
tolerant.
[0054] FIGS. 13-14 illustrate one approach to creating a
defect-and-failure-tolerant demultiplexer that represents one
embodiment of the present invention. A defect-and-failure-tolerant
parallel AND gate can be created by using 2S.times.2P compound PMOS
transistors in place of simple, PMOS transistors. The
defect-and-failure-tolerant, compound-PMOS-transistor-based
parallel AND gate 1302 shown in FIG. 13 can tolerate various
patterns of open-defective and short-defective component
transistors, as discussed above with reference to FIG. 6-7. As
shown in FIG. 14, a defect-and-failure-tolerant demultiplexer
equivalent to the demultiplexer shown in FIGS. 10-11 can be
constructed from four 2S.times.2P compound-PMOS-transistor-based
parallel AND gates. Although this demultiplexer is
defect-and-failure-tolerant, the defect tolerance is achieved at
the expense of a four-fold increase in the number of transistors,
which may, in certain cases, lead to an increase in the area of the
demultiplexer, an increase in the manufacturing costs of the
demultiplexer, and an increase in power consumption of the
demultiplexer.
[0055] FIGS. 15-16 illustrate a defect-and-failure-tolerant
demultiplexer, equivalent to the demultiplexers shown in FIGS.
10-11 and 14, which represents one embodiment of the present
invention. FIG. 15 shows a parallel AND gate with serially
redundant PMOS transistors that is tolerant to short defects. The
parallel AND gate in FIG. 15 is logically equivalent to the
parallel AND gates shown in FIGS. 9B and 13. However, the
short-defect-tolerant parallel AND gate 1502 shown in FIG. 15
interconnects each address line with the output signal line via two
serially linked PMOS transistors. For example, address line A.sub.1
1504 is interconnected to the output signal line 1506 via the two
serially linked PMOS transistors 1508 and 1510. The serially
redundant PMOS-transistor-based AND gate 1502 can tolerate a single
short-defective PMOS transistor in each two-MOS-transistor-based
reversibly switchable interconnection linking an address line to
the output signal line. According to the above-discussed
terminology for compound transistors, each pair of serially linked
PMOS transistors in the defect-and-failure-tolerant demultiplexer
of FIG. 15 can be considered to be an 2S.times.0P compound
transistor.
[0056] FIG. 16 shows a demultiplexer logically equivalent to the
demultiplexers shown in FIGS. 10-11 and 14 that represents one
embodiment of the present invention. This demultiplexer is composed
of four serially redundant AND gates, such as the serially
redundant AND gate shown in FIG. 15. Unlike the previously
discussed multiplexors, the demultiplexer that represents one
embodiment of the present invention, as shown in FIG. 16, includes
two internal supplemental signal lines 1602 and 1604. The first
internal supplemental signal line represents the logical XOR of
address lines A.sub.0 1606 and A.sub.1 1608. A second, supplemental
signal line 1604 is complementary, in logic state, to the XOR
supplemental signal line 1602. These two supplemental signal lines
represent increased redundancy within the demultiplexer, which
allows for an additional reversibly switchable element in each of
the AND gates. In general, a linear-block code or other
error-control coding technique is used to determine the pattern of
interconnections between supplemental signal lines and output
signal lines, these supplemental interconnections corresponding to
the redundant code symbols used in linear-block codes and other
error-control codes, in order to ensure a correct Hamming distance
between adjacent coded addresses so that the maximum number of open
defects, d-1, can be tolerated. In general, encoder circuitry, such
as the encoder circuitry enclosed in dashed rectangle 1620 in FIG.
16, is needed to encode each input k-bit address into an n-bit
internal, coded address according to an [n, k, d] linear-block
code, as discussed in the previous subsection. Other types of
encoders may be needed for other types of error-control codes.
Comparing the demultiplexer shown in FIG. 10 with the demultiplexer
shown in FIG. 16 that represents one embodiment of the present
invention, the switchable element 1610 in the demultiplexer of FIG.
16 can be observed to be newly added with respect to the
demultiplexer shown in FIG. 10. These newly added reversibly
switchable elements, made possible by the additional, redundant
vertical signal lines, provide defect tolerance for open-defective
transistors.
[0057] FIGS. 17A-H illustrate, using the same illustration
conventions as employed in FIGS. 12A-D, various functional states
of the demultiplexer shown in FIG. 16. FIG. 17A shows a fully
functional demultiplexer to which the address "01" is input. As it
should, the output signal line 1702 associated with address "01"
has logic state "1," while the remaining output signal lines have
logic states "0." FIG. 17B shows the functional state of the
demultiplexer with an open-defective switchable element 1704. When
address "01" is input to the demultiplexer with the open-defective
switchable element, the demultiplexer continues to function
normally. FIGS. 17C and 17D show that the demultiplexer that
represents one embodiment of the present invention tolerates a
single open-defective switchable element. However, as shown in
FIGS. 17E-F, two open-defective switchable elements lead to a
nonfunctional device. As shown in FIG. 17F, when the address "00"
is input to the demultiplexer with two open-defective switchable
elements 1708 and 1710, two output signal lines 1702 and 1712 have
logic state "1." Similarly, FIGS. 17G and 17H show that the
demultiplexer that represents one embodiment of the present
invention can tolerate a single short-defective transistor in each
switchable element, but fails when two short-defective transistors
occur in single switchable element.
[0058] Although the present invention has been described in terms
of particular embodiments, it is not intended that the invention be
limited to these embodiments. Modifications within the spirit of
the invention will be apparent to those skilled in the art. For
example, a wide variety of combinations of multi-transistor
reversibly switchable interconnections, such as nS.times.mP
transistors, and supplemental internal signal lines can be used to
create defect-and-failure tolerant demultiplexers according to
various methods of the present invention. Compound nS.times.mP
transistors or higher-order nS.times.mP transistors can be used
without additional internal signal lines to create
defect-and-failure tolerant demultiplexers. Alternatively,
serially-redundant reversibly switchable interconnections, such as
nS.times.0P transistors, can be used for tolerating short-defective
transistors along with supplemental signal lines introduced
according to a linear-block code or other error-control code to
tolerate open-defective transistors. In addition, rectangular
higher-order multi-transistor reversibly switchable
interconnections, such as nS.times.0P transistors, with higher
serial n than parallel in redundancy, can be used in combination
with supplemental signal lines introduced according to a
linear-block code or other error-control code. When analyzed for
cost-effectiveness, complexity, and other such metrics and
parameters, use of serially-redundant reversibly switchable
interconnections for tolerating short-defective transistors along
with supplemental signal lines introduced according to a
linear-block code or other error-control code to tolerate
open-defective transistors appears to be more cost effective and
less complex than using compound or higher-order multi-transistor
reversibly switchable interconnections with both serial and
parallel redundancies, although the optimal approach for designing
defect-and-failure-tolerant demultiplexers may be application
dependent. In the above-described embodiments, a small,
2-bit-addressable demultiplexer is described, but embodiments of
the present invention include demultiplexers with an arbitrary
number of address lines, or address bits, k, and as many as 2.sup.k
output signal lines. Moreover, a wide variety of ranges of
failure-and-defect tolerance can be embodied in demultiplexers of
the present invention, including use of an essentially arbitrary
number of supplemental internal signal lines and higher-order
multi-transistor interconnections with arbitrary levels of serial
and parallel redundancies.
[0059] The foregoing description, for purposes of explanation, used
specific nomenclature to provide a thorough understanding of the
invention. However, it will be apparent to one skilled in the art
that the specific details are not required in order to practice the
invention. The foregoing descriptions of specific embodiments of
the present invention are presented for purpose of illustration and
description. They are not intended to be exhaustive or to limit the
invention to the precise forms disclosed. Obviously many
modifications and variations are possible in view of the above
teachings. The embodiments are shown and described in order to best
explain the principles of the invention and its practical
applications, to thereby enable others skilled in the art to best
utilize the invention and various embodiments with various
modifications as are suited to the particular use contemplated. It
is intended that the scope of the invention be defined by the
following claims and their equivalents:
* * * * *