A class of practical orchard codes on finite field GF（2） are *** coding and decoding algorithms are *** algorithms are implemented in the C programming *** is shown that this class of orchard codes are easy and comp...
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A class of practical orchard codes on finite field GF（2） are *** coding and decoding algorithms are *** algorithms are implemented in the C programming *** is shown that this class of orchard codes are easy and comparatively fast to decode,and are very powerful for applications wheTe channel SER/BBK is high and burst error occurs.
This paper presents a semi-systolic architecture for decoding cyclic linear error-correcting codes at high speed. The architecture implements a variant of Tanner's algorithm B, modified for simpler and faster impl...
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This paper presents a semi-systolic architecture for decoding cyclic linear error-correcting codes at high speed. The architecture implements a variant of Tanner's algorithm B, modified for simpler and faster implementation. The main features of the architecture are low computational complexity, a simple, regular arrangement of cells for easy layout, short critical paths, and a high clock rate. A prototype chip has been designed to decode a 73-bit perfect difference set code. This 4600-mu-m x 6800-mu-m chip should achieve 25MHz decoding in 2-mu-m n-well cMOS. The success of the implementation illustrates the value of using technology dependent constraints and cost measures to guide the design of algorithms and architectures.
A simple complete decoding algorithm for the (11, 6, 5) perfect ternary Golay code is presented. This algorithm is based on a step-by-step method and requires only 17 shift operations for decoding one received word.
A simple complete decoding algorithm for the (11, 6, 5) perfect ternary Golay code is presented. This algorithm is based on a step-by-step method and requires only 17 shift operations for decoding one received word.
It is shown that error-erasure decoding for a cyclic code allows the correction of a combination of t errors and r erasures when 2t+r> sigma /sub 0/; the parameter sigma /sub 0/ denotes a particular instance of...
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It is shown that error-erasure decoding for a cyclic code allows the correction of a combination of t errors and r erasures when 2t+r> sigma /sub 0/; the parameter sigma /sub 0/ denotes a particular instance of the Hartmann-Tzeng bound. This procedure is an improvement on the error-erasure decoding algorithm developed by G.D. Forney (1965), which works when 2t+r> sigma , where sigma denotes the BCH-bound of the code.
A decoding algorithm for algebraic-geometric codes arising from arbitrary algebraic curves is presented. This algorithm corrects any number of errors up to ((d-g-1)/2), where d is the designed distance of the code and...
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A decoding algorithm for algebraic-geometric codes arising from arbitrary algebraic curves is presented. This algorithm corrects any number of errors up to ((d-g-1)/2), where d is the designed distance of the code and g is the genus of the curve. The complexity of decoding equals sigma (n/sup 3/) where n is the length of the code. Also presented is a modification of this algorithm, which in the case of elliptic and hyperelliptic curves is able to correct ((d-1)/2) errors. It is shown that for some codes based on plane curves the modified decoding algorithm corrects approximately d/2-g/4 errors. Asymptotically good q-ary codes with a polynomial construction and a polynomial decoding algorithm (for q<or=361 on some segment their parameters are better than the Gilbert-Varshamov bound) are obtained. A family of asymptotically good binary codes with polynomial construction and polynomial decoding is also obtained, whose parameters are better than the Blokh-Zyablov bound on the whole interval 0> sigma >1/2.
The decoding of unequal error protection product codes, which are a combination of linear unequal error protection (UEP) codes and product codes, is addressed. A nonconstructive proof of the existence of a good error-...
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The decoding of unequal error protection product codes, which are a combination of linear unequal error protection (UEP) codes and product codes, is addressed. A nonconstructive proof of the existence of a good error-erasure-decoding algorithm is presented; however, obtaining the decoding procedure is still an open research problem. A particular subclass of UEP product codes is considered, including a decoding algorithm that is an extension of the Blokh-Zyablov decoding algorithm for product codes. For this particular subclass the decoding problem is solved.
A decoding algorithm, based on Venn diagrams, for decoding the (23, 12, 7) Golay code is presented. The decoding algorithm is based on the design properties of the parity sets of the code. As for other decoding algori...
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A decoding algorithm, based on Venn diagrams, for decoding the (23, 12, 7) Golay code is presented. The decoding algorithm is based on the design properties of the parity sets of the code. As for other decoding algorithms for the Golay code, decoding can be easily done by hand.
A class of codes derived from algebraic plane curves is constructed. The concepts and results from algebraic geometry that were used are explained in detail; no further knowledge of algebraic geometry is needed. Param...
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A class of codes derived from algebraic plane curves is constructed. The concepts and results from algebraic geometry that were used are explained in detail; no further knowledge of algebraic geometry is needed. Parameters, generator and parity-check matrices are given. The main result is a decoding algorithm which turns out to be a generalization of the Peterson algorithm for decoding BCH decoder codes.
In a hybrid forward-error-correction-automatic-repeat-request system one may wish to use an (n,k) cyclic code because its decoding algorithm is well known. An analytic formula is given for determining the fraction of ...
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In a hybrid forward-error-correction-automatic-repeat-request system one may wish to use an (n,k) cyclic code because its decoding algorithm is well known. An analytic formula is given for determining the fraction of undetectable single bursts of different lengths when a cyclic code is used for simultaneous single-burst-error detection and t-random error correction.
The use of sequential decoding in multiple access channels is considered. The Fano metric, which achieves all achievable rates in the one-user case, fails to do so in the multiuser case. A new metric is introduced and...
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The use of sequential decoding in multiple access channels is considered. The Fano metric, which achieves all achievable rates in the one-user case, fails to do so in the multiuser case. A new metric is introduced and an inner bound is given to its achievable rate region. This inner bound region is large enough to encourage the use of sequential decoding in practice. The new metric is optimal, in the sense of achieving all achievable rates, in the case=of one-user and painvise-reversible chan- nels. Whether the metic is optimal for all multiple access channels remains an open problem. It is worth noting that even in the one-user case, the new metric differs from the Fano metric in a nontrivial way, showing that the Fano metric is not uniquely optimal for such channels. A new and stricter criterion of achievability in sequential decoding is also introduced and examined.
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