On binary majority-logic decodable codes (Corresp.)

LetVprimebe a binary(n,k)majority-logic decodable code withgprime (X)as its generator polynomial and odd minimum distanced. LetVbe the(n, k - 1)subset code generated bygprime (X)(1 + X). This correspondence shows thatVis majority-logic deeodable withd + 1orthogonal estimates. This fact is useful in the simultaneous correction of random errors and erasures.     

A note on one-step majority-logic decodable codes (Corresp.)

Construction of shortened geometric codes as Shown here results in 1-step majority-logic deeodable codes. The shortened codes retain the error-correction ability of the parent codes and the decoders for the shortened codes are much simpler than for the parent code. A table of shortened codes is given.     

Extended Varshamov- Gilbert and sphere-packing bounds for burst-correcting codes (Corresp.)

The study of burst-error-correcting codes has generally been made without weight considerations while the random-error-correcting capabilities of a linear code largely depend upon the minimum weight. In this correspondence we have obtained extensions of the Varshamov-Gilbert and sphere-packing hounds to burst-error-correcting codes.     

A class of composite codes (Corresp.)

Certain useful properties of the cyclic codeVare discussed with wordsV(x)=V_{1}(x)(l+x^{n})/(l+x^{n_{1}})+V_{2}(x)(l+x^{n})/(l+x^{n_{2}}), where fori=1,2,V_{i}(x)belongs to a binary codeV_{i}of lengthn_{i}.     

A novel approach to soft decision decoding of threshold decodable codes (Corresp.)

A new method of soft-decision decoding of threshold decodable codes is presented. Excellent error performance, comparable to or better than that of other known practical schemes, is demonstrated by computer simulation and error analysis. The method is an approximate realization, without undue deterioration in performance, of the optimum {em a posteriori} probability (APP) decoding and has a much simpler structure.     

Generalized minimum distance decoding on majority logic decodable codes (Corresp.)

Generalized minimum distance decoding schemes are found for majority logic decodable codes. These decoding schemes are parallel to the classical majority logic decoding schemes and thus can be easily implemented.     

A stochastic model for burst-correcting convolutional decoders (Corresp.)

A stochastic model is described for the decoder of an optimal burst-correcting convolutional code. From this model, an upper bound is obtained forbar{p}, the error probability per word after decoding.     

A class of burst error-correcting array codes (Corresp.)

The usual(k_{2} + 1) times (k_{1} + 1)array code, in which the last row and the last column contain redundant bits, can correct any single error. However, if the bits are read diagonally instead of horizontally, the code can correct bursts of errors. It is shown that the(_{k}2 + 1) times (k_{1} + 1)array code with diagonal readout can correct any burst of length up tok_{1}if and only ifk_{2} geq 2(k_{1} - 1).     

Duadic codes (Corresp.)

The notion of duadic codes over GF(2)is generalized to arbitrary fields. Duadic codes of composite length are constructed. An upper bound is given for the minimum distance of duadic codes of length a prime power.     

Multigram codes (Corresp.)

A multigram code is a list of codewords for multigrams (of various lengths) belonging to a setS. Three interrelated problems require designing a good setS, good codewords, and a good strategy for dissecting messages into multigrams ofS. Focus is placed on the dissection strategy and applications to English.     

Optimal codes (Corresp.)

Some known results on the nonexistence of linear optimal codes can be very easily proved using results on the weight distribution of such codes.     

A new class of binary codes constructed on the basis of BCH codes (Corresp.)

In this correspondence, we present a new class of binary codes that are constructed on the basis of BCH codes. Some examples of these codes are given, having more codewords than the best codes previously known (to the authors) with the same minimum distance and number of check symbols. A decoding algorithm for the codes is also described.     

A class of shortened cyclic codes for a compound channel (Corresp.)

This correspondence presents a class of shortened cyclic codes that are suitable for application on a compound channel. The Chinese remainder theorem is applied to the proof of the error-correcting properties of this class of shortened cyclic codes.     

Universal codes for a class of composite sources (Corresp.)

Fixed rate universal block source coding with a fidelity criterion is considered for classes of composite sources with a finite (fixed) set of modes not an unknown switch process. In particular, it is shown that weakly minimax universal codes of all rates with respect to an arbitrary distortion measure exist for such processes.     

Superimposed concatenated codes (Corresp.)

A family of codes of lengthn=q^{s+l}over GF(q), with2s leq qare presented which are constructed by superimposing concatenated codes on a concatenated code. The raterand the distance ratiodeltaof the new codes satisfy the relationr=1-delta+delta ln (delta)for sufficiently large values ofnandq/s. The new codes are superior to the comparable Bose-Chaudhuri-Hocquenghem (BCH) codes, forsgeq 3, in the sense that they contain more codewords. An asymptotically good code constructed using these new codes has a distance ratio greater than those of other asymptotically good codes known to the authors for rates smaller than 0.007.     

Self-synchronizing Huffman codes (Corresp.)

A problem associated with the use of variable-length source codes is that loss of synchronization may lead to extended errors in the decoded text. In this correspondence it is shown that some binary Huffman codes contain a codeword that resynchronizes the decoder regardless of the synchronization slippage preceding that codeword. Such codes are self-synchronizing in a probabilistic sense, yet require no additional system overhead. Some sufficient conditions are found for the existence or nonexistence of self-synchronizing Huffman codes for many classes of source probabilities. One of our results shows that many common languages can be encoded with self-synchronizing Huffman codes.     

Shortened BCH codes (Corresp.)

By shortening certain binary primitive BCH codes, we derive a number of linear error-correcting codes with minimum distances superior to any known previously. We also give the weight spectra of three nonprimitive BCH codes whose minimum distances likewise constitute a significant improvement over those of the best codes previously known.