We describe a new concatenated decoding scheme based on iterations between an inner sequentially decoded convolutional code of rate R=1/4 and memory M=23, and block interleaved outer Reed-Solomon (RS) codes with nonuniform profile. With this scheme decoding with good performance is possible as low as E/sub b//N/sub 0/=0.6 dB, which is about 1.25 dB below the signal-to-noise ratio (SNR) that marks the cutoff rate for the full system. Accounting for about 0.45 dB due to the outer codes, sequential decoding takes place at about 1.7 dB below the SNR cutoff rate for the convolutional code. This is possible since the iteration process provides the sequential decoders with side information that allows a smaller average load and minimizes the probability of computational overflow. Analytical results for the probability that the first RS word is decoded after C computations are presented. These results are supported by simulation results that are also extended to other parameters.

The concatenated coding system recommended by CCSDS (Consultative Committee for Space Data Systems) uses an outer (255,233) Reed-Solomon (RS) code based on 8-b symbols, followed by the block interleaver and an inner rate 1/2 convolutional code with memory 6. Viterbi decoding is assumed. Two new decoding procedures based on repeated decoding trials and exchange of information between the two decoders and the deinterleaver are proposed. In the first one, where the improvement is 0.3-0.4 dB, only the RS decoder performs repeated trials. In the second one, where the improvement is 0.5-0.6 dB, both decoders perform repeated decoding trials and decoding information is exchanged between them.>

Unit memory convolutional codes with generator matrices, which are composed of circulant submatrices, are introduced. This structure facilitates the analysis of efficient search for good codes. Equivalences among such codes and some of the basic structural properties are discussed. In particular, catastrophic encoders and minimal encoders are characterized and dual codes treated. Further, various distance measures are discussed, and a number of good codes, some of which result from efficient computer search and some of which result from known block codes, are presented.>

This correspondence investigates the error propagation properties of six different systems using a (12, 6) systematic double-error-correcting convolutional encoder and a one-step majority-logic feedback decoder. For the generally accepted assumption that channel errors are much more likely to occur than hardware errors in the decoder, it is shown that the system proposed by Massey outperforms the system proposed by En in the above note.1Further, a third system is found which, even iftemporary hardware errors in the decoder are taken into account, is superior to the system proposed by En.

Fixed binary convolutional codes are considered which are simultaneously optimal or near-optimal according to three criteria: namely, distance profiled, free distanced_{ \infty}, and minimum number of weightd_{\infty}paths. It is shown how the optimum distance profile criterion can be used to limit the search for codes with a large value ofd_{\infty}. We present extensive lists of such robustly optimal codes containing rateR = l/2nonsystematic codes, several withd_{\infty}superior to that of any previously known code of the same rate and memory; rateR = 2/3systematic codes; and rateR = 2/3nonsystematic codes. As a counterpart to quick-look-in (QLI) codes which are not "transparent," we introduce rateR = 1/2easy-look-in-transparent (ELIT) codes with a feedforward inverse(1 + D,D). In general, ELIT codes haved_{\infty}superior to that of QLI codes.

A search procedure is developed to find good short binary(N,N - 1)convolutional codes. It uses simple rules to discard from the complete ensemble of codes a large fraction whose free distanced_{free}either cannot achieve the maximum value or is equal tod_{free}of some code in the remaining set. Farther, the search among the remaining codes is started in a subset in which we expect the possibility of finding codes with large values ofd_{free}to be good. A number of short, optimum (in the sense of maximizingd_{free}), rate-2/3 and 3/4 codes found by the search procedure are listed.