Optimal decoding of linear codes for minimizing symbol error rate (Corresp.)

The general problem of estimating the a posteriori probabilities of the states and transitions of a Markov source observed through a discrete memoryless channel is considered. The decoding of linear block and convolutional codes to minimize symbol error probability is shown to be a special case of this problem. An optimal decoding algorithm is derived.

[1]  Richard W. Hamming,et al.  Error detecting and error correcting codes , 1950 .

[2]  Robert G. Gallager,et al.  Low-density parity-check codes , 1962, IRE Trans. Inf. Theory.

[3]  L. Baum,et al.  Statistical Inference for Probabilistic Functions of Finite State Markov Chains , 1966 .

[4]  R. Chang,et al.  On receiver structures for channels having memory , 1966, IEEE Trans. Inf. Theory.

[5]  Andrew J. Viterbi,et al.  Error bounds for convolutional codes and an asymptotically optimum decoding algorithm , 1967, IEEE Trans. Inf. Theory.

[6]  J. Massey,et al.  Codes, automata, and continuous systems: Explicit interconnections , 1967, IEEE Transactions on Automatic Control.

[7]  R. Gallager.  Information Theory and Reliable Communication , 1968 .

[8]  Daniel J. Costello.  A construction technique for random-error-correcting convolutional codes , 1969, IEEE Trans. Inf. Theory.

[9]  G. David Forney,et al.  Convolutional codes I: Algebraic structure , 1970, IEEE Trans. Inf. Theory.

[10]  John Cocke,et al.  Bootstrap Hybrid Decoding for Symmetrical Binary Input Channels , 1971, Inf. Control..

[11]  Jr. G. Forney,et al.  The viterbi algorithm , 1973 .

[12]  Erik Paaske,et al.  Short binary convolutional codes with maximal free distance for rates 2/3 and 3/4 (Corresp.) , 1974, IEEE Trans. Inf. Theory.

[13]  Daniel J. Costello.  Free distance bounds for convolutional codes , 1974, IEEE Trans. Inf. Theory.

[14]  G. David Forney,et al.  Convolutional Codes II. Maximum-Likelihood Decoding , 1974, Inf. Control..

[15]  O. Antoine,et al.  Theory of Error-correcting Codes , 2022 .