Maximum-Likelihood Soft Decision Decoding of Bch Codes

The problem of efficient maximum-likelihood soft decision decoding of binary BCH codes is considered. It is known that those primitive BCH codes whose designed distance is one less than a power of two, contain subcodes of high dimension which consist of a direct-sum of several identical codes. The authors show that the same kind of direct-sum structure exists in all the primitive BCH codes, as well as in the BCH codes of composite block length. They also introduce a related structure termed the "concurring-sum", and then establish its existence in the primitive binary BCH codes. Both structures are employed to upper bound the number of states in the minimal trellis of BCH codes, and develop efficient algorithms for maximum-likelihood soft decision decoding of these codes. >

[1]  Elwyn R. Berlekamp,et al.  Algebraic coding theory , 1984, McGraw-Hill series in systems science.

[2]  Jack K. Wolf,et al.  Efficient maximum likelihood decoding of linear block codes using a trellis , 1978, IEEE Trans. Inf. Theory.

[3]  Elwyn R. Berlekamp The construction of fast, high-rate, soft decision block decoders , 1983, IEEE Trans. Inf. Theory.

[4]  R. Blahut Theory and practice of error control codes , 1983 .

[5]  N. J. A. Sloane,et al.  Soft decoding techniques for codes and lattices, including the Golay code and the Leech lattice , 1986, IEEE Trans. Inf. Theory.

[6]  Yair Be'ery,et al.  Optimal soft decision block decoders based on fast Hadamard transform , 1986, IEEE Trans. Inf. Theory.

[7]  Tom Verhoeff,et al.  An updated table of minimum-distance bounds for binary linear codes , 1987, IEEE Trans. Inf. Theory.

[8]  G. David Forney,et al.  Coset codes-II: Binary lattices and related codes , 1988, IEEE Trans. Inf. Theory.

[9]  Douglas J. Muder Minimal trellises for block codes , 1988, IEEE Trans. Inf. Theory.

[10]  Yair Be'ery,et al.  Maximum likelihood soft decoding of binary block codes and decoders for the Golay codes , 1989, IEEE Trans. Inf. Theory.

[11]  J. Snyders,et al.  Bounds on the dimension of codes and subcodes with prescribed contraction index , 1990 .

[12]  Victor K.-W. Wei,et al.  Generalized Hamming weights for linear codes , 1991, IEEE Trans. Inf. Theory.

[13]  Alexander Vardy,et al.  Bit-level soft-decision decoding of Reed-Solomon codes , 1991, IEEE Trans. Commun..

[14]  Alexander Vardy,et al.  On the problem of finding zero-concurring codewords , 1991, IEEE Trans. Inf. Theory.

[15]  Alexander Vardy,et al.  More efficient soft decoding of the Golay codes , 1991, IEEE Trans. Inf. Theory.

[16]  Victor K.-W. Wei,et al.  On the generalized Hamming weights of several classes of cyclic codes , 1991, IEEE Trans. Inf. Theory.

[17]  Yair Be'ery,et al.  Bounds on the trellis size of linear block codes , 1993, IEEE Trans. Inf. Theory.

[18]  Maximum-Likelihood Soft Decision Decoding of Bch Codes , 1993, Proceedings. IEEE International Symposium on Information Theory.

[19]  Shu Lin,et al.  On the optimum bit orders with respect to the state complexity of trellis diagrams for binary linear codes , 1993, IEEE Trans. Inf. Theory.

[20]  G. Cohen,et al.  Perfect Tilings of Binary Spaces , 1993, Proceedings. IEEE International Symposium on Information Theory.

[21]  Shu Lin,et al.  On complexity of trellis structure of linear block codes , 1993, IEEE Trans. Inf. Theory.

[22]  Yair Be'ery,et al.  Soft trellis-based decoder for linear block codes , 1994, IEEE Trans. Inf. Theory.