TY - GEN

T1 - Bounded-distance decoding of the leech lattice and the golay code

AU - Amrani, Ofer

AU - Be’Ery, Yair

AU - Vardy, Alexander

N1 - Publisher Copyright:
© 1994, Springer Verlag. All Rights Reserved.

PY - 1994

Y1 - 1994

N2 - We present an efficient algorithm for bounded-distance decoding of the Leech lattice. The new bounded-distance algorithm employs the partition of the Leech lattice into four cosets of Q24, beyond the conventional partition into two H24 cosets. The complexity of the resulting decoder is only 1007 real operations in the worst case, as compared to about 3600 operations for the best known maximum-likelihood decoder and about 2000 operations for the original bounded-distance decoder of Forney. Restricting the proposed Leech lattice decoder to GF(2)24 yields a bounded-distance decoder for the binary Golay code which requires at most 431 operations as compared to 651 operations for the best known maximum-likelihood decoder. Moreover, it is shown that our algorithm decodes correctly at least up to the guaranteed error-correction radius of the Leech lattice. Performance of the algorithm on the AWGN channel is evaluated analytically by explicitly calculating the effective error- coefficient, and experimentally by means of a comprehensive computer simulation. The results show a loss in coding-gain of less than 0.1 dB relative to the maximum-likelihood decoder for BER ranging from 10-1 to 10-7.

AB - We present an efficient algorithm for bounded-distance decoding of the Leech lattice. The new bounded-distance algorithm employs the partition of the Leech lattice into four cosets of Q24, beyond the conventional partition into two H24 cosets. The complexity of the resulting decoder is only 1007 real operations in the worst case, as compared to about 3600 operations for the best known maximum-likelihood decoder and about 2000 operations for the original bounded-distance decoder of Forney. Restricting the proposed Leech lattice decoder to GF(2)24 yields a bounded-distance decoder for the binary Golay code which requires at most 431 operations as compared to 651 operations for the best known maximum-likelihood decoder. Moreover, it is shown that our algorithm decodes correctly at least up to the guaranteed error-correction radius of the Leech lattice. Performance of the algorithm on the AWGN channel is evaluated analytically by explicitly calculating the effective error- coefficient, and experimentally by means of a comprehensive computer simulation. The results show a loss in coding-gain of less than 0.1 dB relative to the maximum-likelihood decoder for BER ranging from 10-1 to 10-7.

UR - http://www.scopus.com/inward/record.url?scp=85026886906&partnerID=8YFLogxK

U2 - 10.1007/3-540-57843-9_24

DO - 10.1007/3-540-57843-9_24

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AN - SCOPUS:85026886906

SN - 9783540578437

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 236

EP - 248

BT - Algebraic Coding - 1st French-Israeli Workshop, Proceedings

A2 - Cohen, Gerard

A2 - Lobstein, Antoine

A2 - Zemor, Gilles

A2 - Litsyn, Simon

PB - Springer Verlag

T2 - 1st French-Israeli Workshop on Algebraic Coding, 1993

Y2 - 19 July 1993 through 21 July 1993

ER -