Bounded-distance decoding of the Leech lattice and the Golay code
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.
KeywordsAdditive White Gaussian Noise Channel Real Operation AWGN Channel Comprehensive Computer Simulation Golay Code
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