On the complexity of minimum distance decoding of long linear codes

Authors:
A. Barg;E. Krouk;H. C.A. van Tilborg
Affiliations:
Math. Sci. Res. Center, AT&T Bell Labs., Murray Hill, NJ;-;-
Venue:
IEEE Transactions on Information Theory
Year:
2006

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Abstract

We suggest a decoding algorithm of q-ary linear codes, which we call supercode decoding. It ensures the error probability that approaches the error probability of minimum-distance decoding as the length of the code grows. For n→∞ the algorithm has the maximum-likelihood performance. The asymptotic complexity of supercode decoding is exponentially smaller than the complexity of all other methods known. The algorithm develops the ideas of covering-set decoding and split syndrome decoding