Soft-decision decoding using punctured codes

Let a -ary linear ( )-code be used over a memoryless channel. We design a soft-decision decoding algorithm that tries to locate a few most probable error patterns on a shorter length [ ]. First, we take cyclically consecutive positions starting from any initial point. Then we cut the subinterval of length into two parts and examine most plausible error patterns on either part. To obtain codewords of a punctured ( )-code, we try to match the syndromes of both parts. Finally, the designed codewords of an ( )-code are re-encoded to find the most probable codeword on the full length . For any long linear code, the decoding error probability of this algorithm can be made arbitrarily close to the probability of its maximum-likelihood (ML) decoding given sufficiently large By optimizing , we prove that this near-ML decoding can be achieved by using only ( ) ( + ) error patterns. For most long linear codes, this optimization also gives about re-encoded codewords. As a result, we obtain the lowest complexity order of ( ) ( + ) known to date for near-ML decoding. For codes of rate 1 2, the new bound grows as a cubic root of the general trellis complexity min . For short blocks of length 63, the algorithm reduces complexity of trellis design by a few decimal orders.