Closest coset decoding of |u|u+v| codes

The general concept of closest coset decoding (CCD) is presented, and a soft-decoding technique for block codes that is based on partitioning a code into a subcode and its cosets is described. The computational complexity of the CCD algorithm is significantly less than that required if a maximum-likelihood detector (MLD) is used. A set-partitioning procedure and details of the CCD algorithm for soft decoding of |u|u+v| codes are presented. Upper bounds on the bit-error-rate (BER) performance of the proposed algorithm are combined, and numerical results and computer simulation tests for the BER performance of second-order Reed-Muller codes of length 16 and 32 are presented. The algorithm is a suboptimum decoding scheme and, in the range of signal-to-noise-power-density ratios of interest, its BER performance is only a few tenths of a dB inferior to the performance of the MLD for the codes examined