Decoding of the (31, 16, 7) quadratic residue code with four-error correcting capability

Abstract

A high-speed algorithm for decoding the binary (31, 16, 7) quadratic residue (QR) code up to four errors is proposed. Core to the key idea lies in an innovative integration of the reliability-search procedure and the insight of the weight distribution of the code for searching the candidate codewords. Accordingly, the maximum-likelihood (ML) criterion is applied to pick the most possible codeword. Through simulation over the additive white Gaussian noise (AWGN) channel, it is concluded that the error-correcting performance of the new decoder is superior to that of a Chase-II decoder when no more than four errors occur. The overall bit error rate (BER) of the proposed decoder is close to that of the Chase-II decoder. More importantly, the new decoder results in great reductions of 72.34% and 92.37% in the signal-to-noise ratio (SNR) values of 0 and 7, respectively. The proposed algorithm suggests an alternative to enhance the error-correcting capability of the hard-decision decoder, but with a lower decoding complexity.