Fast decoding of the binary (31, 16, 7) quadratic residue code

Abstract

A fast and efficient table-lookup decoding algorithm, called message-syndrome decoding algorithm (MSDA), is proposed to correct all patterns of three or fewer errors in the binary systematic (31, 16, 7) quadratic residue code. The decoding technique of the MSDA is based on the properties of the cyclic codes, the one-error syndrome in the message part, the weight of syndrome, and the weight of syndrome difference. Thus, the size of the lookup table and computational complexity in the finite field can be significantly reduced. The MSDA merely needs a very small message-syndrome lookup table (MSLT) which consists of 16 syndromes. The memory size of the MSLT is the smallest compared with other existing lookup tables and the simulation results show that the decoding speed of the MSDA exceeds other proposed table-lookup decoding algorithms.