Soft decoding of the (23, 12, 7) Golay code: simplified algorithm and hardware implementation

Abstract

A simplified soft decoding algorithm for the (23, 12, 7) Golay code that can correct up to six errors is proposed in this study. The emblematic probability value of this algorithm derived from Reed is shown to be the same as the one given by Chase, if a joint estimate of the noise power and the received bit amplitude are carried out at the output of the matched filter in a Costas-loop receiver. Simulation results show that the coding gain obtained by the simplified algorithm is nearly the same as that achieved by Chase's algorithm. Based on the simplified algorithm, this study investigates an efficient hardware implementation on field programmer gate array platform, and presents a detailed architecture of the soft decoder. Experimental result indicates that the proposed algorithm uses less hardware complexity and has high-throughput rate, therefore it is naturally suitable for very large scale integration (VLSI) implementation.