A Test Vector Generation Method Based on Symbol Error Probabilities for Low-Complexity Chase Soft-Decision Reed–Solomon Decoding

Abstract

This paper presents a low-complexity chase (LCC) decoder for Reed–Solomon (RS) codes, which uses a novel method for the selection of test vectors that is based on the analysis of the symbol error probabilities derived from simulations. Our results show that the same performance as the classical LCC is achieved with a lower number of test vectors. For example, the amount of test vectors is reduced by half and by 1/16 for the RS(255,239) and RS(255,129) codes, respectively. We provide an evidence that the proposed method is suitable for RS codes with different rates and Galois fields. In order to demonstrate that the proposed method results in a reduction of the complexity of the decoder, we also present a hardware architecture for an RS(255,239) decoder that uses 16 test vectors. This decoder achieves a coding gain of 0.56 dB at the frame error rate that is equal to 10−6 compared with hard-decision decoding, which is higher than that of an η = 5 LCC. The implementation results in ASIC show that a throughput of 3.6 Gb/s can be reached in a 90-nm process and 29.1XOR˛s are required. The implementation results in Virtex-7 FPGA devices show that the decoder reaches 2.5 Gb/s and requires 5085 LUTs.