Efficient Berlekamp-Massey based recursive decoder for Reed-Solomon codes

This paper presents a high speed low complexity algorithm and architecture for encoding and decoding Reed-Solomon (RS) codes based on evaluation. The recursive use of discrepancy computation step of Berlekamp-Massey (BM) algorithm leads directly to the computation of message symbols without using Chien Search and Forney´s Formula, making the circuitry much simpler for proposed decoder as compared to the classical decoder. Also, the proposed scheme requires less clock cycles compared to the classical decoder leading to reduced energy consumption. In order to make a fair comparison, classical and proposed decoder for RS codes over the field F₂₅₆ has been implemented on TSMC 65nm ASIC process using some arithmetic units. For RS(255, 239) code, the proposed decoder has a total cell count of 16075 which results in a reduction of 57.6% in hardware area as compared to classical decoder. Also, 53.07% timing reduction is obtained with the proposed decoder.