New transmission-decoding schemes based on Reed-Solomon codes

A novel transmission-decoding scheme for Reed-Solomon codes is proposed that can be used for reducing the power requirements in digital communication systems. We take advantage of the erasure correction capability of RS codes and propose a new step by step erasure decoding method based on Berlekamp-Massey (BM) algorithm for them. In this scenario, only one part of the symbols of each RS codeword is sent from the transmitter and the rest are considered as erasures. If the decoding was not successful, the receiver asks for more symbols to be sent. Since the number of required symbols for successful decoding is different for different signal to noise ratios (SNRs), the rate of the equivalent RS code is not constant and depends on the SNR. Our method results in considerable improvement of the performance of the system compared to the standard transmission and hard decision decoding.