Reed–Solomon Codes and Binary Transmission

This chapter further discusses the Reed–Solomon codes which are exceptional, symbol based, because they are maximum distance separable (MDS) codes. Though these codes are not binary codes, they can be used as binary codes. The performance of Reed–Solomon codes when used on a binary channel is explored in this chapter and compared to codes which are designed for binary transmission. The construction of the parity-check matrices of RS codes for use as binary codes is described in detail for specific code examples. The simulation results for three differently constructed (150, 75) codes for the binary AWGN channel using a near maximum likelihood decoder are presented. Surprisingly the best performing code at \(10^{-4}\) error rate is not the best-known (150, 75, 23) code. It is shown that this is due to the higher multiplicities of weight 32–36 codeword errors. However, beyond \(10^{-6}\) error rates the best-known (150, 75, 23) code is the best code.