Exploiting the cannibalistic traits of Reed-Solomon codes

In Reed-Solomon codes and all other maximum distance separable codes, there is an intrinsic relationship between the size of the symbols in a codeword and the length of the codeword. Increasing the number of symbols in a codeword to improve the efficiency of the coding system thus requires using a larger set of symbols. However, long Reed-Solomon codes are difficult to implement and many communications or storage systems cannot easily accommodate an increased symbol size, e.g., M-ary frequency shift keying (FSK) and photon-counting pulse-position modulation demand a fixed symbol size. This article describes a technique for sharing redundancy among many different Reed-Solomon codewords to achieve the efficiency attainable in long Reed-Solomon codes without increasing the symbol size. The article presents techniques both for calculating the performance of these new codes and for determining their encoder and decoder complexities. These complexities are usually found to be substantially lower than conventional Reed-Solomon codes of similar performance.