Cyclic product codes and their implementation

Abstract

In many communication systems, variable-redundancy coding schemes are highly desirable either due to the fact that messages of various degrees of importance are present, or due to some change in the real communication channel. A class of “cyclic product codes” presented in this paper is capable of operating in variable redundancy modes. In the simplest case, the generator polynomial in the high redundancy mode is g(x) = g 1 (x)g 2 (x) , while the generator polynomial in the low redundancy mode is only g 1 (x) . It is shown that efficient product codes can be constructed offering different degrees of protection against independent errors, burst errors, and multiple burst errors. It is also shown that particularly simple implementation for cyclic product codes is possible. In fact, the complexity of the entire decoder can be made roughly the same as that of the decoder for the high redundancy code alone. Hence, the implementation of low-redundancy codes is accomplished with little extra cost.