Reversible codes

Abstract

A code is defined to be reversible if its code-word set is invariant under a reversal of the digits in each code word. Such codes may have application in certain data storage and retrieval systems. It is shown that cyclic codes and convolutional codes are reversible when and only when their code-generating polynomials are self-reciprocal. Reversible codes are quite rare therefore, but it is shown that an important subclass of the Bose-Chaudhuri codes consists entirely of reversible codes. Techniques are developed by which any nonreversible cyclic code can be converted into a reversible cyclic code with at least as much error-correcting power, but at the cost of increased code redundancy. The redundancy of the derived code is at most twice that of the original code, and the derived code can be decoded by a decoder constructed for the original code. Similarly, it is shown how any nonreversible convolutional code can be converted into a reversible convolutional code with at least as much error-correcting power, but at the cost of increased code constraint length. Again the derived code can be decoded by substantially the same decoder as for the original code.