Convolutional Reed-Solomon Codes

Abstract

We derive a new family of convolutional character-error-correcting codes which are a convolutional form of the Reed-Solomon block codes and as such have nonbinary symbols. We also derive a bound on the error correcting capabilities of these codes in which the error-correcting capability per constraint length grows approximately with the square root of the constraint length. When these codes are used on a binary channel they are effective for both random and burst error correction because a single character spans several channel digits. These codes have greater error-correcting capabilities than the Robinson-Bernstein self-orthogonal codes but are harder to decode. The single-character-error-correcting codes, when interleaved, are shown to be more powerful than the equivalent Hagelbarger code and appear to be simpler to implement. They are also slightly better than the interleaved version of Berlekamp's code. We discuss encoding and decoding algorithms and illustrate a simple decoding algorithm for some of the codes. These codes are closely related to the Bose-Chaudhuri-Hocquenghem block codes and share with them the decoding simplification for character erasures in place of errors. Any Bose-Chaudhuri-Hocquenghem decoding algorithm can be used to decode these codes.