Character-correcting convolutional self-orthogonal codes

TLDR: It is shown that, given a t -error-correcting BCSOC of rate b —1/ b, a character-error correcting convolutional self-orthogonal code (CCSOC) can be constructed for any integer k, the rate expansion factor, and the CCSOC so constructed corrects t character errors, and also possesses large simultaneous burst-error- correcting capabilities.

Abstract: A class of convolutional, character-error-correcting codes with limited error propagation is presented. This class of codes is derived from binary convolutional self-orthogonal codes (BCSOC). By character-error-correcting, we mean that the code is character oriented, where each character can be thought of as a string of binary or higher base symbols of fixed length or as a single nonbinary symbol of correspondingly higher base. It is shown that, given a t -error-correcting BCSOC of rate b —1/ b , a character-error correcting convolutional self-orthogonal code (CCSOC) of rate k ( b —1)/( k ( b —1) + 1) can be constructed for any integer k , the rate expansion factor. The CCSOC so constructed corrects t character errors, and also possesses large simultaneous burst-error-correcting capabilities. Lower bounds on the burst-error-correcting capability for both BCSOC and CCSOC are found. Decoding consists of a mixture of majority logic decoding and algebraic computation. The decoding algorithm seems practical if either the rate expansion factor k or the number of errors corrected t are not large. Such codes are most suitable for channels with both random and burst noise, and also effect a compromise between the cost of terminal equipment and the efficient use of channels.