Coding for Multiple Asymmetric Errors in One Channel of a Multichannel System

Abstract

An efficient error correction code for correcting errors of one kind in an arbitrary N-character message is discussed. The coded check character is obtained by summing the weighted coded characters (columns of binary digits where each binary digit assumes a unique weight) within an entire record modulo a prime integer. This check character is then added to the record before transmission over a channel (e.g., magnetic tape). A single parity check is appended to each character of the record to make possible single error detection per character. The received message, perturbed by noise in a constant position or single track, is decoded by again adding up the received information plus check characters in a modulo p counter. Error location is achieved by solving for x in the expression ax mod p, when a, the number of parity checks that failed, and ax mod p, the contents of a mod p counter, are known. This type of residue check may be employed to indicate which track is in error. Thus, error correction can be performed on the characters containig parity check failures.