Linear-recurrent binary error-correcting codes for memoryless channels
William L. Kilmer · IEEE Transactions on Information Theory · 1961
This paper concerns the analysis of recurrent-type, parity-check, error-correcting codes for memoryless, binary symmetric channels. These codes are defined to consist of message sequences augmented by insertions ofrsuccessive parity digits everybsuccessive message digits. An analysis framework is established for the codes which consists mainly of a parity check matrix[M]and a message difference vector[N]. Within this framework, a decoding scheme is developed which renders the codes capable of correcting any set of\eqslantless eerrors inm/bsuccessive(b + r)-digit blocks of coded message sequence, whereeis maximized over all parity-check codes having the same redundancy ratios and maximal lengths of dependence among their digits. An example is given of a linear-recurrent code which has a lower probability of error than the best comparable block code, and several outstanding problems are discussed.