On codes achieving zero error capacities in limited magnitude error channels

Shannon in his 1956 seminal paper introduced the concept of the zero error capacity, Co, of a noisy channel. This is defined as the least upper bound of rates at which it is possible to transmit information with zero probability of error. At present not many codes are known to achieve the zero error capacity. In this paper, some codes which achieve zero error capacities in limited magnitude error channels are described. The code lengths of these zero error capacity achieving codes can be of any finite length n = 1, 2,..., in contrast to the long lengths required for the known regular capacity achieving codes such as turbo codes, LDPC codes and polar codes. Both non-systematic and systematic codes are described.