Integer codes correcting burst and random asymmetric errors within a byte

In most communication networks, error probabilities 1 → 0 and 0 → 1 are equally likely to occur. However, in some optical networks, such as local and access networks, this is not the case. In these networks, the number of received photons never exceeds the number of transmitted ones. Hence, if the receiver operates correctly, only 1 → 0 errors can occur. Motivated by this fact, in this paper, we present a class of integer codes capable of correcting burst and random asymmetric (1 → 0) errors within a b-bit byte. Unlike classical codes, the proposed codes are defined over the ring of integers modulo 2b −1. As a result, they have the potential to be implemented in software without any hardware assist.