Integer Codes Correcting Double Errors and Triple-Adjacent Errors Within a Byte

Abstract

This article presents a class of integer codes that are suitable for use in optical computer networks in which the data are transmitted serially. The presented codes are constructed with the help of a computer and have three desirable properties. First, they use integer and lookup table operations, which make them suitable for software implementation. Second, depending on the application requirements, the proposed codes can be used as low-rate error correction (EC) codes or as high-rate error detection (ED) codes. In the EC mode, which is suited for realtime applications, the receiver can correct all single and double errors, as well as all triple-adjacent (TA) errors within one b-bit byte. On the other hand, if the integrity of data is of high importance, the receiver may operate in the ED mode. In that case, it is able to detect all quadruple errors, all double TA errors within one b-bit byte, and all double TA errors within two b-bit bytes. Finally, it is important to note that the presented codes can be interleaved without delay and without using any additional hardware. Owing to this, it is possible to construct simple codes capable of detecting/correcting multiple TA and random errors.