Recent Developments in Array Error-Control Codes

Abstract

Array error-control codes are linear block or convolutional codes, with codewords or coded sequences constructed by attaching check symbols to arrays of information symbols arranged in two or more dimensions. The check symbols are calculated by taking sums of the the information symbols lying along rows, columns, diagonals or other directions or paths in the information array. The simplest array code is the binary block code obtained by taking single parity checks across the rows and columns of a rectangular array of information bits. Array codes can be constructed with symbols from a .eld, ring or group, can have a wide range of parameters (block or constraint length, rate, distance, etc), and can be designed to detect and correct random and/or bursts or clusters of errors. The motivation for investigating and applying array codes (apart from their interesting mathematical aspects) is that they often provide a good trade-o. between error-control power and complexity of decoding. The rate of a random error-control block array code, such as a product code, for example (classical product codes form a sub-class of array codes), is usually less than that of the best available alternative code with the same distance and length, but in exchange the array code will be much easier to decode [1]. However, in many cases array codes designed to correct burst error patterns can be both optimal (maximum distance separable (MDS), for example) and simpler to decode than other equivalent codes [1].