Trellis Decoding Technique for Array Codes

Abstract

Array codes were first introduced by Elias [1], and have been proposed for many burst and random-error control applications [2–5]. The essence of an array code is that the combination is based on a geometrical construction, the component codes are simple and decoding of array codes is relatively easy. The simplest array code is the row-and-column parity code, which also is called a two-coordinate, bidirectional, bit and block parity and has been widely used in data transmission systems and computer memories [2]. The code may be square or rectangular and has parameters (n₁n₂,k₁k₂,d_min), where (n₁,k₁) and (n₂,k₂) are row and column codes respectively, and minimum Hamming distance d_min=4. These codes are easy and flexible to design and relatively simple to decode. However these codes do not have the full power of block linear code of length n=n₁n₂, and the conventional decoding algorithms [2] for array codes, do not make use of maximum power of the code and are not maximum likelihood decoding algorithms.