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,dmin), where (n1,k1) and (n2,k2) are row and column codes respectively, and minimum Hamming distance dmin=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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Elias P. Error free coding. -“IEEE Transactions”, vol. 4, 1954, p.p.29–37.
Farrell P.G. Array codes. - “Algebraic Coding Theory and Applications”. Ed. G.Longo, Springer-Verlag, 1979, p.p.231–242.
Burton H.O., Weldon EJ. Cyclic product codes. - “IEEE Transactions on Information Theory”, vol. 11, July 1965, p.p.433–439.
Blaum M., Farrell P.G., Tilborg H.C.A. Multiple burst error correcting array codes. -“IEEE Transactions on Information Theory”, vol. IT-34, September 1988, p.p.1061–1064.
Daniel J.S., Farrell P.G. Burst-error correcting array codes: Further Development. - “4-th International Conference on Digital Processing of Signals in Communications”, Loughborough, April 1985, UK.
Viterbi AJ. Convolutional codes and their performance in communication systems. -“IEEE Transactions on Communications”, col.COM-19, N:5, October 1971, p.p.751–772.
Wolf J.K. Efficient maximum likelihood decoding of linear block codes using a trellis.-“IEEE Transactions on Information Theory”, vol. 28, No 2, 1982.
Forney G.D Jr. Coset codes - Part 1: Introduction and Geometrical Classification. - “IEEE Transactions on Information Theory”, vol. 34, No 5, 1988, p.p.1123–1151.
MacWilliams J.K., Sloane NJ. “The theory of error correcting codes.” New York: North Holland, 1977.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag Wien
About this chapter
Cite this chapter
Honary, B., Markarian, G.S., Kaya, L., Darnell, M. (1993). Trellis Decoding Technique for Array Codes. In: Camion, P., Charpin, P., Harari, S. (eds) Eurocode ’92. International Centre for Mechanical Sciences, vol 339. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2786-5_29
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2786-5_29
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82519-8
Online ISBN: 978-3-7091-2786-5
eBook Packages: Springer Book Archive