Erasure correction performance of linear block codes
We estimate the probability of incorrect decoding of a linear block code, used over an erasure channel, via its weight spectrum, and define the weight spectra that allow us to achieve the capacity of the channel and the random coding exponent. We derive the erasure correcting capacity of long binary BCH codes with slowly growing distance and their duals. Concatenated codes of growing length n→∞ and polynomial decoding complexity O(n2), achieving the capacity of the erasure channel (or any other discrete memoryless channel), are considered.
KeywordsLinear Code Binary Symmetric Channel Linear Block Code Weight Spectrum Erasure Channel
Unable to display preview. Download preview PDF.
- 1.R. G. Gallager: Information Theory and Reliable Communications; New York:Wiley, 1968.Google Scholar
- 2.G. D. Forney: Concatenated codes; Cambridge, MA: MIT, 1966.Google Scholar
- 3.G. Zemor and G. Cohen: The threshold probability of a code (submitted to IEEE Trans IT).Google Scholar
- 4.F. J. MacWilliams and N. J. A. Sloane: The Theory of Error-Correcting Codes; North-Holland, 1977.Google Scholar
- 5.V. M. Sidelnikov: Weight Spectrum of Binary BCH Codes, Problemi Peredachi Informatsii, Vol 7, No 1, 1971, pp 14–22.Google Scholar
- 6.V. V. Zyablov: On estimation of complexity of construction of binary linear concatenated codes, Probl. Peredach. Inform., Vol 7, No 1, 1971, pp 5–13.Google Scholar
- 7.P. Delsarte and P. Piret: Algebraic Constructions of Shannon Codes for Regular Channels; IEEE-Trans IT, Vol. IT-28, No. 4, 1982, pp 593–599.Google Scholar
- 8.E. L. Blokh and V.V. Zyablov: Lineinie Kaskadnie Kodi, Moskva, Nauka, 1982 (in Russian).Google Scholar
- 9.Y. Xu: Maximum Likelihood Erasure Decoding Scheme for Concatenated Codes; IEE Proceedings-Part I, Vol 139, No 3, 1992, pp 336–339.Google Scholar
- 10.V.K. Wei: Generalised Hamming weights for linear codes; IEEE-Trans IT, Vol IT-37, No 5, 1991, pp 1412–1418.Google Scholar