Efficient erasure correcting codes
TL;DR: A simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs is introduced and a simple criterion involving the fractions of nodes of different degrees on both sides of the graph is obtained which is necessary and sufficient for the decoding process to finish successfully with high probability.
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Abstract: We introduce a simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs and analyze the algorithm by analyzing a corresponding discrete-time random process. As a result, we obtain a simple criterion involving the fractions of nodes of different degrees on both sides of the graph which is necessary and sufficient for the decoding process to finish successfully with high probability. By carefully designing these graphs we can construct for any given rate R and any given real number /spl epsiv/ a family of linear codes of rate R which can be encoded in time proportional to ln(1//spl epsiv/) times their block length n. Furthermore, a codeword can be recovered with high probability from a portion of its entries of length (1+/spl epsiv/)Rn or more. The recovery algorithm also runs in time proportional to n ln(1//spl epsiv/). Our algorithms have been implemented and work well in practice; various implementation issues are discussed.
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Near Shannon limit error-correcting coding and decoding: Turbo-codes. 1
Claude Berrou,A. Glavieux,Punya Thitimajshima +2 more
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TL;DR: In this article, a new class of convolutional codes called turbo-codes, whose performances in terms of bit error rate (BER) are close to the Shannon limit, is discussed.
Near Shannon limit error-correcting coding and decoding
Claude Berrou
- 01 Jan 1993
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