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Publication# Efficient erasure correcting codes

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 ϵ a family of linear codes of rate R which can be encoded in time proportional to ln(1/ϵ) times their block length n. Furthermore, a codeword can be recovered with high probability from a portion of its entries of length (1+ϵ)Rn or more. The recovery algorithm also runs in time proportional to n ln(1/ϵ). Our algorithms have been implemented and work well in practice; various implementation issues are discussed

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In computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The central idea is that the sender encodes the message in a redundant way, most often by using an error correction code or error correcting code (ECC). The redundancy allows the receiver not only to detect errors that may occur anywhere in the message, but often to correct a limited number of errors.

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