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A Decoding Algorithm for LDPC Codes Over Erasure Channels with Sporadic Errors

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  • Digitale Netze
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  • Computer Science
  • Design
  • Mathematics

Abstract

Allerton_10_CR_3.dvi A Decoding Algorithm for LDPC Codes Over Erasure Channels with Sporadic Errors Gianluigi Liva, Enrico Paolini, Balazs Matuz, and Marco Chiani Abstract— An efficient decoding algorithm for low-density parity-check (LDPC) codes on erasure channels with sporadic errors (i.e., binary error-and-erasure channels with error prob- ability much smaller than the erasure probability) is proposed and its performance analyzed. A general single-error multiple- erasure (SEME) decoding algorithm is first described, which may be in principle used with any binary linear block code. The algorithm is optimum whenever the non-erased part of the received word is affected by at most one error, and is capable of performing error detection of multiple errors. An upper bound on the average block error probability under SEME decoding is derived for the linear random code ensemble. The bound is tight and easy to implement. The algorithm is then adapted to LDPC codes, resulting in a simple modification to a previously proposed efficient maximum likelihood LDPC erasure decoder which exploits the parity-check matrix sparseness. Numerical results reveal that LDPC codes under efficient SEME decoding can closely approach the average performance of random codes. I. INTRODUCTION The design and decoding of low-density parity-check (LDPC) codes [1] applied to erasure channels has been vastly explored in the past decade (see e.g. [2]–[7]). While origi- nally most of the attention has been paid to the construction of LDPC codes able to approach the channel capacity under iterative (IT) decoding, more recently practical maximum- likelihood (ML) decoding algorithms for LDPC codes over erasure channels have been devised [6], [8], paving the way for the design of codes for hybrid IT/ML decoders [9], [10]. It has been shown that ML decoding of LDPC codes can largely outperform its iterative counterpart, attaining on the binary erasure channel (BEC) performances close to those of idealized maximum distance sepa

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