Advanced Hardware Design for Error Correcting Codes by Cyrille Chavet, Philippe Coussy

By Cyrille Chavet, Philippe Coussy

This booklet presents thorough insurance of mistakes correcting ideas. It comprises crucial easy innovations and the newest advances on key subject matters in layout, implementation, and optimization of hardware/software platforms for mistakes correction. The book’s chapters are written by way of the world over well-known specialists during this box. subject matters comprise evolution of errors correction concepts, business person wishes, architectures, and layout methods for the main complex blunders correcting codes (Polar Codes, Non-Binary LDPC, Product Codes, etc). This publication presents entry to contemporary effects, and is appropriate for graduate scholars and researchers of arithmetic, desktop technology, and engineering.

• Examines how one can optimize the structure of layout for blunders correcting codes;

• offers blunders correction codes from conception to optimized structure for the present and the subsequent new release standards;

• offers insurance of commercial consumer wishes complicated mistakes correcting techniques.

Advanced layout for errors Correcting Codes features a foreword through Claude Berrou.

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The code rate R p is given by R p = R1 × R2 . Thus, it is possible to construct powerful product codes using two linear block codes. In the following sections, without loss of generality, we consider a squared product code, meaning that n1 = n2 = n. The most commonly used component codes are Bose Chaudhuri Hocquenghem (BCH) codes. These codes are an infinite class of linear cyclic block codes that have capabilities for multiple error detection and correction. Reed–Solomon (RS) codes can also be used as component codes.

1) using αv as the LLR value. 3 Implementation of Polar Decoders 39 It was noted in [10] that a node whose descendants are all frozen nodes corresponds to code of rate 0 and its output βv is known a priori. More importantly, it was shown that a node whose children are all information bits corresponds to code of rate 1 that can be decoded using maximum-likelihood decoding by applying threshold detection on αv directly to obtain βv . Therefore, constituent codes of rate 0 and rate 1 can be decoded directly without traversing the corresponding sub-trees in the decoder graph.

IEEE Trans Commun 53(8):1288 43. Schläfer P, Alles M, Weis C, Wehn N (2012) Design space of flexible multi-gigabit LDPC decoders. VLSI Des J 2012. 1155/2012/942893 44. Blanksby A, Howland CJ (2002) A 690-mW 1-Gb/s, rate-1/2 low-density parity-check code decoder. IEEE J Solid State Circuits 37(3):404 45. Onizawa N, Hanyu T, Gaudet V (2010) Design of high-throughput fully parallel LDPC decoders based on wire partitioning. IEEE Trans Very Large Scale Integr (VLSI) Syst 18(3):482. 2011360 46. Schläfer P, Wehn N, Lehnigk-Emden T, Alles M (2013) A new dimension of parallelism in ultra high throughput LDPC decoding.

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