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Information, Physics, and Computation$
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Marc Mézard and Andrea Montanari

Print publication date: 2009

Print ISBN-13: 9780198570837

Published to Oxford Scholarship Online: September 2009

DOI: 10.1093/acprof:oso/9780198570837.001.0001

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Low-density parity-check codes

Low-density parity-check codes

(p.219) 11 Low-density parity-check codes
Information, Physics, and Computation

Marc Mézard

Andrea Montanari

Oxford University Press

Low-density parity-check (LDPC) codes are among the most efficient error correcting codes in use. This chapter introduces an important family of LDPC ensembles, based on random factor graphs, and studies some of their basic properties. It focuses on performances under optimal decoding, when no constraint is imposed on the computational complexity of the decoding procedure. Bounds in their performances are derived through an analysis of the geometric properties of their codebook. In particular, it shows that appropriately chosen LDPC ensembles allow for communication reliably at rates close to Shannon's capacity.

Keywords:   low density, parity check, error correcting code, codebook, geometry, optimal decoding

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