Yoshiyuki Kabashima and David Saad 2004 J. Phys. A: Math. Gen. 37 R1 doi:10.1088/0305-4470/37/6/R01
Yoshiyuki Kabashima1 and David Saad2
Show affiliationsWe review recent theoretical progress on the statistical mechanics of error correcting codes, focusing on low-density parity-check (LDPC) codes in general, and on Gallager and MacKay–Neal codes in particular. By exploiting the relation between LDPC codes and Ising spin systems with multi-spin interactions, one can carry out a statistical mechanics based analysis that determines the practical and theoretical limitations of various code constructions, corresponding to dynamical and thermodynamical transitions, respectively, as well as the behaviour of error-exponents averaged over the corresponding code ensemble as a function of channel noise. We also contrast the results obtained using methods of statistical mechanics with those derived in the information theory literature, and show how these methods can be generalized to include other channel types and related communication problems.
02.50.-r Probability theory, stochastic processes, and statistics
75.10.Hk Classical spin models
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.)
Issue 6 (13 February 2004)
Received 9 October 2003, in final form 23 October 2003
Published 28 January 2004
Yoshiyuki Kabashima and David Saad 2004 J. Phys. A: Math. Gen. 37 R1
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