Statistical mechanics analysis of LDPC coding in MIMO Gaussian channels

Roberto C. Alamino*, David Saad

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Using analytical methods of statistical mechanics, we analyse the typical behaviour of a multiple-input multiple-output (MIMO) Gaussian channel with binary inputs under low-density parity-check (LDPC) network coding and joint decoding. The saddle point equations for the replica symmetric solution are found in particular realizations of this channel, including a small and large number of transmitters and receivers. In particular, we examine the cases of a single transmitter, a single receiver and symmetric and asymmetric interference. Both dynamical and thermodynamical transitions from the ferromagnetic solution of perfect decoding to a non-ferromagnetic solution are identified for the cases considered, marking the practical and theoretical limits of the system under the current coding scheme. Numerical results are provided, showing the typical level of improvement/deterioration achieved with respect to the single transmitter/receiver result, for the various cases. © 2007 IOP Publishing Ltd.

Original languageEnglish
Pages (from-to)12259-12279
Number of pages21
JournalJournal of Physics A: Mathematical and Theoretical
Issue number41
Publication statusPublished - 25 Sep 2007

Bibliographical note

Copyright of Institute of Physics


  • statistical mechanics
  • multiple-input multiple-output
  • Gaussian channel
  • low-density parity-check
  • network coding
  • joint decoding
  • transmitter
  • receiver
  • interference
  • transition


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