Statistical Mechanics Analysis of LDPC Coding in MIMO Gaussian Channels

TL;DR

This paper applies statistical mechanics to analyze the behavior of LDPC-coded MIMO Gaussian channels with binary inputs, identifying phase transitions and limits of decoding performance across various configurations.

Contribution

It introduces an analytical framework using replica symmetry to study the typical behavior and phase transitions of LDPC-coded MIMO channels with different transmitter-receiver setups.

Findings

Identification of dynamical and thermodynamical phase transitions

Numerical results showing performance variations across configurations

Analysis of single and multiple transmitter/receiver scenarios

Abstract

Using analytical methods of statistical mechanics, we analyse the typical behaviour of a multiple-input multiple-output (MIMO) Gaussian channel with binary inputs under 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 the symmetric and asymmetric interference channels. 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.