LDPC Code Design for the Two-User Gaussian Multiple Access Channel

Abstract

We study code design for two-user Gaussian multiple access channels (GMACs) under fixed channel gains and under quasi-static fading. We employ low-density parity-check (LDPC) codes with BPSK modulation and utilize an iterative joint decoder. Adopting a belief propagation (BP) algorithm, we derive the PDF of the log-likelihood-ratios (LLRs) fed to the component LDPC decoders. Via examples, it is illustrated that the characterized PDF resembles a Gaussian mixture (GM) distribution, which is exploited in predicting the decoding performance of LDPC codes over GMACs. Based on the GM assumption, we propose variants of existing analysis methods, named modified density evolution (DE) and modified extrinsic information transfer (EXIT). We derive a stability condition on the degree distributions of the LDPC code ensembles and utilize it in the code optimization. Under fixed channel gains, the newly optimized codes are shown to perform close to the capacity region boundary outperforming the existing designs and the off-the-shelf point-to-point (P2P) codes. Under quasi-static fading, optimized codes exhibit consistent improvements upon the P2P codes as well. Finite block length simulations of specific codes picked from the designed ensembles are also carried out and it is shown that optimized codes perform close to the outage limits.

Achievable Rate Region for Iterative Multi-User Detection via Low-cost Gaussian Approximation

“…The code design for multi-user can be complicated [36]- [39]. For simplicity, we consider a single-input single-output (SISO) setup.…”

Near-Capacity Detection and Decoding: Code Design for Dynamic User Loads in Gaussian Multiple Access Channels

“…Recent works in [34], [35], [36] address LDPC code design with two users applying optimal joint detection and a Gaussian-mixture model to approximate the message probability density function (PDF) at the CNs. In [37], the LDPC codes are optimized for IDMA systems with a relatively large number of users (6 to 10), again with an optimum joint MUD.…”

Design of LDPC Codes for the Unequal Power Two-User Gaussian Multiple Access Channel

“…However, the authors of [3] considered only the case where the two users have equal power. The problem was recently re-examined in [4], where a Gaussian mixture (GM) model was used for the state-tovariable messages. This GM model was shown to improve the accuracy of the EXIT chart based method of [3], at the cost of increased code design complexity due to the need for an expectation-maximization step at each iteration to estimate the parameters of the GM and because the resulting optimization problem is non-linear.…”

“…Contribution: In this work, we describe an LDPC code design method for the unequal power two-user GMAC, which generalizes the method of [3] and is a low-complexity alternative to [4]. As part of the derivation of this method, we also provide a rigorous proof of the all-one/one-half codeword assumption that has been used throughout the relevant literature [3]- [6] without an explicit proof.…”