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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.

We focus on Gaussian interference channels (GICs) and study the Han-Kobayashi (HK) coding strategy for the twouser case with the objective of designing implementable (explicit) channel codes. Specifically, low-density parity-check (LDPC) codes are adopted for use over the channel, their benefits are studied and suitable codes are designed. Iterative joint decoding is used at the receivers, where independent and identically distributed (i.i.d.) channel adapters are used to prove that loglikelihood-ratios (LLRs) exchanged among the nodes of the Tanner graph enjoy symmetry when BPSK or QPSK with Gray coding is employed. This property is exploited in the proposed code optimization algorithm adopting a random perturbation technique. Code optimization and convergence threshold computations are carried out for different GICs employing finite constellations by tracking the average mutual information. Furthermore, stability conditions for the admissible degree distributions under strong and weak interference levels are determined. Via examples, it is observed that the optimized codes using BPSK or QPSK with Gray coding operate close to the capacity boundary for strong interference. For the case of weak interference, it is shown that nontrivial rate pairs are achievable via the newly designed codes which are not possible by single user codes with time-sharing. Performance of the designed codes is also studied for finite block lengths through simulations of specific codes picked with the optimized degree distributions with random constructions, where, for one instance, the results are compared with those of some structured designs.

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We study the design of explicit and implementable codes for the two-user discrete memoryless interference channels (DMICs). We consider Han-Kobayashi (HK) type encoding where both public and private messages are used and propose coding techniques utilizing a serial concatenation of a nonlinear trellis code (NLTC) with an outer low-density paritycheck (LDPC) code. Since exact analytical treatment of the BCJR decoder for the inner trellis-based code appears infeasible, we analytically investigate the iterative decoding process in the asymptotic regime where the probability of decoding error tends to zero. Based on this approximate analysis, we derive a stability condition for this type of a concatenated coding scheme for the first time in the literature. Furthermore, we use an extrinsic information transfer analysis to design the outer LDPC code while fixing the inner NLTC, and utilize the derived stability condition to accelerate the design process and to avoid code ensembles that potentially produce high error floors. Via numerical examples, we demonstrate that our designed codes achieve rate pairs close the optimal boundary of the HK subregion, which cannot be obtained without the use of nonlinear codes. Also, we verify that the estimated thresholds of the designed codes via finite block length simulations and show that our designs significantly outperform the point-to-point optimal codes, hence demonstrating the need for designs specifically tailored for DMICs. Index Terms-Discrete memoryless interference channels, nonlinear trellis codes, low-density parity-check codes, concatenated codes, stability condition. I. INTRODUCTION A N interference channel (IC) is a communication medium shared by several sender-receiver pairs. Transmission of Manuscript