On LDPC Codes for Gaussian Interference Channels

In this paper, we focus on the two-user Gaussian interference channel (GIC), and study the Han-Kobayashi (HK) coding/decoding strategy with the objective of designing low-density parity-check (LDPC) codes. A code optimization algorithm is proposed which adopts a random perturbation technique via tracking the average mutual information. The degree distribution optimization and convergence threshold computation are carried out for strong and weak interference channels, employing binary phase-shift keying (BPSK). Under strong interference, it is observed that optimized codes operate close to the capacity boundary. For the case of weak interference, it is shown that via the newly designed codes, a nontrivial rate pair is achievable, which is not attainable by single user codes with time-sharing. Performance of the designed LDPC codes are also studied for finite block lengths through simulations of specific codes picked from the optimized degree distributions.Comment: ISIT 201

On Code Design for Interference Channels

abstract: There has been a lot of work on the characterization of capacity and achievable rate regions, and rate region outer-bounds for various multi-user channels of interest. Parallel to the developed information theoretic results, practical codes have also been designed for some multi-user channels such as multiple access channels, broadcast channels and relay channels; however, interference channels have not received much attention and only a limited amount of work has been conducted on them. With this motivation, in this dissertation, design of practical and implementable channel codes is studied focusing on multi-user channels with special emphasis on interference channels; in particular, irregular low-density-parity-check codes are exploited for a variety of cases and trellis based codes for short block length designs are performed. Novel code design approaches are first studied for the two-user Gaussian multiple access channel. Exploiting Gaussian mixture approximation, new methods are proposed wherein the optimized codes are shown to improve upon the available designs and off-the-shelf point-to-point codes applied to the multiple access channel scenario. The code design is then examined for the two-user Gaussian interference channel implementing the Han-Kobayashi encoding and decoding strategy. Compared with the point-to-point codes, the newly designed codes consistently offer better performance. Parallel to this work, code design is explored for the discrete memoryless interference channels wherein the channel inputs and outputs are taken from a finite alphabet and it is demonstrated that the designed codes are superior to the single user codes used with time sharing. Finally, the code design principles are also investigated for the two-user Gaussian interference channel employing trellis-based codes with short block lengths for the case of strong and mixed interference levels.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201

Short block length code design for interference channels

We focus on short block length code design for Gaussian interference channels (GICs) using trellis-based codes. We employ two different decoding techniques at the receiver side, namely, joint maximum likelihood (JML) decoding and single user (SU) minimum distance decoding. For different interference levels (strong and weak) and decoding strategies, we derive error-rate bounds to evaluate the code performance. We utilize the derived bounds in code design and provide several numerical examples for both strong and weak interference cases. We show that under the JML decoding, the newly designed codes offer significant improvements over the alternatives of optimal point-to-point (P2P) trellis-based codes and off-the-shelf low density parity check (LDPC) codes with the same block lengths. © 2016 IEEE

Analysis of low-density parity-check codes on impulsive noise channels

PhD ThesisCommunication channels can severely degrade a signal, not only due to fading effects but also interference in the form of impulsive noise. In conventional communication systems, the additive noise at the receiver is usually assumed to be Gaussian distributed. However, this assumption is not always valid and examples of non-Gaussian distributed noise include power line channels, underwater acoustic channels and manmade interference. When designing a communication system it is useful to know the theoretical performance in terms of bit-error probability (BEP) on these types of channels. However, the effect of impulses on the BEP performance has not been well studied, particularly when error correcting codes are employed. Today, advanced error-correcting codes with very long block lengths and iterative decoding algorithms, such as Low-Density Parity-Check (LDPC) codes and turbo codes, are popular due to their capacity-approaching performance. However, very long codes are not always desirable, particularly in communications systems where latency is a serious issue, such as in voice and video communication between multiple users. This thesis focuses on the analysis of short LDPC codes. Finite length analyses of LDPC codes have already been presented for the additive white Gaussian noise channel in the literature, but the analysis of short LDPC codes for channels that exhibit impulsive noise has not been investigated. The novel contributions in this thesis are presented in three sections. First, uncoded and LDPC-coded BEP performance on channels exhibiting impulsive noise modelled by symmetric -stable (S S) distributions are examined. Different sub-optimal receivers are compared and a new low-complexity receiver is proposed that achieves near-optimal performance. Density evolution is then used to derive the threshold signal-tonoise ratio (SNR) of LDPC codes that employ these receivers. In order to accurately predict the waterfall performance of short LDPC codes, a nite length analysis is proposed with the aid of the threshold SNRs of LDPC codes and the derived uncoded BEPs for impulsive noise channels. Second, to investigate the e ect of impulsive noise on wireless channels, the analytic BEP on generalized fading channels with S S noise is derived. However, it requires the evaluation of a double integral to obtain the analytic BEP, so to reduce the computational cost, the Cauchy- Gaussian mixture model and the asymptotic property of S S process are used to derive upper bounds of the exact BEP. Two closed-form expressions are derived to approximate the exact BEP on a Rayleigh fading channel with S S noise. Then density evolution of different receivers is derived for these channels to nd the asymptotic performance of LDPC codes. Finally, the waterfall performance of LDPC codes is again estimated for generalized fading channels with S S noise by utilizing the derived uncoded BEP and threshold SNRs. Finally, the addition of spatial diversity at the receiver is investigated. Spatial diversity is an effective method to mitigate the effects of fading and when used in conjunction with LDPC codes and can achieve excellent error-correcting performance. Hence, the performance of conventional linear diversity combining techniques are derived. Then the SNRs of these linear combiners are compared and the relationship of the noise power between different linear combiners is obtained. Nonlinear detectors have been shown to achieve better performance than linear combiners hence, optimal and sub-optimal detectors are also presented and compared. A non-linear detector based on the bi-parameter Cauchy-Gaussian mixture model is used and shows near-optimal performance with a significant reduction in complexity when compared with the optimal detector. Furthermore, we show how to apply density evolution of LDPC codes for different combining techniques on these channels and an estimation of the waterfall performance of LDPC codes is derived that reduces the gap between simulated and asymptotic performance. In conclusion, the work presented in this thesis provides a framework to evaluate the performance of communication systems in the presence of additive impulsive noise, with and without spatial diversity at the receiver. For the first time, bounds on the BEP performance of LDPC codes on channels with impulsive noise have been derived for optimal and sub-optimal receivers, allowing other researchers to predict the performance of LDPC codes in these type of environments without needing to run lengthy computer simulations