Practical distributed source coding with impulse-noise degraded side information at the decoder

International audienceThis paper introduces a practical method for distributed lossy compression (Wyner-Ziv quantization) with side information available only at the decoder, where the side information is equal to the signal affected by background noise and additional impulse noise. At the core of the method is an LDPC-based lossless distributed (Slepian-Wolf) source code for q-ary alphabets, which is matched to the impulse probability and allows to remove the scalar-quantized impulse noise. Applications of this method to distributed compressed sensing of signals that differ in a sparse set of locations is also discussed, as well as some differences and similarities of variable- and fixed-length coding of sparse signals

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

Network flow algorithms for wireless networks and design and analysis of rate compatible LDPC codes

While Shannon already characterized the capacity of point-to-point channels back in 1948, characterizing the capacity of wireless networks has been a challenging problem. The deterministic channel model proposed by Avestimehr, etc. (2007 - 1) has been a promising approach for approximating the Gaussian channel capacity and has been widely studied recently. Motivated by this model, an improved combinatorial algorithm is considered for finding the unicast capacity for wireless information flow on such deterministic networks in the first part of this thesis. Our algorithm fully explores the useful combinatorial features intrinsic in the problem. Our improvement applies generally with any size of finite fields associated with the channel model. Comparing with other related algorithms, our improved algorithm has very competitive performance in complexity. In the second part of our work, we consider the design and analysis of rate-compatible LDPC codes. Rate-compatible LDPC codes are basically a family of nested codes, operating at different code rates and all of them can be encoded and decoded using a single encoder and decoder pair. Those properties make rate-compatible LDPC codes a good choice for changing channel conditions, like in wireless communications. The previous work on the design and analysis of LDPC codes are all targeting at a specific code rate and no work is known on the design and analysis of rate-compatible LDPC codes so that the code performance at all code rates in the family is manageable and predictable. In our work, we proposed algorithms for the design and analysis of rate-compatible LDPC codes with good performance and make the code performance at all code rates manageable and predictable. Our work is based on E2RC codes, while our approaches in the design and analysis can be applied more generally not only to E2RC codes, but to other suitable scenarios, like the design of IRA codes. Most encouragingly, we obtain families of rate-compatible codes whose gaps to capacity are at most 0.3 dB across the range of rates when the maximum variable node degree is twenty, which is very promising compared with other existing results

On generalized LDPC codes for ultra reliable communication

Ultra reliable low latency communication (URLLC) is an important feature in future mobile communication systems, as they will require high data rates, large system capacity and massive device connectivity [11]. To meet such stringent requirements, many error-correction codes (ECC)s are being investigated; turbo codes, low density parity check (LDPC) codes, polar codes and convolutional codes [70, 92, 38], among many others. In this work, we present generalized low density parity check (GLDPC) codes as a promising candidate for URLLC. Our proposal is based on a novel class of GLDPC code ensembles, for which new analysis tools are proposed. We analyze the trade-o_ between coding rate and asymptotic performance of a class of GLDPC codes constructed by including a certain fraction of generalized constraint (GC) nodes in the graph. To incorporate both bounded distance (BD) and maximum likelihood (ML) decoding at GC nodes into our analysis without resorting to multi-edge type of degree distribution (DD)s, we propose the probabilistic peeling decoding (P-PD) algorithm, which models the decoding step at every GC node as an instance of a Bernoulli random variable with a successful decoding probability that depends on both the GC block code as well as its decoding algorithm. The P-PD asymptotic performance over the BEC can be efficiently predicted using standard techniques for LDPC codes such as Density evolution (DE) or the differential equation method. We demonstrate that the simulated P-PD performance accurately predicts the actual performance of the GLPDC code under ML decoding at GC nodes. We illustrate our analysis for GLDPC code ensembles with regular and irregular DDs. This design methodology is applied to construct practical codes for URLLC. To this end, we incorporate to our analysis the use of quasi-cyclic (QC) structures, to mitigate the code error floor and facilitate the code very large scale integration (VLSI) implementation. Furthermore, for the additive white Gaussian noise (AWGN) channel, we analyze the complexity and performance of the message passing decoder with various update rules (including standard full-precision sum product and min-sum algorithms) and quantization schemes. The block error rate (BLER) performance of the proposed GLDPC codes, combined with a complementary outer code, is shown to outperform a variety of state-of-the-art codes, for URLLC, including LDPC codes, polar codes, turbo codes and convolutional codes, at similar complexity rates.Programa Oficial de Doctorado en Multimedia y ComunicacionesPresidente: Juan José Murillo Fuentes.- Secretario: Matilde Pilar Sánchez Fernández.- Vocal: Javier Valls Coquilla