Density Evolution for the Design of Non-Binary Low Density Parity Check Codes for Slepian-Wolf Coding (original) (raw)
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Density Evolution Technique for LDPC Codes in Slepian-Wolf Coding of Nonuniform Sources
International Journal of Computer Applications, 2010
This paper attempts to examine the optimality of LDPC codes for compression of nonuniform source with Slepian-Wolf coding using density evolution technique. The primary goal is to evaluate the performance of LDPC codes with reference to turbo codes (in SF-ISF setup). The appreciable difference between LDPC and turbo codes is also discussed in this paper. The threshold values obtained from the density evolution technique indicate that the conditional entropy H(X/Y) is nearly constant with source distribution. This feature is useful in calculating the threshold values for any given source distribution analytically. This special feature is true for only LDPC codes. Several well known LDPC codes, both regular and irregular are critically analyzed using density evolution technique. This analysis reveals that the capacity approaching LDPC codes with respect to error correction codes do indeed approach the Slepian-Wolf bound for nonuniform sources as well. The threshold values show that the nonuniform source can be compressed to near about 0.01bits/sample away from Slepian-Wolf bound even for highly decorrelated side information.
Density Evolution for Nonbinary LDPC Codes Under Gaussian Approximation
IEEE Transactions on Information Theory, 2009
This paper extends the work on density evolution for binary low-density parity-check (LDPC) codes with Gaussian approximation to LDPC codes over GF (q). We first generalize the definition of channel symmetry for nonbinary inputs to include q-ary phase-shift keying (PSK) modulated channels for prime q and binary-modulated channels for q that is a power of 2. For the well-defined q-ary-input symmetric-output channel, we prove that under the Gaussian assumption, the density distribution for messages undergoing decoding is fully characterized by (q 0 1) quantities. Assuming uniform edge weights, we further show that the density of messages computed by the check node decoder (CND) is fully defined by a single number. We then present the approximate density evolution for regular and irregular LDPC codes, and show that the (q 0 1)-dimensional integration involved can be simplified using a dimensionality reduction algorithm for the important case of q = 2 p. Through application of approximate density evolution and linear programming, we optimize the degree distribution of LDPC codes over GF(3) and GF(4). The optimized irregular LDPC codes demonstrate performance close to the Shannon capacity for long codewords. We also design GF(q) codes for high-order modulation by using the idea of a channel adapter. We find that codes designed in this fashion outperform those optimized specifically for the binary additive white Gaussian noise (AWGN) channel for a short codewords and a spectral efficiency of 2 bits per channel use (b/cu). Index Terms-density evolution, Gaussian approximation, lowdensity parity-check (LDPC) codes. I. INTRODUCTION T HIS paper is motivated by the impressive performance of irregular low-density parity-check (LDPC) codes over a wide class of channels [1]-[5]. Irregular LDPC codes are commonly designed using a numerical technique called density evolution. Developed by Richardson and Urbanke [1], the method of density evolution is one of the most powerful tools known for analyzing the asymptotic performance of an LDPC Manuscript
Density evolution-based analysis and design of LDPC codes with a priori information
2010 Information Theory and Applications Workshop (ITA), 2010
In this paper, we consider multiple access schemes with correlated sources, where a priori information, in terms of source correlation, is available at the access point (AP). In particular, we assume that each source uses a proper low-density parity-check (LDPC) code to transmit, through an additive white Gaussian noise (AWGN) channel, its information sequence to the AP. At the AP, the information sequences are recovered by an iterative decoder, with component decoders associated with the sources, which exploit the available a priori information. In order to analyze the behaviour of the considered multiple access coded system, we propose a density evolution-based approach, which allows to determine a signal-to-noise ratio (SNR) transfer chart and compute the system multi-dimensional SNR feasible region. The proposed technique, besides characterizing the performance of LDPC-coded multiple access scheme, is expedient to design optimized LDPC codes for this application.
A New Density Evolution Approximation for LDPC and Multi-Edge Type LDPC Codes
IEEE Transactions on Communications, 2016
This paper considers density evolution for lowdensity parity-check (LDPC) and multi-edge type low-density parity-check (MET-LDPC) codes over the binary input additive white Gaussian noise channel. We first analyze three singleparameter Gaussian approximations for density evolution and discuss their accuracy under several conditions, namely at low rates, with punctured and degree-one variable nodes. We observe that the assumption of symmetric Gaussian distribution for the density-evolution messages is not accurate in the early decoding iterations, particularly at low rates and with punctured variable nodes. Thus single-parameter Gaussian approximation methods produce very poor results in these cases. Based on these observations, we then introduce a new density evolution approximation algorithm for LDPC and MET-LDPC codes. Our method is a combination of full density evolution and a single-parameter Gaussian approximation, where we assume a symmetric Gaussian distribution only after density-evolution messages closely follow a symmetric Gaussian distribution. Our method significantly improves the accuracy of the code threshold estimation. Additionally, the proposed method significantly reduces the computational time of evaluating the code threshold compared to full density evolution thereby making it more suitable for code design.
A New Fast Density Evolution Method for LDPC Codes Using Higher Order Statistics
2006 40th Annual Conference on Information Sciences and Systems, 2006
Density Evolution (DE) is a technique for tracking the distribution of the Log Likelihood Ratio (LLR) messages exchanged between the variable nodes and the check nodes in a bipartite graph [1]. It is widely assumed that these distributions are close to Gaussian. However, in many scenarios, this assumption is not valid, e.g., the case that the Signal to Noise Ratio (SNR) is low, or the degree of variable nodes exceeds a certain threshold [2]. This article introduces a new (suboptimal) method for DE algorithm in Low-Density Parity-Check (LDPC) codes. We provide a more accurate model for the distribution of message bits (as compared to Gaussian) through matching the first n statistical moments. An iterative message passing algorithm is proposed to compute these moments from the graphical representation of the underlying code. We show that the proposed algorithm results in an improved estimate of the underlying EXIT chart as compared to using a Gaussian assumption. In this respect, the proposed method achieves a performance very close to that of the best earlier methods reported in [2] and [3], while it offers a much lower complexity
LDPCA Code Construction for Slepian-Wolf Coding
IEEE Communications Letters, 2000
Error correcting codes used for Distributed Source Coding (DSC) generally assume a random distribution of errors. However, in certain DSC applications, prediction of the error distribution is possible and thus this assumption fails, resulting in a sub-optimal performance. This letter considers the construction of rate-adaptive Low-Density Parity-Check (LDPC) codes where the edges of the variable nodes receiving unreliable information are distributed evenly among all the check nodes. Simulation results show that the proposed codes can reduce the gap to the theoretical bounds by up to 56% compared to traditional codes.
Density evolution for two improved BP-Based decoding algorithms of LDPC codes
IEEE Communications Letters, 2000
In this letter, we analyze the performance of two improved belief propagation (BP) based decoding algorithms for LDPC codes, namely the normalized BP-based and the offset BP-based algorithms, by means of density evolution. The numerical calculations show that with one properly chosen parameter for each of these two improved BP-based algorithms, performances very close to that of the BP algorithm can be achieved. Simulation results for LDPC codes with code length moderately long validate the proposed optimization.
On the design of LDPC code ensembles for BIAWGN channels
IEEE Transactions on Communications, 2000
Existing design methods for irregular Low-Density Parity-Check (LDPC) codes over the additive white Gaussian noise channel are based on using asymptotic analysis tools such as density evolution in an optimization process. Such a process is computationally expensive particularly when a large number of constituent variable node degrees are involved in the design. In this paper, we propose a systematic approach for the design of irregular LDPC codes. The proposed method, which is based on a pre-computed upper bound on the fraction of edges connected to variable nodes of degree 3, is considerably less complex than the conventional optimization approach. Through a number of examples, we demonstrate that using our method, ensembles with performance very close to those devised based on optimization, can be designed. In addition to having very good performance, the number of constituent variable node degrees in the designed ensembles is only three or four. This, in some cases, is much smaller than the corresponding number for optimization-based designs with similar performance.
Density Evolution Analysis of Robustness for LDPC Codes over the Gilbert-Elliott Channel
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2008
In this paper, we analyze the robustness for low-density parity-check (LDPC) codes over the Gilbert-Elliott (GE) channel. For this purpose we propose a density evolution method for the case where LDPC decoder uses the mismatched parameters for the GE channel. Using this method, we derive the region of tuples of true parameters and mismatched decoding parameters for the GE channel, where the decoding error probability approaches asymptotically to zero.
arXiv (Cornell University), 2017
The theoretical analysis of detection and decoding of low-density parity-check (LDPC) codes transmitted over channels with two-dimensional (2D) interference and additive white Gaussian noise (AWGN) is provided in this paper. The detection and decoding system adopts the joint iterative detection and decoding scheme (JIDDS) in which the log-domain sum-product algorithm is adopted to decode the LDPC codes. The graph representations of the JIDDS are explained. Using the graph representations, we prove that the message-flow neighborhood of the detection and decoding system will be treelike for a sufficiently long code length. We further confirm that the performance of the JIDDS will concentrate around the performance in which message-flow neighborhood is tree-like. Based on the treelike message-flow neighborhood, we employ a modified density evolution algorithm to track the message densities during the iterations. A threshold is calculated using the density evolution algorithm which can be considered as the theoretical performance limit of the system. Simulation results demonstrate that the modified density evolution is effective in analyzing the performance of 2D interference systems.