Waterfall performance analysis of finite-length LDPC codes on symmetric channels

An efficient method for analyzing the performance of finite-length low-density parity-check (LDPC) codes in the waterfall region, when transmission takes place on a memoryless binary-input output-symmetric channel is proposed. This method is based on studying the variations of the channel quality around its expected value when observed during the transmission of a finite-length codeword. We model these variations with a single parameter. This parameter is then viewed as a random variable and its probability distribution function is obtained. Assuming that a decoding failure is the result of an observed channel worse than the code?s decoding threshold, the block error probability of finite-length LDPC codes under different decoding algorithms is estimated. Using an extrinsic information transfer chart analysis, the bit error probability is obtained from the block error probability. Different parameters can be used for modeling the channel variations. In this work, two of such parameters are studied. Through examples, it is shown that this method can closely predict the performance of LDPC codes of a few thousand bits or longer in the waterfall region.     

Design of efficiently encodable moderate-length high-rate irregular LDPC codes

This paper presents a new class of irregular low-density parity-check (LDPC) codes of moderate length (10/sup 3//spl les/n/spl les/10/sup 4/) and high rate (R/spl ges/3/4). Codes in this class admit low-complexity encoding and have lower error-rate floors than other irregular LDPC code-design approaches. It is also shown that this class of LDPC codes is equivalent to a class of systematic serial turbo codes and is an extension of irregular repeat-accumulate codes. A code design algorithm based on the combination of density evolution and differential evolution optimization with a modified cost function is presented. Moderate-length, high-rate codes with no error-rate floors down to a bit-error rate of 10/sup -9/ are presented. Although our focus is on moderate-length, high-rate codes, the proposed coding scheme is applicable to irregular LDPC codes with other lengths and rates.     

On the application of LDPC codes to arbitrary discrete-memoryless channels

We discuss three structures of modified low-density parity-check (LDPC) code ensembles designed for transmission over arbitrary discrete memoryless channels. The first structure is based on the well-known binary LDPC codes following constructions proposed by Gallager and McEliece, the second is based on LDPC codes of arbitrary (q-ary) alphabets employing modulo-q addition, as presented by Gallager, and the third is based on LDPC codes defined over the field GF(q). All structures are obtained by applying a quantization mapping on a coset LDPC ensemble. We present tools for the analysis of nonbinary codes and show that all configurations, under maximum-likelihood (ML) decoding, are capable of reliable communication at rates arbitrarily close to the capacity of any discrete memoryless channel. We discuss practical iterative decoding of our structures and present simulation results for the additive white Gaussian noise (AWGN) channel confirming the effectiveness of the codes.     

Jitter and error performance analysis of trellis coded M-PSK overpartial response fading channels

For the first time, a partial response fading channel is introduced. The new channel model acts in a similar way to partial response signalling (PRS) with a Rayleigh probability density function. Emphasis is given to jitter and error performances of M-PSK schemes in the proposed channel with ideal channel state information, but with no side information existing on the phase noise process. Analytical upper bounds are derived using the Chernoff bounding technique, combined with the modified generating functional approach. Simulation studies confirming analytically obtained curves are carried out     

编码协作MARC上全分集LDPC码的实现与性能分析

本文研究了多接入中继信道(MARC)上全分集LDPC码的实现与性能。首先,分析了MARC模型及其固有分集,然后构造了在MARC上能取得全分集的LDPC码,新构造的码字采用根校验节点把源节点传输与中继节点传输联系起来,从而获得全分集。接着,研究了所构造码字的密度演化过程,在密度演化的基础上,进一步分析了全分集LDPC码校验矩阵的结构,给出了通过提高全分集校验比特的比例,改善全分集LDPC码在MARC上编码增益的方法。仿真结果表明,本文所提算法在MARC信道上不仅能实现全分集,而且能取得较高的编码增益。     

LDPC codes for fading Gaussian broadcast channels

In this work, we study coding over a class of two-user broadcast channels (BCs) with additive white Gaussian noise and multiplicative fading known at the receivers only. Joint decoding of low-density parity-check (LDPC) codes is analyzed. The message update rule at the mapping node linking the users' codes is derived and is found to exhibit an interesting soft interference cancellation property. High performance codes are found using the differential evolution optimization technique and extrinsic information transfer analysis adapted to our multiuser setting. The optimized codes have rates very close to the boundary of the achievable region for binary constrained input for both faded and unfaded channels. Simulation results for moderate block lengths show that our codes operate within less than 1 dB of their respective threshold.     

Quasi-cyclic LDPC codes with high-rate and low error floor based on Euclidean geometries

An improved Euclidean geometry approach to design quasi-cyclic (QC) Low-density parity-check (LDPC) codes with high-rate and low error floor is presented.The constructed QC-LDPC codes with high-rate ha...     

LDPC码译码算法及性能分析

为了进一步降低低密度奇偶校验(LDPC)码译码算法的复杂度,基于经典置信传播(BP)译码算法,给出了对数域迭代后验概率对数似然比(APP LLR)算法。通过概率域的和积算法(SPA)和对数域的迭代APP LLR算法的性能仿真及分析可见,迭代APP LLR算法能以较小的性能损失换取复杂度的大幅降低。进一步选用迭代APP LLR算法,结合不同地形条件下的VHF频段信道模型,仿真了LDPC码编译码系统的性能。理论分析及仿真结果均表明,基于迭代APP LLR算法的LDPC码,实现简单,性能优异,具有良好的工程应用前景。     

多元LDPC码与二元LDPC码的性能分析

为了比较多元LDPC码与二元LDPC码的性能,文章从校验矩阵、Tanner图、BP译码算法等方面将两者进行有效的分析,并结合具体的Monte Carlo仿真实验,得出多元LDPC码的性能确实优于等长度码长的二元LDPC码.     

Design and analysis of nonbinary LDPC codes for arbitrary discrete-memoryless channels

We present an analysis under the iterative decoding of coset low-density parity-check (LDPC) codes over GF(q), designed for use over arbitrary discrete-memoryless channels (particularly nonbinary and asymmetric channels). We use a random- coset analysis to produce an effect that is similar to output symmetry with binary channels. We show that the random selection of the nonzero elements of the GF(q) parity-check matrix induces a permutation-invariance property on the densities of the decoder messages, which simplifies their analysis and approximation. We generalize several properties, including symmetry and stability from the analysis of binary LDPC codes. We show that under a Gaussian approximation, the entire q-1-dimensional distribution of the vector messages is described by a single scalar parameter (like the distributions of binary LDPC messages). We apply this property to develop extrinsic information transfer (EXIT) charts for our codes. We use appropriately designed signal constellations to obtain substantial shaping gains. Simulation results indicate that our codes outperform multilevel codes at short block lengths. We also present simulation results for the additive white Gaussian noise (AWGN) channel, including results within 0.56 dB of the unrestricted Shannon limit (i.e., not restricted to any signal constellation) at a spectral efficiency of 6 bits/s/Hz.     

On performance bounds for space-time codes on fading channels

We evaluate truncated union bounds on the frame-error rate (FER) performance of space-time (ST) codes operating over the quasi-static fading channel and compare them with computer simulation results. We consider both ST trellis and block codes. We make the following contributions. For the case of ST trellis codes, we develop a general method, which we denote as measure spectrum analysis, that characterizes ST codeword differences and accommodates the combined influences of the ST code and channel scenario. We propose a numerical bounding method that converges in the measure spectrum to within a very small fraction of a decibel to the simulated FER over the full range of signal-to-noise ratio. In addition, we demonstrate the existence of dominant quasi-static fading error events and detail a method for predicting them. Using only this set of dominant measure spectrum elements, very rapid and tight numerical estimation of FER performance is attained.     

On the performance of rate 1/2 convolutional codes with QPSK onRician fading channels

Consideration is given to the bit error probability performance of rate 1/2 convolutional codes in conjunction with quaternary phase shift keying (QPSK) modulation and maximum-likelihood Viterbi decoding on fully interleaved Rician fading channels. Applying the generating function union bounding approach, an asymptotically tight analytic upper bound on the bit error probability performance is developed under the assumption of using the Viterbi decoder with perfect fading amplitude measurement. Bit error probability performance of constraint length K=3-7 codes with QPSK is numerically evaluated using the developed bound. Tightness of the bound is examined by means of computer simulation. The influence of perfect amplitude measurement on the performance of the Viterbi decoder is observed. A performance comparison with rate 1/2 codes with binary phase shift keying (BPSK) is provided     

Kikuchi approximation method for joint decoding of LDPC codes and partial-response channels

In this letter, we apply the Kikuchi approximation method to the problem of joint decoding of a low-density parity-check code and a partial-response channel. The Kikuchi method is, in general, more powerful than the conventional loopy belief propagation (BP) algorithm, and can produce better approximations to an underlying inference problem. We will first review the Kikuchi approximation method and the generalized BP algorithm, which is an iterative message-passing algorithm based on this method. We will then report simulation results which show that the Kikuchi method outperforms the best conventional iterative method.     

On coded modulation using LDPC convolutional codes

A new construction combining LDPC convolutional codes and multilevel coding/modulation is suggested and analyzed. In the case of QPSK, we demonstrate that it has a better performance than an LDPC convolutional code combined with conventional Gray mapping.     

On the stopping distance of finite geometry LDPC codes

In this letter, the stopping sets and stopping distance of finite geometry LDPC (FG-LDPC) codes are studied. It is known that FG-LDPC codes are majority-logic decodable and a lower bound on the minimum distance can be thus obtained. It is shown in this letter that this lower bound on the minimum distance of FG-LDPC codes is also a lower bound on the stopping distance of FG-LDPC codes, which implies that FG-LDPC codes have considerably large stopping distance. This may explain in one respect why some FG-LDPC codes perform well with iterative decoding in spite of having many cycles of length 4 in their Tanner graphs.     

LDPC码在相干光通信下的性能分析与研究

对于相干光通信系统,相位噪声成为影响系统性能的重要因素之一,并严重影响LDPC码(低密度奇偶校验码)软译码的性能.仿真结果表明,在16QAM调制方式下,500kHz线宽的激光器相位噪声将导致1.5dB的性能损失.为了降低相位噪声的影响,提出了一种基于相位噪声估计值修正LLR(对数似然比信息)的方法.经仿真验证,该LLR修正方法能够挽回0.5dB的译码性能损失.     

On the performance of space-time codes over spatially correlated Rayleigh fading channels

We derive the exact pairwise error probability (PEP) for space-time coding over quasi-static Rayleigh fading channels in the presence of spatial fading correlation. We show that receive correlation always degrades the PEP for all signal-to-noise ratios (SNRs). We quantify the effect of receive correlation by employing the notion of "majorization". We show that the stronger the receive correlation, the worse the PEP for all SNRs. We show that at low SNR, depending on the codes, transmit correlation can either improve or degrade the PEP performance. We show that to guarantee robust performance for arbitrary transmit correlation, the minimum eigenvalue of the codeword pair difference matrix should be maximized among all codeword pairs.     

On the active distances of partial unit memory codes based on LDPC codes

Partial unit memory (PUM) convolutional codes constructed from block codes make it possible to obtain convolutional codes with high correcting properties. An ensemble of binary PUM convolutional codes based on low-density parity-check block codes is introduced. This ensemble is specified by semi-infinite parity-check matrices with partial unit memory. The asymptotic bounds on a free distance and active row distances are derived for codes of the specified ensemble. It is proved that the ensemble codes have the positive slope of active row distances.     

Turbo codes cascaded with high-rate block codes for (O,κ)-constrained channels

We consider several issues in the analysis and design of turbo coded systems for (O, κ) input-constrained channels. These constraints commonly arise in magnetic recording channels. This system is characterized by a high-rate turbo code driving a high-rate (n-1)/n, small-length (O, κ) block code. We discuss the properties of the (O, κ) code that affect its performance on both an additive white Gaussian noise (AWGN) and a precoded dicode channel. We address soft-in soft-out (SISO) decoding of linear and nonlinear (O, κ) codes and show that good (O, κ) codes exist even when d_min=1. For the (O, κ) constrained AWGN channel, we present several rate (n-1)/n block codes that optimally tradeoff bit-error-rate performance with κ. For the precoded dicode channel, we show that the systematic (O, n-1) modulation codes are superior to most other rate (n-1)/n block codes in terms of error-rate performance, and their attractiveness is increased by the fact that they do not contribute any significant complexity to the overall system     

Joint iterative decoding of LDPC codes for channels with memory and erasure noise

This paper investigates the joint iterative decoding of low-density parity-check (LDPC) codes and channels with memory. Sequences of irregular LDPC codes are presented that achieve, under joint iterative decoding, the symmetric information rate of a class of channels with memory and erasure noise. This gives proof, for the first time, that joint iterative decoding can be information rate lossless with respect to maximum-likelihood decoding. These results build on previous capacity-achieving code constructions for the binary erasure channel. A two state intersymbol-interference channel with erasure noise, known as the dicode erasure channel, is used as a concrete example throughout the paper.