On reverse concatenation and soft decoding algorithms for PRMLmagnetic recording channels

High-density magnetic recording systems require increasingly sophisticated signal processing techniques. In magnetic recording channels, the information bits are encoded by the concatenation of an outer nonbinary error correcting code (ECC) and an inner line code. Furthermore, the high intersymbol interference that characterizes the channel is controlled by “partial response” equalization. This paper presents a study on a better-integrated decoding procedure between the inner and outer codes. Inversion of the concatenated codes (reverse concatenation) allows the direct mapping of soft information from the partial response channel to the outer ECC. A simplified soft decoding technique, based on the use of erasures, is applied to two typical magnetic recording systems. Performance curves are obtained by an analysis of the distributions of the reliability measures associated with incorrect and correct symbols     

LMMSE channel estimation with soft statistics for turbo-MIMO receivers

Channel estimation techniques for turbo multipleinput multiple-output receivers are addressed, which exploit a priori information to refine the poor performance of initial channel estimates solely using training symbols. We study linear minimum mean squared error channel estimation (LMMSE-CE) using second-order soft statistics to incorporate the degree of decoding reliability. Utilizing this additional information effectively minimizes the error propagation which the maximum likelihood based expectation maximization channel estimation (ML-CE) suffers. The LMMSE-CE provides a smaller mean square error of channel estimation and block error rate than the ML-CE.     

一种频选衰落信道下的Turbo多用户检测算法

联合MAP多用户检测与信道解码的迭代多用户检测(MUD)技术可显著提高宽带移动CDMA系统的容量和性能.在多径时变衰落的编码信道下,提出一种迭代实现干扰抑制、符号估计、信道解码的Turbo多用户检测算法.在每次迭代中,MUD自适应地实现干扰抑制并输出符号估计的软信息,软输入软输出的信道解码器使用LOG MAP方法实现信道解码并反馈符号估计的软信息作为下一次TurboMUD迭代的先验信息.仿真结果证实了该算法在频选衰落信道下经两次迭代就能逼近单用户编码CDMA系统的接收性能.     

Unified design of iterative receivers using factor graphs

Iterative algorithms are an attractive approach to approximating optimal, but high-complexity, joint channel estimation and decoding receivers for communication systems. We present a unified approach based on factor graphs for deriving iterative message-passing receiver algorithms for channel estimation and decoding. For many common channels, it is easy to find simple graphical models that lead directly to implementable algorithms. Canonical distributions provide a new, general framework for handling continuous variables. Example receiver designs for Rayleigh fading channels with block or Markov memory, and multipath fading channels with fixed unknown coefficients illustrate the effectiveness of our approach     

基于CHASE译码思想的PCMA信号盲分离算法

在软输出逐幸存路径处理（SOVA-PSP）算法的基础上,提出了基于Chase译码思想的载波成对复用多址（PCMA）信号的盲分离算法。该算法对SOVA-PSP软输出的结果进行可靠性排序,对于排序中可靠性较低的混合符号进行信号重构,通过重构信号和接收信号之间的欧式距离对比纠正其中的错误结果。仿真结果表明,所提算法与SOVA-PSP算法相比,性能有2 dB左右的增益。     

A note on soft decision decoding with successive erasures (Corresp.)

This paper deals with soft decision as a means to bridge the gap in performance between a receiver using hard decision symbol estimation followed by an algebraic decoder and a maximum-likelihood receiver. A measure of the reliability of the code symbol estimates is introduced to facilitate the decoding process. The decoding operation studied erases the least reliable received symbols and then applies an algorithm capable of correcting errors and erasures. This procedure, termed successive-erasure decoding (SED), was introduced by G. D. Forney in connection with general minimum-distance decoding (GMD). It is studied for binary and nonbinary transmission using polyphase signals on the additive white Gaussian noise (AWGN) channel. The exponential behavior of the error probability at high signal-to-noise ratio (SNR) is calculated and is supplemented by computer simulations. The results indicate that soft decision by successive erasures for binary transmission has properties not present in the nonbinary case. In the binary case the procedure is asymptotically optimum for increasing SNR's. On the nonbinary channel, however, the procedure is only capable of bridging part of the gap in performance between maximum-likelihood decoding (MLD) and hard decision decoding (HDD).     

宽范围的码辅助载波恢复算法

码辅助同步算法将译码软信息引入到同步参数的估计过程,能够在更低的信噪比区间有效实现载波同步,但是这类算法存在同步范围小、复杂度高的问题。首先针对判决可靠性较高的符号,定义一种新的评价函数,用其最大值对应的参数粗估计值补偿信号;然后利用后验均值对补偿后的信号去调制,再分别采用改进的自相关函数方法和最大似然方法来纠正剩余的频偏和相偏,进而有效实现载波恢复。仿真结果表明,该算法能够以较少的计算复杂度为代价,大幅提高同步范围,可获得近似理想同步条件下的译码性能。      

First-order approximation of the ordered binary-symmetric channel

Soft-decision decoding algorithms of binary linear block codes require reordering of the received symbols within each block in decreasing reliability. Efficient decoding algorithms based on reordering have been devised. This paper presents different results related to the ordering of a sequence of N received symbols with respect to their reliability measure, for BPSK transmission over the AWGN channel model. First, a tight approximation of Pe(i; N), the probability that the hard decision associated with the ith symbol of the ordered sequence is in error, is derived. Then, it is shown that despite the fact that the random variables representing the noise at positions n₁, n₂,...,n_j of the ordering are no longer independent, the events of having a hard decision decoding error at these positions remain almost independent. Pe(n₁,n₂ ,...,n_j; N), the probability that the hard decisions associated with the symbols at positions n₁, n₂,...n_j in the ordered sequence are in error, is thus well approximated from each of the Pe (n_i; N), for i∈[1,j]. Finally, based on the independence of these events, the fully connected 2^N-state BSC representing the channel after ordering is simplified by N independent time-shared 2-state BSCss. This new model allows one to easily and tightly approximate the capacity of the channel after ordering     

List and soft symbol output Viterbi algorithms: extensions andcomparisons

The Viterbi algorithm (VA) is the maximum likelihood decoding algorithm for convolutionally encoded data. Improvements in the performance of a concatenated coding system that uses VA decoding (inner decoder) can be obtained when, in addition to the standard VA output, an indicator of the reliability of the VA decision is delivered to the outer stage of processing. Two different approaches of extending the VA are considered. In the first approach, the VA is extended with a soft output (SOVA) unit that calculates reliability values for each of the decoded output information symbols. In the second approach, coding gains are obtained by delivering a list of the L best estimates of the transmitted data sequence, namely the list Viterbi decoding algorithm (LVA). Our main interest is to evaluate the LVA and the SOVA in comparison with each other, determine suitable applications for both algorithms and to construct extended versions of the LVA and the SOVA with low complexity that perform the task of the other algorithm. We define a list output VA using the output symbol reliability information of the SOVA to generate a list of size L and that also has a lower complexity than the regular LVA for a long list size. We evaluate the list-SOVA in comparison to the LVA. Further, we introduce a low complexity soft symbol output viterbi algorithm that accepts the (short) list output of the LVA and calculates for each of the decoded information bits a reliability value. The complexity and the performance of the soft-LVA (LVA and soft decoding unit) is a function of the list size L. The performance of the soft-LVA and the SOVA are compared in a concatenated coding system. A new software implementation of the iterative serial version of the LVA is also included     

基于Polar码的速率兼容调制方案设计

提出了一种基于Polar码的速率兼容调制（rate compatible modulation,RCM）联合设计方案,用于提高无线通信频谱利用率.相应地设计了基于置信度传播（belief propagation,BP）和软抵消（soft cancellation,SCAN）的接收端高效联合迭代译码算法.根据该算法可通过优化变量节点对数似然比（log-likelihood ratio,LLR）信息迭代方式以及采用限制译码符号上限的改进措施,提高译码过程的稳定性与时效性.与距离优化的级联低密度奇偶校验（low-density parity-check codes,LDPC）码RCM方案对比结果表明,提出的高效联合迭代译码算法在低信噪比（signal noise ratio,SNR）下有更低的译码复杂度,并且具有更优的吞吐量和误码率性能.因此,本文所提方案适合在恶劣信道条件下的无线传输.     

一种新的缩短RS码迭代译码方案

为了在EPON中应用GF(256)标准RS码对信息帧长大于255位的信息流进行编码,并提高RS码的编码增益,提出了一种新的缩短RS码的编译码方案。该方案通过两个缩短RS码的交叠编码和互相迭代译码,可以提高编译码增益。RS码BM硬判决译码和chase软判决译码的计算机仿真表明,该方案对缩短RS码的软硬判决译码性能都有明显提高。     

Iterative channel estimation and decoding for convolutionally codedanti-jam FH signals

An iterative algorithm for joint decoding and channel estimation in frequency-hopping (FH) networks is proposed. In the proposed algorithm, soft decoder outputs are used in the iterative estimation of the time-varying variance of the additive interference resulting from the sum of the thermal noise, partial-band noise jamming, and other-user interference. The soft outputs are also used in the estimation of the independent random carrier phases and multiplicative Rayleigh fading coefficients in different frequency dwells. The estimation process is further enhanced through the insertion of known symbols in the transmitted data stream. The proposed iterative symbol-aided demodulation scheme is compared with the coherent scenario, where the channel state information is assumed to be known a priori at the receiver, for both convolutionally coded and turbo coded FH systems. The proposed iterative channel estimation approach is suited for slow FH systems where the channel dynamics are much slower than the hopping rate. This observation motivates the consideration of another robust approach for generating the log-likelihood ratios for fast hopping systems in additive white Gaussian noise channels. Simulation results that demonstrate the excellent performance of the proposed algorithms in various scenarios are also presented     

Pattern-Flipping Chase-Type Decoders with Error Pattern Extracting Viterbi Algorithm over Partial Response Channels

Towards the goal of achieving better error correction performance in data storage systems, iterative soft decoding of low density parity check (LDPC) codes and soft-decision decoding of Reed-Solomon (RS) codes have started receiving increasing research attention. However, even with increased computing power, complexities of soft-decision decoding algorithms are still too high for real products which require high throughput and small hardware area. Another problem is that the performance gains of those approaches are smaller for magnetic recording channels than they are for memoryless additive white Gaussian noise (AWGN) channels. We propose a new soft-decision decoding algorithm (based on the Chase algorithm), which takes advantage of pattern reliability instead of symbol reliability or bit reliability. We also present a modified Viterbi algorithm that provides probable error patterns with corresponding reliabilities. Simulation results of the proposed algorithms over the partial response (PR) channel show attractive performance gains. The proposed algorithm dramatically reduces the number of iterations compared to the conventional Chase2 algorithm over the PR channel.     

SFBC-OFDM系统中联合迭代信道估计与空频解码算法

提出了一种基于SFBC-OFDM系统的联合迭代信道估计与空频解码算法。首先为提高初始信道估计器的性能,提出了一种基于时频变换(TFT)的信道估计算法;其次提出了利用信道估计值与解码符号进行联合迭代信道估计与空频解码算法。分析与仿真结果显示,在准静态、快时变以及相关信道条件下,新的联合迭代信道估计与空频解码算法都有效地提高了系统性能。     

Soft decision metric generation for QAM with channel estimation error

The channel code bit log likelihood ratio (LLR) for soft decision decoding is derived for quadrature amplitude modulated signals (QAM). The effect of imperfect channel knowledge on soft decision decoding performance is studied. Our results indicate this effect increases with channel estimation error and/or QAM modulation level. A metric based on generalized log likelihood ratio (GLLR) is derived for soft decision channel decoding with imperfect channel knowledge. Numerical results show that the GLLR-based metric outperforms the conventional minimum distance decoding metric that does not take into account channel estimation error.     

Tail Extrapolation in MLSE Receivers Using Nonparametric Channel Model Estimation

This paper presents a method for determining the probability of rare events, in particular for probability density function (pdf) and bit error rate (BER) estimation. The derivation of the method is based on the presumption that the pdf is a member of a family of distributions very often named as the generalized exponential (GE) class of distributions. Based on high reliability estimations obtained in short simulation/measurement times, the low probably events are estimated accurately by extrapolation. The suggested method can be applied to some distributions that are different from GE distributions, such as noncentral chi-square distributions, to extrapolate to low probability events, with some extrapolation error. It can also be applied to BER estimation. The method is in particular helpful for estimating channels suffering from both severe signal distortion causing undesired intersymbol interference (ISI) of several symbols, and from severe noise. Such conditions prevail, for example, in metro and long haul high-speed optical fiber communication systems. So the method may be implemented in particular in maximum-likelihood sequence estimation (MLSE) optical receivers using nonparametric channel model estimation. A special use of the extrapolation method is explained for practical systems using trellis branch metrics derived from the estimated pdf to decode the transmitted sequence of symbols.     

一种基于分散导频块的频偏估计新算法

针对短突发信号解调的需要,提出了一种基于分散导频块的频偏估计新算法。区别于以往基于连续导频的频偏估计算法,该算法除利用了导频本身已知信息外,还充分利用了导频的位置信息。在相同的帧效率下,相比于基于连续导频的频偏估计算法,该算法可以获得更好的估计性能。理论分析和仿真结果都表明,该算法在其无偏估计范围内估计性能达到了相应帧结构下的克拉美罗界。     

EM‐based iterative receiver for coded MIMO systems in unknown spatially correlated noise

We present iterative channel estimation and decoding schemes for multi‐input multi‐output (MIMO) Rayleigh block fading channels in spatially correlated noise. An expectation‐maximization (EM) algorithm is utilized to find the maximum likelihood (ML) estimates of the channel and spatial noise covariance matrices, and to compute soft information of coded symbols which is sent to an error‐control decoder. The extrinsic information produced by the decoder is then used to refine channel estimation. Several iterations are performed between the above channel estimation and decoding steps. We derive modified Cramer–Rao Bound (MCRB) for the unknown channel and noise parameters, and show that the proposed EM‐based channel estimation scheme achieves the MCRB at medium and high SNRs. For a bit error rate of 10⁻⁶ and long frame length, there is negligible performance difference between the proposed scheme and the ideal coherent detector that utilizes the true channel and noise covariance matrices. Copyright © 2006 John Wiley & Sons, Ltd.     

Soft Decoding Assisted SNR Estimation Under Block Fading Channels for Orthogonal Modulations

The performance of the coded orthogonal modulation (OM) system under slow fading channels heavily depends on the estimation of the signal-to-noise ratio (SNR), including the fading amplitude and the noise spectral density. However, a relatively long packet of pilot symbols is often required to guarantee the accuracy of the SNR estimation, which makes it impractical in some situations. To address this problem, this paper proposes an iterative SNR estimation algorithm using the soft decoding information based on the expectation-maximization algorithm. In the proposed method, a joint iterative loop between the SNR estimator and decoder is performed, where the extrinsic information generated by the soft decoder is employed to enhance the estimation accuracy and the SNR estimated by the estimator is used to generate the soft information to the decoder. Also, no pilot symbols are needed to estimate the SNR in the proposed estimator. The Cramer–Rao lower bound (CRLB) of fully data-aided (FDA) estimation is derived to works as the final benchmark. The performance of the proposed algorithm is evaluated in terms of the normalized mean square errors (NMSEs) and the bit error rates (BERs) under block fading channels. Simulation results indicate that the NMSE of the proposed estimator reaches the CRLB of the FDA estimator and outperforms that of the approximate ML (ML-A) estimator proposed by Hassan et al. by 4.1 dB. The BER performance of coded OM system with the proposed estimation algorithm is close to the ideal case where the channel fading and the noise spectral density are known at the receiver.     

基于循环检测的LDPC比特翻转译码算法研究

提出一种基于循环检测的低密度奇偶校验码的比特翻转(BF)译码算法,采用对译码翻转比特的循环检测和对接受符号可靠性信息的软判决,使译码性能大大改善.理论分析表明,该译码运算复杂度低,仿真结果表明,改进的算法优于加权比特翻转译码LP-WBF算法约0.3 dB,误码性能改善明显.