High-Speed Recursion Architectures for MAP-Based Turbo Decoders

The maximum a posterior probability (MAP) algorithm has been widely used in Turbo decoding for its outstanding performance. However, it is very challenging to design high-speed MAP decoders because of inherent recursive computations. This paper presents two novel high-speed recursion architectures for MAP-based Turbo decoders. Algorithmic transformation, approximation, and architectural optimization are incorporated in the proposed designs to reduce the critical path. Simulations show that neither of the proposed designs has observable decoding performance loss compared to the true MAP algorithm when applied in Turbo decoding. Synthesis results show that the proposed Radix-2 recursion architecture can achieve comparable processing speed to that of the state-of-the-art recursion (Radix-4) architecture with significantly lower complexity while the proposed Radix-4 architecture is 32% faster than the best existing design     

Turbo Code译码方法的改进

在文章中，首先介绍Turbo码的基本编译码结构和它的译码算法MAP。在此基础上，尝试对MAP算法的循环译码的后向递推的起点以及循环译码结构的最终判决条件根据实际应用情况进行改进。将译码的后向递推的起点定义为译码的前向递推的终点，并且将每一轮译码结果进行加权相加，得到最后系统输出。最后，根据MATLAB仿真的结果论证改进后的算法能减少系统的误码率。     

Turbo码的一种高效改进型MAP译码算法

该文给出了一种改进型最大后验概率(MAP)译码算法用于实现并行级联卷积码(Turbo码)的最优译码。与基于对数域的Log-MAP算法相比较,该文给出的算法不引入对数域,但能够完全消除标准MAP算法在迭代过程中必须进行的大量指数和对数运算。计算机仿真结果表明,这种具有最优纠错性能的改进型MAP算法能够显著减少运行时间,其译码效率甚至优于牺牲了较多纠错性能的最快速的对数域MAP译码算法(Max-Log-MAP)。     

一种基于SOVA的改进的Turbo码译码方案

本文在研究Ｔｕｒｂｏ 码反向ＳＯＶＡ（Ｓｏｆｔ－Ｏｕｔｐｕｔ ＶｉｔｅｒｂｉＡｌｇｏｒｉｔｈｍ ）译码性能的基础上,提出了一种同时利用正向和反向ＳＯＶＡ译码软输出信息的基于ＳＯＶＡ 的改进译码结构及其相应的软输出修正公式。计算机模拟结果表明,所提出的改进方案与传统的ＳＯＶＡ算法相比,其译码性能有明显的改善,并略优于Ｍａｘ－Ｌｏｇ－ＭＡＰ的性能     

Reduced-state variant of optimum MAP equaliser

Although the reduced-state technique has been widely used in Viterbi equalisers, its application to maximum a posteriori probability (MAP) equalisers is not satisfactory because it cannot operate due to the backward recursion of the conventional MAP algorithm. A new kind of MAP algorithm is proposed in which the forward and backward recursions are exactly symmetric. The reduced-state technique can thus be applied to both forward and backward recursions and a gain in performance is achieved over that of conventional reduced-state MAP equalisers at the cost of double the computational overhead     

一种低复杂度双二元卷积Turbo码译码算法

双二元卷积Turbo码（ DB CTC)的非二进制编码使得译码复杂度增加,限制了其在某些实际通信工程中的使用。在最大后验概率（ MAP)译码算法的基础上,提出了一种优化算法,将译码的存储量和计算量降为原来的1/4。仿真结果表明：在不同编码长度和码率的情况下,优化算法与原算法性能相当;在误码率为10-5的条件下,两者的Eb/N0差异同样不大于0.1 dB。     

Modification of the MAP algorithm for memory savings

It is usually assumed that all state metric values are necessary in the maximum a posteriori (MAP) algorithm in order to compute the a posteriori probability (APP) values. This work extends the mathematical derivation of the original MAP algorithm and shows that the log likelihood values can be computed using only partial state metric values. By processing N stages in a trellis concurrently, the proposed algorithm results in savings in the required memory size and leads to a power efficient implementation of the MAP algorithm in channel decoding. The computational complexity analysis for the proposed algorithm is presented. Especially for the N=2 case, we show that the proposed algorithm halves the memory requirement without increasing the computational complexity.     

未知相位信道下 Turbo码编码DPSK信号的联合迭代解调解码

本文提出了未知相位信道下Turbo码编码DPSK信号的联合迭代解调解码算法 .推导了未知相位信道的最大后验概率 (MAP)算法 ,推导表明该MAP算法同样可用前向、后向递推方程来有效实现 .其次 ,采用等效信道的方法将未知相位信道的Turbo码解码问题化为AWGN信道下Turbo码的解码问题 .最后 ,引进了联合迭代解调解码算法 ,可用于Turbo码的解调解码 .模拟表明本文算法可有效用于未知相位信道Turbo码的解码     

An algorithm for calculating the exact bit error probability of a binary linear code over the binary symmetric channel

An efficient algorithm for calculating the ith bit error probability of a binary linear code over the binary symmetric channel (BSC) is presented. It is proved that the exact ith bit error probability of maximum-likelihood (ML) decoding, bounded distance decoding, and symbol-wise maximum a posteriori probability (MAP) decoding can be obtained with time complexity O(n2/sup n-k/), where n and k denote the length and the dimension of the target code. The proposed methods are applicable to any binary linear code with redundancy up to nearly 25-30 bits with a typical personal computer.     

Modified MAP algorithm incorporated with PSA technique for turbocodes in Rayleigh fading channels

A modified MAP algorithm for decoding turbo codes in Rayleigh fading channels is proposed. The algorithm is based on a newly derived transition probability for use in turbo codes incorporated with pilot symbol aided (PSA) techniques. The superior performance of the algorithm is verified via computer simulation     

Symbol-by-symbol MAP demodulation of CPM and PSK signals onRayleigh flat-fading channels

Demodulation using the symbol-by-symbol maximum a posteriori probability (MAP) algorithm is presented. The algorithm is derived for the case of continuous phase modulation (CPM) signals transmitted over Rayleigh flat-fading channels, and a corresponding receiver structure is specified. It is shown that the MAP algorithm requires computing, for each trellis branch, the sum of the products of the weights of all paths through the trellis which pass through that branch, and that this generic computational problem can be solved efficiently by an approach that uses a forward and backward recursion through the trellis. Simulation results are presented which show both the hard and soft decision performance of the MAP receiver to be robust, even in the presence of fade rates of up to 30% of the symbol rate. The application of the receiver concept to phase-shift keying (PSK) signals is also discussed, and then evaluated via simulation. The concept of joint demodulation and decoding using iterative processing techniques is introduced. It is shown that the MAP receiver is well suited for iterative processing applications due to its use of a priori symbol probabilities and its production of optimal soft decisions. Simulation results for the reception of quaternary PSK (QPSK) show that the bit error rate (BER) performance of the iterative MAP receiver can approach that of a receiver operating with perfect knowledge of the fading process     

The max-log list algorithm (MLLA)-a list-sequence decoding algorithm that provides soft-symbol output

We present a soft decoding algorithm for convolutional codes that simultaneously yields soft-sequence output, i.e., list sequence (LS) decoding, and soft-symbol output. The max-log list algorithm (MLLA) introduced in this paper provides near-optimum soft-symbol output equal to that of the max-log maximum a posteriori (MAP) probability algorithm. Simultaneously, the algorithm produces an ordered list containing LS-MAP estimates. The MLLA exists in an optimum and a suboptimum version that are different in that the optimum version produces optimum LS-MAP decoding for arbitrary list lengths, while the suboptimum low-complexity version only provides the MAP, the second-order MAP, and the third-order MAP sequence estimates. For lists with more than three elements, MAP decoding is not guaranteed, but the LS decoding is close to the optimal. It is demonstrated that the suboptimum/optimum MLLA can be used to obtain the combination of soft-symbol and soft-sequence outputs at lower complexity than a previously published algorithm. Furthermore, the suboptimum MLLA is well suited for operation in an iterative list (turbo) decoder, since it is obtained by only minor modifications of the well-known Max-Log-MAP algorithm frequently used for decoding of the component codes of turbo codes. Another potential area of application for the suboptimum/optimum MLLA is joint source-channel LS decoding. Estimates of complexity and memory use, as well as performance evaluations of the suboptimum/optimum MLLA, are provided in this paper.     

On turbo code decoder performance in optical-fiber communication systems with dominating ASE noise

In this paper, we study the effects of different ASE noise models on the performance of turbo code (TC) decoders. A soft-decoding algorithm, the Bahl, Cocke, Jelinek, and Raviv (BCJR) decoding algorithm, is generally used in TC decoders. The BCJR algorithm is a maximum a posteriori probability (MAP) algorithm, and is very sensitive to noise statistics. The Gaussian approximation of ASE noise is widely used in the study of optical-fiber communication systems, and there exist standard TCs for additive white Gaussian noise (AWGN) channels. We show that using a MAP decoding algorithm based on the Gaussian noise assumptions, however, may significantly degrade the TC decoder performance in an optical-fiber channel with non-Gaussian ASE noise. To take full advantage of TC, accurate noise statistics in optical-fiber transmissions should be used in the MAP decoding algorithm.     

基于SCCC结构非相干MAP译码的简化算法

差分编码和序列译码相结合是实现高性能非相干解调的主要方式。对采用差分编码的SCCC结构进行非相干译码,其性能近乎于相干解调,但在估计信道转移概率时引入了修正的零阶贝塞尔函数,因此译码复杂度过高,不利于工程实现。针对该问题,该文提出了两种基于SCCC结构的非相干MAP译码的简化算法。该算法利用对贝塞尔函数的近似式,简化了内码译码log-MAP算法中分支度量的计算。理论分析和仿真结果表明,简化后的算法在保证译码性能的前提下,显著地减小了译码复杂度。     

一种高速率的重叠复用传输系统及检测译码性能

该文研究了AWGN信道下重叠时分复用系统(OvTDM)及性能;在此基础上,研究了信道编码的OvTDM系统,并给出了最佳的检测译码算法-最大后验概率准则下的软入软出迭代算法。OvTDM系统与同频谱效率的QAM调制相比较,随着频谱效率的提高显示出性能增益。信道编码的OvTDM系统接收端在最大后验概率(MAP)准则下,检测与译码之间传递软信息进行迭代处理。仿真结果表明,软入软出迭代算法充分利用了符号重叠所自然形成的编码约束关系,获得了最大编码增益。     

DPCM picture transmission over noisy channels with the aid of aMarkov model

The problem of DPCM picture transmission over noisy channels is considered. It is well known that DPCM systems are very sensitive to channel errors. The goal in this work is to build robustness against channel errors. Three methods are proposed in this paper and are obtained by modeling the encoded signal as a Markov sequence. First, an optimum method for decoding correlated sequences is derived, and it is shown to require Viterbi decoding. Then, a modified MAP method (MMAP) for Markov sequences is described. A maximal signal-to-noise (MSNR) receiver for DPCM systems is also developed that minimizes the distortion power due to channel errors. The appropriate cost matrix for this receiver is computed. These methods are applied to DPCM picture transmission over noisy channels and are compared with a another method. The SNR graphs, as well as subjective examination of the received pictures, demonstrate that the proposed procedures are quite effective and superior to that method. Among the proposed methods, the MSNR receiver was found to be more effective than the others for a given order of the Markov model. It is observed that the proposed methods are most beneficial for low detail pictures.     

Simple MAP decoding of first-order Reed-Muller and Hamming codes

A maximum a posteriori (MAP) probability decoder of a block code minimizes the probability of error for each transmitted symbol separately. The standard way of implementing MAP decoding of a linear code is the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm, which is based on a trellis representation of the code. The complexity of the BCJR algorithm for the first-order Reed-Muller (RM-1) codes and Hamming codes is proportional to n/sup 2/, where n is the code's length. In this correspondence, we present new MAP decoding algorithms for binary and nonbinary RM-1 and Hamming codes. The proposed algorithms have complexities proportional to q/sup 2/n log/sub q/n, where q is the alphabet size. In particular, for the binary codes this yields complexity of order n log n.     

CPM调制的迭代检测技术

CPM信号具有包络恒定、峰均比小、功率利用率高的优点。针对CPM信号的特征,比较了最大似然序列检测Viterbi算法和逐符号的最大后验概率(MAP)解调算法的特点,重点研究了使用迭代检测技术进行软输入输出解调及译码的MAP解调方法。在AWGN信道条件下对CPM全响应和部分响应信号进行了误码性能仿真,结果表明采用相干解调和译码,迭代检测方案可得到较高的编码增益。     

MIMO-OFDM系统中基于迭代MAP算法的RLS信道估计

该文提出了一种适用于MIMO-OFDM系统的迭代最大后验概率(Iterative-MAP)信道估计算法。接收机利用MAP译码算法中的信息位和校验位软信息,经过非线性映射将信息反馈至信道估计模块,采用递归最小二乘(RLS)自适应滤波算法对信道时变状态参数进行跟踪,提高了信道估计的精度。仿真结果表明,该方法与最小二乘(LS)算法相比,估计的均方误差(MSE)和误帧率(FER)性能都有较大改善。     

MAP decoding in channels with memory

The expectation-maximization (EM) algorithm is popular in estimating the parameters of various statistical models. We consider applications of the EM algorithm to the maximum a posteriori (MAP) sequence decoding assuming that sources and channels are described by hidden Markov models (HMMs). The HMMs can accurately approximate a large variety of communication channels with memory and, in particular, wireless fading channels with noise. The direct maximization of the a posteriori probability (APP) is too complex. The EM algorithm allows us to obtain the MAP sequence estimation iteratively. Since each step of the EM algorithm increases the APP, the algorithm can improve the performance of any decoding procedure