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     

基于改进型SOVA的Turbo译码

第三代移动通信系统IMT-2000的高速率业务倾向于选择Turbo码,这就要求采用低时延、低复杂度的迭代译码技术,主要是软输出Viterbi算法(SOVA)和Max-Log-MAP算法.在先验等概和无限译码深度条件下,已证明略加修改的SOVA等效于Max-Log-MAP算法.由于在迭代译码中,先验概率须不断更新,本文证明了在存在先验概率的条件下改进型SOVA与Max-Log-MAP也是等效的,并讨论了有限译码深度限制下改进型SOVA与滑动窗口Max-Log-MAP算法的等效性.     

Non‐binary SOVA algorithms for decoding of block codes on a sectionalized trellis

In this paper, we explore computationally efficient implementations of the soft output viterbi algorithm (SOVA) applied to Soft‐Input Soft‐Output (SISO) decoding of linear block codes. In order to simplify the trellis‐based decoding of binary block codes with SOVA, we use the technique of sectionalization of the trellis, which has been successfully applied to the simplification of the MAP and Max‐Log‐MAP algorithms. Due to the branch complexity of the sectionalized trellis, we define a generalization of a non‐binary version of SOVA. However, the computational complexity of directly applying this approach remains too high for efficient implementation; we thus introduce the concept of non‐binary SOVA (NSOVA) with propagation of bit‐level reliabilities (BLR). This new algorithm is analyzed from a computational complexity viewpoint. Both serial and parallel implementations are explored. Finally, optimal sectionalizations are derived for selected codes; since the normal SOVA decoding is a particular case of NSOVA with BLR, we show that our approach is more efficient than a bit‐level trellis by showing that, for all the codes tested, the optimal trellis is a sectionalized one. Copyright © 2007 John Wiley & Sons, Ltd.     

Turbo码的一种全新的SOVA译码算法

SOVA算法因其译码时延低于MAP算法已成为Turbo码的实用译码算法。本文提出了一种放弃软判决值更新处理的全新的SOVA算法。该算法的独到之处在于,综合利用对栅格图的正向和反向搜索,从而实现了通过全局路径比较来产生软输出值。仿真结果表明,与传统SOVA算法相比这种全新的SOVA算法在不会明显增加译码计算量的前提下,显著地改善了译码性能。同时,其误码率性能在高信噪比时略优于Max-Log-MAP算法,并且已经逼近MAP算法。     

Complexity Reduction in SISO Decoding of Block Codes

SISO decoding for block codes can be carried out based on a trellis representation of the code. However, the complexity entailed by such decoding is most often prohibitive and thus prevents practical implementation. This paper examines a new decoding scheme based on the soft-output Viterbi algorithm (SOVA) applied to a sectionalized trellis for linear block codes. The computational complexities of the new SOVA decoder and of the conventional SOVA decoder, based on a bit-level trellis, are theoretically analyzed and derived for different linear block codes. These results are used to obtain optimum sectionalizations of a trellis for SOVA. For comparisons, the optimum sectionalizations for Maximum A Posteriori (MAP) and Maximum Logarithm MAP (Max-Log-MAP) algorithms, and their corresponding computational complexities are included. The results confirm that the new SOVA decoder is the most computationally efficient SISO decoder, in comparisons to MAP and Max-Log-MAP algorithms. The simulation results of the bit error rate (BER) performance, assuming binary phase -- shift keying (BPSK) and additive white Gaussian noise (AWGN) channel, demonstrate that the performance of the new decoding scheme is not degraded. The BER performance of iterative SOVA decoding of serially concatenated block codes shows no difference in the quality of the soft outputs of the new decoding scheme and of the conventional SOVA.     

On the equivalence between SOVA and max-log-MAP decodings

It is shown that after a proper simple modification, the soft-output Viterbi algorithm (SOVA) proposed by Hagenauer and Hoeher (1989) becomes equivalent to the max-log-maximum a posteriori (MAP) decoding algorithm. Consequently, this modified SOVA allows to implement the max-log-MAP decoding algorithm by simply adjusting the conventional Viterbi algorithm. Hence, it provides an attractive solution to achieve low-complexity near-optimum soft-input soft-output decoding     

Turbo码SOVA译码的一种新的改进算法

SOVA算法由于低复杂度和低译码延时,已成为Turbo码的实用译码算法。该文针对SOVA译码算法的软判决值不精确对译码性能的影响,借鉴非均匀量化思想,提出了一种新的改进算法。仿真结果表明,在几乎不增加译码复杂度的情况下能够明显地改善译码性能。     

等价于MAP的SOVA译码方法

不同于MAP(Maximum A Posteriori)算法,SOVA(Soft-Output Viterbi Algorithm)算法的软输出不是真正意义上的后验概率,很少有文献给出SOVA算法的完整数学解释。该文给出了一种完整的SOVA的数学表达形式,并从SOVA的数学表达出发推导出了两种等价于MAP,具有SOVA形式的译码方法,一种是Li等人(1995)给出的适用于连续传输的最佳软输出算法(Optimal Soft output Algorithm, OSA);后一种是对OSA算法的改进,后者可以得到与前者等价的软输出,但是降低了运算复杂度。     

低莱斯因子衰落信道下的Turbo码性能研究

基于Turbo码编译码技术,在Rician衰落信道模型下,详细研究了Turbo码Log-MAP译码算法和SOVA译码算法在低Rician因子衰落信道下的性能,并结合调制技术对整个编译码系统进行Matlab仿真。仿真结果表明,在低Rician因子信道下,Log-MAP译码算法的性能优于SOVA译码算法。     

New Soft Output Viterbi Algorithm for Mobile Communication System

Soft output Viterbi algorithm(SOVA) is a turbo decoding algorithm that is suitable for hardware implementation. But its performance is not so good as maximum a posterior probability(MAP) algorithm. So it is very important to improve its performance. The non-correlation between minimum and maximum likelihood paths in SOVA is analyzed. The metric difference of both likelihood paths is used as iterative soft information, which is not the same as the traditional SOVA. The performance of the proposed SOVA is demonstrated by the simulations. For 1024-bit frame size and 9 iterations with signal to noise ratio from 1dB to 4dB, the experimental results show that the new SOVA algorithm obtains about more 0.4dB and 0.2dB coding gains more than the traditional SOVA and Bi-SOVA algorithms at bit error rate(BER) of 1×10~ -4 , while the latency is only half of the Bi-direction SOVA decoding.     

Two step SOVA-based decoding algorithm for tailbiting codes

In this work we propose a novel decoding algorithm for tailbiting convolutional codes and evaluate its performance over different channels. The proposed method consists on a fixed two-step Viterbi decoding of the received data. In the first step, an estimation of the most likely state is performed based on a SOVA decoding. The second step consists of a conventional Viterbi decoding that employs the state estimated in the previous step as the initial and final states of the trellis. Simulations results show a performance close to that of maximum-likelihood decoding.     

一种新的基-4SOVA译码算法

SOVA (Soft Output Viterbi Algorithm)类算法因其译码时延远低于MAP类算法已成为Turbo码的实用译码算法,为了进一步减小译码延迟,提高译码速度,该文在简单分析基-4Max-Log-MAP算法的基础上,提出了一种新的基-4SOVA算法,并进行了完整的数学推导.该算法的关键是提出了一种新...     

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     

SOVA算法对Viterbi算法的修正

在Viterbi算法中引入软值进行修正之后的算法称作SOVA算法(Soft Output Viterbi Algorithm)。SOVA算法在Viterbi算法的基础上,路径量度引入了比特先验信息,对每位译码比特以后验概率似然比的形式提供软输出,因而可提供更高的译码性能。特别,SOVA算法可用于级联码的迭代译码,采用Tuobo原理使不同分量码之间交换软信息,从而可显著提高这类码的纠错能力。     

A simple remedy for the exaggerated extrinsic information produced by the SOVA algorithm

In this paper, we propose a novel and simple approach for dealing with the exaggerated extrinsic information produced by the soft-output Viterbi algorithm (SOVA). The proposed remedy is based on mathematical analysis and it involves using two attenuators, one applied to the immediate output of the SOVA and another applied to the extrinsic information before it is passed to the other decoder (assuming iterative decoding). The use of these attenuators aims at reducing the inherent strong correlation between the intrinsic information (input to the SOVA) and extrinsic information (output of the SOVA). We examine the modified SOVA (MSOVA) on additive white Gaussian noise (AWGN) and flat fading channels for parallel concatenated codes (PCCs) and serial concatenated codes (SCCs). We show that the MSOVA provides substantial performance improvements over both channels. For example, it provides improvements of about 0.8 to 1.0 dB at P/sub b/ = 10/sup -5/ in AWGN, and about 1.4 to 2.0 dB at P/sub b/ = 10/sup -5/ on fading channels. We also show that there are cases where the MSOVA is superior to the a posteriori probability (APP) algorithm. With this motivation, we extend the proposed modification to the APP algorithm with favorable results. We demonstrate that the modified APP (MAPP) provides performance improvements between 0.3 to 0.6 dB at P/sub b/ = 10/sup -5/ relative to the APP. We lastly mention that the proposed modifications, while they provide considerable performance improvements, keep the complexity of these decoders almost the same, which is remarkable.     

Turbo译码器在数据协调中的应用与仿真

Turbo码以其几乎接近Shannon理论极限的译码性能而成为目前为止最好的信道编码方案。为了减少信道传输引起的误码,提高传输可靠性,设计了一种基于SOVA算法的Turbo译码器,并介绍了Turbo译码器在数据协调中的应用。与传统的Turbo译码器相比,增加了两个权重模块,这样可提高译码的性能。同时,通过Matlab仿真,验证了所设计的Turbo译码器功能的正确性。     

Performance of parallel and serial concatenated codes on fading channels

The performance of parallel and serial concatenated codes on frequency-nonselective fading channels is considered. The analytical average upper bounds of the code performance over Rician channels with independent fading are derived. Furthermore, the log-likelihood ratios and extrinsic information for maximum a posteriori (MAP) probability and soft-output Viterbi algorithm (SOVA) decoding methods on fading channels are developed. The derived upper bounds are evaluated and compared to the simulated bit-error rates over independent fading channels. The performance of parallel and serial codes with MAP and SOVA iterative decoding methods, with and without channel state information, is evaluated by simulation over independent and correlated fading channels. It is shown that, on correlated fading channels, the serial concatenated codes perform better than parallel concatenated codes. Furthermore, it has been demonstrated that the SOVA decoder has almost the same performance as the MAP decoder if ideal channel state information is used on correlated Rayleigh fading channels.     

MAP算法在Turbo码译码中的应用和研究进展

对Turbo码译码算法进行了综述,包括SOVA、MAP、LOG-MAP、MAX-LOG-MAP等算法,并对这几种算法进行了比较。同时根据近年来对Turbo码译码算法的研究,对几种新的译码算法进行了介绍和讨论。     

Truncated Turbo Decoding with Reduced Computational Complexity

The concept of concatenated codes and turbo decoding is well known and leads to a remarkably good performance in many applications. The resulting signal processing for this concept shows high complexity relative to conventional Viterbi decoding. This paper, therefore, considers an alternative concept of turbo decoding to reduce the computational complexity. In thiscase, those sections of the sequence to be decoded, where changes of bit decisions (compared to the previous iteration step) are very unlikely,are excluded from the soft-output viterbi algorithm (SOVA). This decoding is much easier to process and the loss of bit error rate (BER) performance isquite small or even negligible in comparison to conventional turbo decoding.     

一种性能优越的Turbo码SOVA译码算法

MAP译码算法性能上是最优的,但是其复杂度也是十分高的,影响了硬件的实现,介绍了一种性能上接近于MAP译码算法,复杂度上有明显减少的译码算法,并且对其进行了完善,仿真结果表明对于二进制Turbo码,改进后的译码算法与MAP算法的译码性能更为接近。