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。     

极化码序列连续删除译码算法的改进设计

极化码连续删除译码算法性能和传统的LDPC码存在一定差距。序列连续删除算法(SCL)的提出极大地改善译码性能,是极化码推向实际应用中的重要一步。但是该算法复杂度较高,延迟大。改进的序列连续删除(SCL)译码算法是基于改善极化码码长受限的情况,文中描述SCL算法是通过码树上的搜索序列路径来表示译码过程。改进的算法通过减少译码算法在码树上的序列路径来降低时间和空间复杂度。通过仿真表明,改进的算法有效地降低了译码的复杂度同时在性能上也接近最大似然(ML)译码算法。     

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。     

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.     

一种简化的SOVA算法

软输出维特比(SOVA)算法广泛应用于硬盘读出、连接码和TURBO码.特别是TURBO码,目前已经被采用到第三代通信标准中.在这些应用中,特别是第三代通信终端应用中,虽然对性能有很高的要求,但对价格和功耗的要求更苛刻.降低算法复杂度是降低电路复杂度和功耗的主要手段.本文提出了一种简化的软输出维特比(SOVA)算法,显著减少了算法的复杂度,减少了L×(L-1)次比较运算.提出的算法对SOVA算法的纠错性能没有影响.新算法应用到TURBO码解码器中,纠错性能仅仅比传统的算法相差0.4 dB左右.     

FSO中分层空时编码的误码性能

分层空时编码(BLAST)虽然具有极高的频谱效率,能成倍提高光通信系统的信息传输速率,但BLAST系统的误码率较大,严重影响了光通信系统的可靠性。在描述了湍流信道中多输入多输出(MIMO)系统的信道模型后,针对多进制脉冲位置调制(Q-PPM)技术,推导出了采用线性译码算法时分层空时码的极大似然判决准则及其误码率公式,并比较了最大似然译码算法、线性译码算法、串行干扰消除译码算法的误码性能。最后,利用仿真实验进行了验证。结果表明:在自由空间光通信(FSO)中,串行干扰消除译码算法的误码性能更接近最大似然译码算法的性能,明显优于线性译码算法。在4×4系统中,当误比特率为2×10-2时,相对于最小均方误差(MMSE)译码算法,最大似然译码算法和MMSE-SIC译码算法的信噪比分别改善了约14.5 dB和7 dB。理论分析与实验结果相一致。     

LDPC码的一种高效加权比特翻转译码算法

针对低密度奇偶校验(LDPC)码中加权比特翻转(WBF)译码算法在迭代过程中绝大多数情况都是进行单比特翻转,导致译码效率低并且可能会发生比特翻转"死循环"的现象,提出一种更为高效的加权比特翻转(EWBF)算法.该算法对翻转阈值进行了改进,使得每次迭代能够翻转多个比特,提高译码效率,并且能够避免译码过程出现的翻转"死循环"现象.仿真结果表明,所提译码算法与WBF算法、改进的WBF(MWBF)算法和IMWBF(Improved MWBF)算法相比,平均迭代次数分别降低51.6%~56.2%、49.6%~54.2%和48.1%~51.3%;而在译码性能方面,算法性能接近甚至优于IMWBF算法,当最大迭代次数设定为30次时,相比于IMWBF算法,在误码率为10-4时可获得0.92 dB的增益.     

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     

基于分段循环冗余校验的极化码自适应连续取消列表译码算法

针对极化码连续取消列表(SCL)译码算法为获取较好性能而采用较多的保留路径数,导致译码复杂度较高的缺点,自适应SCL译码算法虽然在高信噪比下降低了一定的计算量,却带来了较高的译码延时。根据极化码的顺序译码结构,该文提出了一种分段循环冗余校验(CRC)与自适应选择保留路径数量相结合的SCL译码算法。仿真结果表明,与传统CRC辅助SCL译码算法、自适应SCL译码算法相比,该算法在码率R=0.5时,低信噪比下(–1 dB)复杂度降低了约21.6%,在高信噪比下(3 dB)复杂度降低了约64%,同时获得较好的译码性能。     

A two-dimensional product code with robust soft-decision decoding

The performance of a relatively simple two-dimensional (2-D) product code is considered. The row code is a short constraint length convolutional code, and the column code is a high-rate block code. Both the rows and columns are decoded with soft-decision maximum likelihood decoding. The soft output Viterbi algorithm (SOVA) is used to decode the rows. In one case, the same decoder may be used for the rows and the columns. It is shown that, depending on the rate of the row code, reliable signaling is achieved within about 1.0 to 1.5 dB of the R₀ limit. Results are given for a particular impulsive noise channel; it is seen that performance is robust over a wide range of channel conditions     

复数域网络编码中最大似然解码算法的改进

针对复数域网络编码中继网络,提出一种改进的中继处的最大似然解码算法。当传统的最大似然解码算法使用在复数域网络编码中继网络中时,计算复杂度会随着信息星座图映射方式的改变而大大增加。为了降低计算复杂度,在前人研究的基础上提出一种改进的最大似然解码算法,该算法利用无线中继网络通信系统的非对称性,在解码时,先进行预判决,然后进行精确判决,这样可以大大降低计算复杂度,提高了系统性能。     

High performance, high throughput turbo/SOVA decoder design

Two efficient approaches are proposed to improve the performance of soft-output Viterbi (1998) algorithm (SOVA)-based turbo decoders. In the first approach, an easily obtainable variable and a simple mapping function are used to compute a target scaling factor to normalize the extrinsic information output from turbo decoders. An extra coding gain of 0.5 dB can be obtained with additive white Gaussian noise channels. This approach does not introduce extra latency and the hardware overhead is negligible. In the second approach, an adaptive upper bound based on the channel reliability is set for computing the metric difference between competing paths. By combining the two approaches, we show that the new SOVA-based turbo decoders can approach maximum a posteriori probability (MAP)-based turbo decoders within 0.1 dB when the target bit-error rate (BER) is moderately low (e.g., BER<10/sup -4/ for 1/2 rate codes). Following this, practical implementation issues are discussed and finite precision simulation results are provided. An area-efficient parallel decoding architecture is presented in this paper as an effective approach to design high-throughput turbo/SOVA decoders. With the efficient parallel architecture, multiple times throughput of a conventional serial decoder can be obtained by increasing the overall hardware by a small percentage. To resolve the problem of multiple memory accesses per cycle for the efficient parallel architecture, a novel two-level hierarchical interleaver architecture is proposed. Simulation results show that the proposed interleaver architecture performs as well as random interleavers, while requiring much less storage of random patterns.     

光通信中基于分组Turbo码的一种改进Chase译码算法

为了适应光通信发展的要求,依据分组Turbo码(BTC)传统Chase译码算法的分析,提出了一种基于不对等可靠位数的改进新译码算法。使用该算法在每次迭代时将产生一个可靠度参数对外部信息进行修正,从而提高BTC的译码性能。仿真结果表明:在误码率(BER)为10-5且迭代4次的情况下,新BTC译码算法与传统Chase译码算法相比,其净编码增益(NCG)提高了0.9dB,并且在最差情况下给系统增加的译码复杂度都不大。     

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...     

Combined simplified maximum likelihood and sphere decoding algorithm for MIMO system

In this article, a new system model for sphere decoding （SD） algorithm is introduced. For the 2 × 2 multipleinput multiple-out （MIMO） system, a simplified maximum likelihood （SML） decoding algorithm is proposed based on the new model. The SML algorithm achieves optimal maximum likelihood （ML） performance, and drastically reduces the complexity as compared to the conventional SD algorithm. The improved algorithm is presented by combining the sphere decoding algorithm based on Schnorr-Euchner strategy （SE-SD） with the SML algorithm when the number of transmit antennas exceeds 2. Compared to conventional SD, the proposed algorithm has low complexity especially at low signal to noise ratio （SNR）. It is shown by simulation that the proposed algorithm has performance very close to conventional SD.     

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.     

A novel BTC decoding algorithm based on the genetic algorithm in optical communication systems

Combining the advantages of both the genetic algorithm （GA） and the chase decoding algorithm, a novel improved decoding algorithm of the block turbo code （BTC） with lower computation complexity and more rapid decoding speed is proposed in order to meet the developing demands of optical communication systems. Compared with the traditional chase decoding algorithm, the computation complexity can be reduced and the decoding speed can be accelerated by applying the novel algorithm. The simulation results show that the net coding gain （NCG） of the novel BTC decoding algorithm is 1.1 dB more than that of the traditional chase decoding algorithm at the bit error rate （BER） of 10^-6. Therefore, the novel decoding algorithm has better decoding correction-error performance and is suitable for the BTC in optical communication systems.     

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.     

适于匙孔信道的准正交极化空时分组码及性能分析

构建了一种适于匙孔信道的满码率极化准正交空时分组码以改善其误比特率性能,采用快速最大似然译码算法进行译码,并与匙孔信道的传统准正交空时分组码、单中继瑞利信道和单中继匙孔信道的极化准正交空时分组码分别进行误比特率的仿真和比较.结果表明:在相同SNR条件下,本文构建的分组码比传统准正交分组码具有更低的误比特率;与两种单中继极化准正交空时分组码相比,在SNR较高情况下本文分组码具有更好的性能.