A coded ARQ scheme with the generalized Viterbi algorithm

A coded automatic repeat request (ARQ) scheme based on a generalized Viterbi decoding algorithm is proposed. The scheme utilizes the error propagation, which is commonly observed in reduced-complexity decoding, as a means of error detection. It is shown that a small undetectable error probability is obtained with a small retransmission probability for a discrete memoryless channel, contrary to the conventional convolutionally coded ARQ schemes with Viterbi decoding where a compromise between the retransmission probability and the undetectable error probability must be reached     

Error probability for repeat request systems with convolutionalcodes

A new decoding algorithm based on the modified Viterbi algorithm for repeat request systems is considered. A new asymptotic error probability bound is derived. It is shown that the error exponent for convolutional coding can be related to the exponent for block coding by a graphical method known as inverse concatenation construction     

相关跳频序列的Viterbi译码算法及其纠错性能分析

该文分析了相关跳频通信系统中频率转移函数的纠错性能,将Viterbi算法应用于接收端跳变频点序列的译码,并结合相关跳频转移函数的特点对译码过程作出了改进.针对满足最大相关纠错性能的频率转移函数,详细分析了Viterbi算法的译码性能.仿真结果表明,通过相关纠错,对随机错误在低信噪比条件下可以获得5-8dB的增益.     

一种M-FSK信号的能量度量Viterbi软译码算法性能分析

Viterbi译码算法广泛应用于无线数字通信系统,一般采用比特对数似然信息(LLR)作为译码器的输入。针对M-FSK信号,该文提出一种采用信号解调得到的M维能量信息,直接作为译码器分支度量值,并给出了相应的Viterbi译码算法。在加性高斯白噪声(AWGN)和瑞利(Rayleigh)衰落信道下对所提算法的BER性能进行了理论推导,得到了闭合表达式。通过仿真验证了理论推导的正确性,与常规Viterbi算法相比,所提算法避免了比特LLR和分支度量值的计算,降低了算法复杂度和减少了信息损失,提高了M-FSK信号软解调Viterbi译码算法的BER性能,是一种更适用于工程实现的M-FSK信号的Viterbi译码算法。     

基于GPU的Viterbi并行解码算法的设计与实现

针对GPU并行计算特征,对Viterbi解码自身做了并行处理探索,并提出使用Zero-Termination卷积码来实现基于GPU的Viterbi解码分块并行处理.设计的实现结果表明:Zero-Termination卷积码的简单而适用于GPU分块并行;误码率降低,特别是在信噪比低的情况下,Zero-Termination卷积码误码率比不损失码率的卷积码要低.同时,还实现了基于GPU的7,9,15三种不同约束长度的Viterbi解码,获得了良好的误码性能曲线及高吞吐率表现.     

Two decoding algorithms for tailbiting codes

The paper presents two efficient Viterbi decoding-based suboptimal algorithms for tailbiting codes. The first algorithm, the wrap-around Viterbi algorithm (WAVA), falls into the circular decoding category. It processes the tailbiting trellis iteratively, explores the initial state of the transmitted sequence through continuous Viterbi decoding, and improves the decoding decision with iterations. A sufficient condition for the decision to be optimal is derived. For long tailbiting codes, the WAVA gives essentially optimal performance with about one round of Viterbi trial. For short- and medium-length tailbiting codes, simulations show that the WAVA achieves closer-to-optimum performance with fewer decoding stages compared with the other suboptimal circular decoding algorithms. The second algorithm, the bidirectional Viterbi algorithm (BVA), employs two wrap-around Viterbi decoders to process the tailbiting trellis from both ends in opposite directions. The surviving paths from the two decoders are combined to form composite paths once the decoders meet in the middle of the trellis. The composite paths at each stage thereafter serve as candidates for decision update. The bidirectional process improves the error performance and shortens the decoding latency of unidirectional decoding with additional storage and computation requirements. Simulation results show that both proposed algorithms effectively achieve practically optimum performance for tailbiting codes of any length.     

一种Viterbi译码的改进算法

Viterbi译码是一种应用广泛的最大似然估计算法。本文利用相邻几组判决数据之间的相互关系，对这几组数据进行联合判决估计，从而提高了译码性能。从仿真结果来看，当译码深度不大时，译码性能得到明显的改善。因此该算法可以在保证同等性能前提下，减小硬件规模，降低功耗。     

A Multiple Stack Algorithm for Erasurefree Decoding of Convolutional Codes

A new algorithm for erasurefree sequential decoding of convolutional codes is introduced which achieves low error probabilities at substantially higher decoding speeds than the Viterbi decoding algorithm. The algorithmic properties of the Multiple Stack Algorithm (MSA) are investigated and it is demonstrated that the MSA reaches a decision with an exponentially rather than Pareto distributed computational effort. The MSA's error probability on the binary symmetric channel is studied as a function of its parameters and its performance and complexity compared to that of the Viterbi algorithm. The MSA is seen to achieve equal and lower error probabilities with a significantly lower average decoding effort. The new algorithm can thus be considered an attractive alternative to the Viterbi algorithm where low error probabilities and high decoding speeds are required simultaneously.     

Parity retransmission hybrid ARQ using rate 1/2 convolutional codeson a nonstationary channel

A parity retransmission hybrid automatic repeat request (ARQ) scheme is proposed which uses rate 1/2 convolutional codes and Viterbi decoding. A protocol is described which is capable of achieving higher throughputs than previously proposed parity retransmission schemes. The performance analysis is based on a two-state Markov model of a nonstationary channel. This model constitutes a first approximation to a nonstationary channel. The two-state channel model is used to analyze the throughput and undetected error probability of the protocol presented when the receiver has both an infinite and a finite buffer size. It is shown that the throughput improves as the channel becomes more bursty     

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.     

低复杂度的TBCC自适应循环VA译码算法

咬尾是一种将卷积码转换为块码的技术,它消除了归零状态所造成的码率损失,同时避免了截尾带来的性能降低,在短块编码中具有明显优势.针对咬尾卷积码(TBCC)现有译码算法复杂度过大和收敛性问题,提出一种低复杂度的TBCC自适应循环维特比(VA)译码算法.该算法根据信道变化自适应调整译码迭代次数,使咬尾路径收敛到最佳.通过仿真...     

A new sequential decoding algorithm based on branch metric

A new sequential decoding algorithm with an adjustable threshold and a new method of moving through the decoding tree is proposed. Instead of the path metric of the conventional sequential decoding algorithms, the proposed algorithm uses a branch metric based on maximum-likelihood criterion. Two new parameters, the jumping-back distance and going-back distance, are also introduced. The performance of the algorithm for long constraint length convolutional codes is compared to those of the other sequential decoding algorithms and the Viterbi algorithm. The results show that the proposed algorithm is a good candidate for decoding of convolutional codes due to its fast decoding capability and good bit error rate (BER) performance. This work was supported in part by the Research Foundation at Karadeniz Technical University under Grant 2004.112.004.01 and 2005.112.009.2.     

一种新型的卷积码混合译码算法

该文提出了一种级联的卷积码混合译码算法。该算法由两级译码实现,第1级采用置信传播(Belief-Propagation, BP)算法,而第2级采用修改的维特比译码(Modified Viterbi Decoding, MVD)算法。BP首先对接收序列进行预译码,并利用伴随式将译码输出的对数似然比值分为可靠的和不可靠的两类。不可靠的对数似然比值用接收符号取代,可靠的部分硬判决为编码符号,它们共同组成混合序列。随后,MVD对该混合序列作进一步纠错译码。仿真表明,与传统的维特比算法相比,所提出的混合译码算法的误码性能只有很小的损失,其译码平均复杂度在中高信噪比条件下有明显降低。     

FPGA design and implementation of a low-power systolic array-based adaptive Viterbi decoder

In this paper, by modifying the well-known Viterbi algorithm, an adaptive Viterbi algorithm that is based on strongly connected trellis decoding is proposed. Using this algorithm, the design and a field-programmable gate array implementation of a low-power adaptive Viterbi decoder with a constraint length of 9 and a code rate of 1/2 is presented. In this design, a novel systolic array-based architecture with time multiplexing and arithmetic pipelining for implementing the proposed algorithm is used. It is shown that the proposed algorithm can reduce by up to 70% the average number of ACS computations over that by using the nonadaptive Viterbi algorithm, without degradation in the error performance. This results in lowering the switching activities of the logic cells, with a consequent reduction in the dynamic power. Further, it is shown that the total power consumption in the implementation of the proposed algorithm can be reduced by up to 43% compared to that in the implementation of the nonadaptive Viterbi algorithm, with a negligible increase in the hardware.     

Viterbi译码的FPGA免回溯实现

卷积码在多种通信领域中广泛应用,Viterbi译码是对卷积码的一种最大似然译码算法。随着卷积码约束度的增加,并行维特比译码所需的硬件资源呈指数增长,限制其硬件实现。介绍了一种串行译码结构的FPGA实现方案,在保证性能译码的前提下有效地节省资源。同时提出了充分利用FPGA的RAM存储单元的免回溯Viterbi解码实现算法,减少了译码时延,这种算法在串行和并行译码中都可以应用。     

Noncoherent iterative (turbo) decoding

Previously, noncoherent sequence detection schemes for coded linear and continuous phase modulations have been proposed, which deliver hard decisions by means of a Viterbi algorithm. The current trend in digital transmission systems toward iterative decoding algorithms motivates an extension of these schemes. In this paper, we propose two noncoherent soft-output decoding algorithms. The first solution has a structure similar to that of the well-known algorithm by Bahl et al. (1974), whereas the second is based on noncoherent sequence detection and a reduced-state soft-output Viterbi algorithm. Applications to the combined detection and decoding of differential or convolutional codes are considered. Further applications to noncoherent iterative decoding of turbo codes and serially concatenated interleaved codes are also considered. The proposed noncoherent detection schemes exhibit moderate performance loss with respect to corresponding coherent schemes and are very robust to phase and frequency instabilities     

New stopping criteria for iterative decoding of LDPC codes in H‐ARQ systems

Under severely unreliable channel, decoding of error‐correcting codes frequently fails, which requires a lot of computational complexity, especially, in the iterative decoding algorithm. In hybrid automatic repeat request systems, most of computation power is wasted on failed decoding if a codeword is retransmitted many times. Therefore, early stopping of iterative decoding needs to be adopted. In this paper, we propose a new stopping algorithm of iterative belief propagation decoding for low‐density parity‐check codes, which is effective on both high and low signal‐to‐noise ratio ranges and scalable to variable code rate and length. The proposed stopping algorithm combines several good stopping criteria. Each criterion is extremely simple and will not be a burden to the overall system. With the proposed stopping algorithm, it is shown via numerical analysis that the decoding complexity of hybrid automatic repeat request system with adaptive modulation and coding scheme can be fairly reduced. Copyright © 2012 John Wiley & Sons, Ltd.     

New Syndrome Check Error Estimation and Its Concatenated Coding

A low-complexity and high performance SCEE (Syndrome Check Error Estimation) decoding method for convolutional codes and its concatenated SCEE/RS (Reed–Solomon) coding scheme are proposed. First, we describe the operation of the decoding steps in the proposed algorithm. Then deterministic values on the decoding operation are derived when some combination of predecoder-reencoder is used. Computer simulation results show that the computational complexity of the proposed SCEE decoder is significantly reduced compared to that of conventional Viterbi decoder without degradation of the P_e performance. Also, simulation results of BER performance of the concatenated SCEE/Hard Decision Viterbi (HD-Viterbi) and SCEE/RS (Reed–Solomon) codes are presented.     

一种改进的堆栈译码算法

深太空通信对编译码的性能有十分高的要求,卷积码的性能和约束长度密切相关,约束长度越大卷积码的编码增益越大,则其性能越好。维特比译码算法由于受译码开销的限制,并且其译码开销随约束长度增加呈指数增长,维特比译码算法仅适用于短约束长度的卷积码。目前仅有序列译码算法适用于大约束长度卷积码译码。由于堆栈译码算法中堆栈的大小是有限的,在信道受扰较为严重的情况下,潜在的正确路径有可能被删除,这将影响到译码的性能。多堆栈译码算法不存在潜在删除的问题,多堆栈译码算法完成译码所需计算量远小于堆栈译码算法。     

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