Joint Early Detection and Early Stopping scheme for complexity reduction of turbo decoding

In this paper,a Joint Early Detection and Early Stopping (JEDES) approach for effectively reducing the complexity of turbo decoding with negligible performance loss is proposed. It combines the effectiveness of both early detection and early stopping techniques. Our simulation results demon-strated that the proposed JEDES scheme based on cyclic redundancy check and trellis splicing can achieve a complexity saving of 15% to 20% at practical bit error rates over the idealized GENIE stopping scheme,which is widely accepted as the theoretically best possible early stopping scheme.     

一种改进的无线光通信LDPC码译码算法

针对无线光通信中低密度奇偶校验码(LDPC)置信传播(BP)译码算法复杂度高及置信度振荡造成译码错误等缺点,基于对数BP算法提出了一种改进的译码算法。改进的译码算法在校验节点运算时,判断输入到校验节点消息的最小值与某个门限的大小,根据比较结果,分别用消息最小值或若干个最小值进行运算,在损失很少性能的情况下降低了运算复杂度;同时在比特节点采用振荡抵消处理运算,提高了算法的性能增益。最后在对数正态分布湍流信道模型下,分别对比特充分交织和交织深度为16的情况进行了仿真实验。仿真结果表明,改进的译码算法与BP算法相比,大幅度降低了计算复杂度,而且译码性能有一定的优势,收敛速度损失很少;而相对于最小和算法,改进的算法虽然译码复杂度有所增加,但误码率性能有明显的优势,并且收敛速度也优于最小和算法。因此,改进的译码算法是无线光通信中LDPC码译码算法复杂度和性能之间一个较好的折中处理方案。     

A new framework for soft decision equalization in frequency selective MIMO channels

We introduce a novel framework for soft-input, soft-output (SISO) equalization in frequency selective multipleinput multiple-output (MIMO) channels based on the well-known belief propagation (BP) algorithm. As in the BP equalizer, we model the multipath channels using factor graphs (FGs) where the transmitted and received signals are represented by the function and variable nodes respectively. The edges connecting the function and variable nodes illustrate the dependencies of the multipath channel and soft decisions are developed by exchanging information on these edges iteratively. We incorporate powerful techniques such as groupwise iterative multiuser detection (IMUD), probabilistic data association (PDA) and sphere decoding (SD) in order to reduce the computational complexity of BP equalizer with relatively small degradation in performance. The computational complexity of this new reduced-complexity BP (RCBP) equalizer grows linearly with block size and memory length of the channel. The proposed framework has a flexible structure that allows for parallel as well as serial detection. We will illustrate through simulations that the RCBP equalizer can even handle overloaded scenarios where the channel matrix is rank deficient, and it can achieve excellent performance by applying iterative equalization using the low-density parity check codes (LDPC).     

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.     

对LDPC码的LLRBP算法研究

在LDPC译码时,使用IJLRBP算法其校验节点的计算复杂度十分高,而且当LDPC码中有许多的短环时,译码性能也会降低。基于以上的这些问题提出了一个新的混合校验变量过程,通过调整校验节点的处理振幅和变量节点的信息相关性来降低计算复杂度,其仿真过程表明在译码性能和运算复杂度上与LLRBP算法都有较大的提高。     

Low‐complexity turbo detection for single‐carrier low‐density parity‐check‐coded multiple‐input multiple‐output underwater acoustic communications

A low‐complexity turbo detection scheme is proposed for single‐carrier multiple‐input multiple‐output (MIMO) underwater acoustic (UWA) communications using low‐density parity‐check (LDPC) channel coding. The low complexity of the proposed detection algorithm is achieved in two aspects: first, the frequency‐domain equalization technique is adopted, and it maintains a low complexity irrespective of the highly dispersive UWA channels; second, the computation of the soft equalizer output, in the form of extrinsic log‐likelihood ratio, is performed with an approximating method, which further reduces the complexity. Moreover, attributed to the LDPC decoding, the turbo detection converges within only a few iterations. The proposed turbo detection scheme has been used for processing real‐world data collected in two different undersea trials: WHOI09 and ACOMM09. Experimental results show that it provides robust detection for MIMO UWA communications with different modulations and different symbol rates, at different transmission ranges. Copyright © 2011 John Wiley & Sons, Ltd.     

低复杂度的自适应置信差分迭代译码算法

针对中短码长的低密度奇偶校验规则码(Low Density Parity Check, LDPC)规则码,该文采用消息更新规则改进和因子图变换方法,提出一种低复杂度差分迭代译码算法。在置信传播算法的基础上,仅当变量节点的消息值振荡时引入差分映射策略,得出一种选择性的置信差分规则,自适应地调整校验节点消息的归一化系数,提高译码性能。同时,采用展开校验节点的图变换方法,将计算复杂度从随节点度分布指数性增长降至线性增长。分别在高斯白噪声信道和瑞利衰落信道下进行仿真实验,结果表明该算法和基于图变换的其他低复杂度译码算法相比,性能优越且复杂度低,和对数似然比的置信传播算法(LLR-BP)相比,高信噪比区域内的性能优异,低信噪比区域内的计算复杂度明显降低。     

基于SSCANL译码器的联合迭代检测译码算法

为了提升基于极化码的稀疏码多址接入（sparse code multiple access,SCMA）系统接收机性能,提出了基于简化软消除列表（simplify soft cancellation list,SSCANL）译码器的循环冗余校验（cyclic redundancy check,CRC）辅助联合迭代检测译码接收机方案。该方案中极化码译码器使用SSCANL译码算法,采用译码节点删除技术对软消除列表（soft cancellation list,SCANL）算法所需要的L次软消除译码（soft cancellation, SCAN）进行简化,通过近似删除冻结位节点,简化节点间软信息更新计算过程,从而降低译码算法的计算复杂度。仿真结果表明,SSCANL算法可获得与SCANL算法一致的性能,其计算复杂度与SCANL算法相比有所降低,码率越低,算法复杂度降低效果越好;且基于SSCANL译码器的CRC 辅助联合迭代检测译码接收机方案相较基于SCAN译码器的联合迭代检测译码（joint iterative detection and decoding based on SCAN decoder, JIDD-SCAN）方案、基于SCAN译码器的CRC辅助联合迭代检测译码（CRC aided joint iterative detection and decoding based on SCAN decoder,C-JIDD-SCAN）方案,在误码率为10^-4时,性能分别提升了约0.65 dB、0.59 dB。     

A simple soft linear detection for coded multi‐input multi‐output systems

We propose a very simple and efficient soft linear multi‐input multi‐output (MIMO) detection scheme. The detection process is divided into two separate problems. The proposed scheme first detects MIMO symbols using conventional linear detection methods and produces soft bit information using a simple soft demapping method. Next, we refine the soft information by accounting for uneven post‐detection noise variance across MIMO layers. From the simulation result investigated in this paper, we first emphasize that powerful channel coding may suppress the differences of diversity gains among various MIMO detection schemes. This implies that the channel decoding operation may not be transparent to performance gain that resulted from MIMO detection process. The proposed scheme concentrates on accurate estimation of soft post‐MIMO detected information in a very simple manner, rather than concentrating on a complex MIMO detection scheme prior to decoding process. In combination with turbo codes, the proposed scheme produces comparable performance to maximum likelihood detection, even with the simplest scheme such as zero forcing detection, with drastically reduced complexity. Copyright © 2011 John Wiley & Sons, Ltd.     

Early detection and trellis splicing: reduced-complexity iterativedecoding

The bit-error rate (BER) performance of new iterative decoding algorithms (e,g,, turbodecoding) is achieved at the expense of a computationally burdensome decoding procedure. We present a method called early detection that can be used to reduce the computational complexity of a variety of iterative decoders. Using a confidence criterion, some information symbols, state variables, and codeword symbols are detected early on during decoding. In this way, the computational complexity of further processing is reduced with a controllable increase in the BER. We present an easily implemented instance of this algorithm, called trellis splicing, that can be used with turbodecoding. For a simulated system of this type, we obtain a reduction in the computational complexity of up to a factor of four, relative to a turbodecoder that obtains the same increase in the BER by performing fewer iterations     

基于额外列多元LDPC码网格最小最大译码算法

为了降低多元LDPC(Low Density Parity Check Code)码网格最小最大(Trellis Min-Max,T-MM)译码算法复杂度,减少译码过程中所需存储空间,提出一种基于额外列的T-MM译码算法(Extra-Column-based Trellis Min-Max,EC-T-MM).选取网格中可靠度最高的信息构造出优化的配置集,生成一列用于更新校验节点的q维额外列信息,再根据网格路径中偏移量信息,从最小值、次小值和额外列信息中得到校验节点的外在输出信息,通过网格的路径优化降低校验节点的更新复杂度.在译码过程中,用偏移量信息代替所有变量节点输入信息,减少存储空间.仿真结果表明:该算法在几乎不损失性能的前提下,降低了计算复杂度及所需的存储空间.     

基于分布式奇偶校验码的低复杂度极化码SCLF译码算法

针对极化码串行抵消列表比特翻转(Successive Cancellation List Bit-Flip, SCLF)译码算法复杂度较高的问题,提出一种基于分布式奇偶校验码的低复杂度极化码SCLF译码(SCLF Decoding Algorithm for Low-Complexity Polar Codes Based on Distributed Parity Check Codes, DPC-SCLF)算法。与仅采用循环冗余校验(Cyclic Redundancy Check, CRC)码校验的SCLF译码算法不同,该算法首先利用极化信道偏序关系构造关键集,然后采用分布式奇偶校验(Parity Check, PC)码与CRC码结合的方式对错误比特进行检验、识别和翻转,提高了翻转精度,减少了重译码次数。此外,在译码时利用路径剪枝操作,提高了正确路径的竞争力,改善了误码性能,且利用提前终止译码进程操作,减少了译码比特数。仿真结果表明,与D-Post-SCLF译码算法和RCS-SCLF译码算法相比,所提出算法具有更低的译码复杂度且在中高信噪比下具有更好的误码性能。     

A simple low-complexity algorithm for generalized spatial modulation

Generalized spatial modulation (GSM) is an extension of spatial modulation which is significant for the next generation communication systems. Optimal detection process for the GSM is the maximum-likelihood (ML) detection which jointly detects the antenna combinations and transmitted symbols. However, the receiver is much more complicated than SM due to inter-antenna interference and/or increased number of combinations. Therefore, the computational complexity of the ML detection grows with the number of transmit antennas and the signal constellation size. In this letter, we introduce a novel and simple detection algorithm which uses sub-optimal method based on the least squares solution to detect likely antenna combinations. Once the antenna indices are detected, ML detection is utilized to identify the transmitted symbols. For obtaining near-ML performance while keeping lower complexity than ML detection, sphere decoding is applied. Our proposed algorithm reduces the search complexity while achieving a near optimum solution. Computer simulation results show that the proposed algorithm performs close to the optimal (ML) detection resulting in a significant reduction of computational complexity.     

New Min‐sum LDPC Decoding Algorithm Using SNR‐Considered Adaptive Scaling Factors

This paper proposes a new min‐sum algorithm for low‐density parity‐check decoding. In this paper, we first define the negative and positive effects of the received signal‐to‐noise ratio (SNR) in the min‐sum decoding algorithm. To improve the performance of error correction by considering the negative and positive effects of the received SNR, the proposed algorithm applies adaptive scaling factors not only to extrinsic information but also to a received log‐likelihood ratio. We also propose a combined variable and check node architecture to realize the proposed algorithm with low complexity. The simulation results show that the proposed algorithm achieves up to 0.4 dB coding gain with low complexity compared to existing min‐sum‐based algorithms.     

Computationally efficient decoding of LDPC codes

A computationally efficient algorithm for the decoding of low-density parity check codes is introduced. Instead of updating all bit and check nodes at each decoding iteration, the developed algorithm only updates unreliable check and bit nodes. A simple reliability criteria is developed to determine the active bit and check nodes per decoding iteration. Based on the developed technique, significant computation reductions are achieved with very little or no loss in the BER performance of the LDPC codes. The proposed method can be implemented with a slight modification to the sum-product algorithm with negligible additional hardware complexity.     

Degree-Matched Check Node Decoding for Regular and Irregular LDPCs

This brief examines different parity-check node decoding algorithms for low-density parity-check (LDPC) codes, seeking to recoup the performance loss incurred by the min-sum approximation compared to sum-product decoding. Two degree-matched check node decoding approximations that depend on the check node degree d_c are presented. Both have low complexity and can be applied to any degree distribution. Simulation results show near sum-product decoding performance for both degree-matched check node approximations for regular and irregular LDPCs     

CRC-aided turbo equalization for MIMO frequency selective fading channels

This paper presents a CRC （Cyclic Redundancy Check）-aided turbo equalization approach to reduce the computational complexity. In this approach, CRC code bits are padded to the end of each transmit block, and a cyclic redundancy check is performed after decoding each block at the receiver en.d. If the check sum is zero, which means the receive block is correct, the corresponding LLRs （Log Likelihood Ratios） of this block are set high reliable values, and all the computations corresponding to this block can be cancelled for the subsequent outer iterations. With a lower computational complexity the proposed approach can achieve the same as or even better performance than the conventional non-CRC method.     

一种基于量化预处理的低复杂度LDPC译码算法

为了降低低密度奇偶校验(Low Density Parity Check,LDPC)码译码算法的复杂度,提出了一种基于量化预处理的LDPC迭代大数逻辑译码算法。该算法在迭代译码过程中,校验节点采用基于伴随式的信息处理方式,避免了外信息的计算;同时,变量节点基于回传的伴随式信息进行可靠度偏移大小的计算,并结合与当前码位相对应的调制映射信息进行可靠度偏移方向的设计。迭代更新时,变量节点采用基于信息匹配的可靠度更新规则。迭代前的量化预处理能避免实数乘法运算进入迭代过程,使其只涉及整数加法操作和逻辑操作。仿真结果表明,在保持译码性能的前提上,所提算法具有更低的译码复杂度。     

一种低复杂度空间调制球形译码检测算法

现有的空间调制系统球形译码（Sphere-Decoding,SD）检测算法虽然能够较大地降低最大似然（Maximum-Likelihood,ML）检测算法的计算复杂度,但由于其更新半径比较松散、收敛较慢,计算复杂度降低的水平仍十分有限,尤其是在高阶调制系统下.针对上述问题,采用统计分布的思想对现有算法更新半径中的冗余项进行估计,提出了两种改进的球形译码检测算法.理论分析与仿真结果表明,改进算法在达到最优检测性能的同时,极大地降低了传统球形译码的计算复杂度,具有较好的理论和实际应用意义.     

消息复用下的空间耦合LDPC码窗译码优化算法

空间耦合低密度奇偶校验（Spatially Coupled Low Density Parity Check,SC-LDPC）码由于其奇偶校验矩阵呈现对角带非零项的特点,采用窗译码可获得较低的时延及复杂度。针对SC-LDPC码窗译码性能损失、译码复杂度依然较高的问题,提出了消息复用（Message Reuse for Window Decoding,MR-WD）算法和动态多目标符号输出（Dynamic Multi-target-symbol Output for Window Decoding,DMO-WD）算法。消息复用算法以外部对数似然比值作为边信息传入窗口,与传统窗译码相比,译码性能得到了提升,译码复杂度降低。动态多目标符号输出算法在连续若干个窗口均满足奇偶校验方程判定为零时,增加目标符号的输出数量,反之减少目标符号的输出数量。该算法在误码率损失可忽略不计的情况下降低译码复杂度最大达20%,且在动态多目标符号窗译码中使用消息复用更新边信息时,相比于传统窗译码性能提升约0.2 dB,复杂度下降约35%。