Highly-Parallel Decoding Architectures for Convolutional Turbo Codes

Highly parallel decoders for convolutional turbo codes have been studied by proposing two parallel decoding architectures and a design approach of parallel interleavers. To solve the memory conflict problem of extrinsic information in a parallel decoder, a block-like approach in which data is written row-by-row and read diagonal-wise is proposed for designing collision-free parallel interleavers. Furthermore, a warm-up-free parallel sliding window architecture is proposed for long turbo codes to maximize the decoding speeds of parallel decoders. The proposed architecture increases decoding speed by 6%-34% at a cost of a storage increase of 1% for an eight-parallel decoder. For short turbo codes (e.g., length of 512 bits), a warm-up-free parallel window architecture is proposed to double the speed at the cost of a hardware increase of 12%     

乘积码迭代译码算法研究

介绍了在分组码的软输入软输出译码基础上以扩展BCH码为子码的乘积码的迭代译码算法,提出了在高带宽利用率调制方式下的算法应用方式,并给出了仿真结果。最后与传统的并联卷级码代译码方案比较,发现在高编码效率时,乘积码迭代译码方案有着较好的应用性。     

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)。     

Serial Concatenation of Space‐Time and Recursive Convolutional Codes

We propose a new serial concatenation scheme for space‐time and recursive convolutional codes, in which a space‐time code is used as the outer code and a single recursive convolutional code as the inner code. We discuss previously proposed serial concatenation schemes employing multiple inner codes and compare them with the new one. The proposed method and the previous one with joint decoding, both performing a combined decoding of the simultaneous output signals from multiple antennas, give a large performance gain over the separate decoding method. In decoding complexity, the new concatenation scheme has a lower complexity compared with the multiple encoding/joint decoding scheme due to the use of the single inner code. Simulation results for a communication system with two transmit and one receive antennas in a quasi‐static Rayleigh fading channel show that the proposed scheme outperforms the previous schemes.     

Braided Convolutional Codes: A New Class of Turbo-Like Codes

We present a new class of iteratively decodable turbo-like codes, called braided convolutional codes. Constructions and encoding procedures for tightly and sparsely braided convolutional codes are introduced. Sparsely braided codes exhibit good convergence behavior with iterative decoding, and a statistical analysis using Markov permutors shows that the free distance of these codes grows linearly with constraint length, i.e., they are asymptotically good.     

Improved Analysis of List Decoding and Its Application to Convolutional Codes and Turbo Codes

A list decoder generates a list of more than one codeword candidates, and decoding is erroneous if the transmitted codeword is not included in the list. This decoding strategy can be implemented in a system that employs an inner error correcting code and an outer error detecting code that is used to choose the correct codeword from the list. Probability of codeword error analysis for a linear block code with list decoding is typically based on the "worst case" lower bound on the effective weights of codewords for list decoding evaluated from the weight enumerating function of the code. In this paper, the concepts of generalized pairwise error event and effective weight enumerating function are proposed for evaluation of the probability of codeword error of linear block codes with list decoding. Geometrical analysis shows that the effective Euclidean distances are not necessarily as low as those predicted by the lower bound. An approach to evaluate the effective weight enumerating function of a particular code with list decoding is proposed. The effective Euclidean distances for decisions in each pairwise error event are evaluated taking into consideration the actual Hamming distance relationships between codewords, which relaxes the pessimistic assumptions upon which the traditional lower bound analysis is based. Using the effective weight enumerating function, a more accurate approximation is achieved for the probability of codeword error of the code with list decoding. The proposed approach is applied to codes of practical interest, including terminated convolutional codes and turbo codes with the parallel concatenation structure     

On Tail Biting Convolutional Codes

In this paper, we introduce generalized tail biting encoding as a means to ameliorate the rate deficiency caused by zero-tail convolutional encoding. This technique provides an important link between quasi-cyclic block and convolutional codes. Optimum and suboptimum decoding algorithms for these codes are described and their performance determined by analytical and simulation techniques.     

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     

Symbol-by-symbol MAP decoding algorithm for high-rate convolutionalcodes that use reciprocal dual codes

A symbol-by-symbol maximum a posteriori (MAP) decoding algorithm for high-rate convolutional codes applying reciprocal dual convolutional codes is presented. The advantage of this approach is a reduction of the computational complexity since the number of codewords to consider is decreased. All requirements for iterative decoding schemes are fulfilled. Since tail-biting convolutional codes are equivalent to quasi-cyclic block codes, the decoding algorithm for truncated or terminated convolutional codes is modified to obtain a soft-in/soft-out decoder for high-rate quasi-cyclic block codes which also uses the dual code because of complexity reasons. Additionally, quasi-cyclic block codes are investigated as component codes for parallel concatenation. Simulation results obtained by iterative decoding are compared with union bounds for maximum likelihood decoding. The results of a search for high-rate quasi-cyclic block codes are given in the appendix     

高性能时不变LDPC卷积码构造算法研究

该文基于由QC-LDPC码获得时不变LDPC卷积码的环同构方法,设计了用有限域上元素直接获得时不变LDPC卷积码多项式矩阵的新算法。以MDS卷积码为例,给出了一个具体的构造过程。所提构造算法可确保所获得的时不变LDPC卷积码具有快速编码特性、最大可达编码记忆以及设计码率。基于滑动窗口的BP译码算法在AWGN信道上的仿真结果表明,该码具有较低的误码平台和较好的纠错性能。     

CSS型量子卷积码的编译码方法

该文给出了 型量子卷积码的一般结构,并计算得到其稳定子, 算子与 算子的标准型,重点讨论了这类码的编译码实现方法,描述了其编译码网络。 型量子卷积码的编译码过程只涉及Hadamard操作与控制非操作,因此编译码复杂度低,网络结构非常简单。     

State Transparent Convolutional Codes and Their Novel Maximum-Likelihood Decoding Algorithm

Almost all the probabilistic decoding algorithms known for convolutional codes, perform decoding without prior knowledge of the error locations. Here, we introduce a novel maximum-likelihood decoding algorithm for a new class of convolutional codes named as the state transparent convolutional (STC) codes, which due to their properties error detection and error locating is possible prior to error correction. Hence, their decoding algorithm, termed here as the STC decoder, allows an error correcting algorithm to be applied only to the erroneous portions of the received sequence referred to here as the error spans (ESPs). We further prove that the proposed decoder, which locates the ESPs and applies the Viterbi algorithm (VA) only to these portions, always yields a decoded path in trellis identical to the one generated by the Viterbi decoder (VD). Due to the fact that the STC decoder applies the VA only to the ESPs, hence percentage of the single-stage (per codeword) trellis decoding performed by the STC decoder is considerably less than the VD, which is applied to the entire received sequence and this reduction is overwhelming for the fading channels, where the erroneous codewords are mostly clustered. Furthermore, through applying the VA only to the ESPs, the resulting algorithm can be viewed as a new formulation of the VD for the STC codes that analogous to the block decoding algorithms provides a predecoding error detection and error locating capabilities, while performing less single-stage trellis decoding.     

Soft-Decision Decoding of Punctured Convolutional Codes in Asynchronous-CDMA Communications Under Perfect Phase-Tracking Conditions

In this paper, the performance of punctured convolutional codes of short constraint lengths is discussed. The punctured codes are used to provide error protection to a particular user in an asynchronous CDMA system. A perfect phase reference is assumed to be available throughout this paper. A slow fading Rician channel is assumed. Maximum likelihood decoding through a Viterbi algorithm is used to decode the information symbols. Soft-decision decoding of punctured convolutional codes is considered in this paper. The upper bounds with Viterbi decoding are derived and plotted for the various punctured codes considered. The simulated results are found to agree very well with their upper and lower bounds.     

Convolutional Codes Under a Minimal Trellis Complexity Measure

We conduct a code search, restricted to the recently introduced class of generalized punctured convolutional codes, under the minimal trellis complexity measure defined by McEliece and Lin. For the same decoding complexity and the same code rate, new codes are compared to well-known existing classes of convolutional codes. Some of the best convolutional codes (in a distance spectrum sense) of existing and new trellis complexities are tabulated.     

An Analysis of the Orthogonality Structures of Convolutional Codes for Iterative Decoding

The structures of convolutional self-orthogonal codes and convolutional self-doubly-orthogonal codes for both belief propagation and threshold iterative decoding algorithms are analyzed on the basis of difference sets and computation tree. It is shown that the double orthogonality property of convolutional self-doubly-orthogonal codes improves the code structure by maximizing the number of independent observations over two successive decoding iterations while minimizing the number of cycles of lengths$6$and$8$on the code graphs. Thus, the double orthogonality may improve the iterative decoding in both convergence speed and error performance. In addition, the double orthogonality makes the computation tree rigorously balanced. This allows the determination of the best weighing technique, so that the error performance of the iterative threshold decoding algorithm approaches that of the iterative belief propagation decoding algorithm, but at a substantial reduction of the implementation complexity.     

Rate Variable, Multi-Binary Turbo Codes with Controlled Error-Floor

In this letter we propose rate variable turbo codes based on the parallel concatenation of tailbiting Recursive Systematic multi-binary (m-ary) convolutional codes. Rate variability is not achieved by puncturing, which can have adverse effects on the minimum distance of the code. Using a variable number of input lines of the encoder, we obtain several different overall rates ranging from 1/2 to 7/8. The most suitable Soft-In- Soft-Out decoding algorithm for these turbo codes is based on the Dual Reciprocal Code, which is very efficient for high rate codes. A particular interleaver design, namely the ?backbone? interleaver, guarantees a high Hamming weight in codewords with information weight 2 and 3, as well as good minimum distances and fairly low multiplicities for higher information weights. Therefore, these codes have very low error floors.     

Turbo码译码性能的研究

Turbo码基于随机编码的思想,将卷积编码与交织器结合使其性能接近香农极限,所以Turbo码被3G移动通信系统所采纳并在深海通信、卫星通信等功率受限领域得以应用.文中介绍了Turbo码的译码原理并分析了几种主要的译码方法,在Matlab环境下对Turbo码进行了仿真研究,分析了不同的迭代次数、译码算法、帧长、码率及分量码对其译码性能的影响.仿真结果表明Turbo码纠错性能优良,具有广泛的应用前景.     

一种新的准随机LDPC卷积码及窗译码

以Gallager随机LDPC分组码为基础,通过列置换、置数、剪切与合并,构造了一种新的（l,3,6）准随机LDPC卷积码.针对该码类,提出了一种窗扇尺寸固定、滑动步长可选的窗译码算法,大幅降低了寄存器开销和译码延时.仿真实验界定了滑动步长的取值范围,验证了构造方案和窗译码的有效性,测试了不同约束度的准随机LDPC卷积码的误码性能,结果显示约束度l仅为1535即可获得距离香农限约1dB的纠错能力.     

MAP decoding of convolutional codes using reciprocal dual codes

A new symbol-by-symbol maximum a posteriori (MAP) decoding algorithm for high-rate convolutional codes using reciprocal dual convolutional codes is presented. The advantage of this approach is a reduction of the computational complexity since the number of codewords to consider is decreased for codes of rate greater than 1/2. The discussed algorithms fulfil all requirements for iterative (“turbo”) decoding schemes. Simulation results are presented for high-rate parallel concatenated convolutional codes (“turbo” codes) using an AWGN channel or a perfectly interleaved Rayleigh fading channel. It is shown that iterative decoding of high-rate codes results in high-gain, moderate-complexity coding     

Fast Decodable Turbo Codes

Decoding delay is an important consideration for the use of turbo codes in practical applications. We propose a new structure for turbo codes which is very suitable for parallel decoding. It is shown by union bound analysis and simulation results that the proposed system performance is comparable to that of the classical turbo codes