On Convolutional Coupled Codes

The error correcting performance of the parallel concatenation of two convolutional codes is very promising. Inspired from this construction which is near the Shannon limit error correction performance, we consider a further development of concatenated codes. In this construction systematic convolutional codes and rate 1/2 systematic block codes are linked together such that only the systematic part of the convolutional codes is encoded with the block encoders. The bits of each information vector of the convolutional codes are scrambled by a given interleaving before entering to the block encoders. Then, differently from the Turbo codes, in which information symbols and the redundancy from the constituent codes are transmitted [1], we transmit only the redundancy from the convolutional and block codes. We call this construction convolutional coupled codes and code coupling is the new scheme of code concatenation. The structural properties of the generator matrix of the convolutional coupled code is investigated. It's minimum distance is lower and upper bounded and we introduce the term of the effective free distance. Simulation results will show, that convolutional coupled codes have the potential of being a realistic alternative to Turbo codes.     

On the MacWilliams Identity for Convolutional Codes

The adjacency matrix associated with a convolutional code collects in a detailed manner information about the weight distribution of the code. A MacWilliams identity conjecture, stating that the adjacency matrix of a code fully determines the adjacency matrix of the dual code, will be formulated, and an explicit formula for the transformation will be stated. The formula involves the MacWilliams matrix known from complete weight enumerators of block codes. The conjecture will be proven for the class of convolutional codes where either the code itself or its dual does not have Forney indices bigger than one. For the general case, the conjecture is backed up by many examples, and a weaker version will be established.     

Turbo Product Codes Based on Convolutional Codes

In this article, we introduce a new class of product codes based on convolutional codes, called convolutional product codes. The structure of product codes enables parallel decoding, which can significantly increase decoder speed in practice. The use of convolutional codes in a product code setting makes it possible to use the vast knowledge base for convolutional codes as well as their flexibility in fast parallel decoders. Just as in turbo codes, interleaving turns out to be critical for the performance of convolutional product codes. The practical decoding advantages over serially‐concatenated convolutional codes are emphasized.     

卷积码的线性系统

介绍了卷积码的线性离散时不变系统模型。从建立卷积码的状态变量方程出发,研究了卷积码的代数结构,并详细论述了基于状态变量方程描述的迭代译码算法。     

Syndrome Decoding of Convolutional Codes

The classical Viterbi decoder recursively finds the trellis path (code word) closest to the received data. Given the received data, the syndrome decoder first forms a syndrome, instead. A recursive algorithm like Viterbi's is used to determine the noise sequence of minimum Hamming weight that can be a possible cause of this syndrome. Given the estimate of the noise sequence, one derives an estimate of the original data sequence. While the bit error probability of the syndrome decoder is no different from that of the classical Viterbi decoder, the syndrome decoder can be implemented using a read only memory (ROM), thus obtaining a considerable saving in hardware.     

On Unequal Error Protection of Convolutional Codes From an Algebraic Perspective

In this paper, convolutional codes are studied for unequal error protection (UEP) from an algebraic theoretical viewpoint. We first show that for every convolutional code there exists at least one optimal generator matrix with respect to UEP. The UEP optimality of convolutional encoders is then combined with several algebraic properties, e.g., systematic, basic, canonical, and minimal, to establish the fundamentals of convolutional codes for UEP. In addition, a generic lower bound on the length of a UEP convolutional code is proposed. Good UEP codes with their lengths equal to the derived lower bound are obtained by computer search.     

Sliding Block Decoding of Convolutional Codes

It is shown that a convolutional code can be decoded with a sliding-block decoder, a time-invariant nonlinear digital filter with finite memory and delay. If the memory and delay are small, then the sliding-block decoder can be implemented as a table lookup procedure in ROM, resulting in a low cost, high speed, and high reliability decoder.     

系统卷积码盲识别

在未知情况下如何仅仅根据接收的数据识别出信道纠错码的参数,目前还是个很难解决的问题。文章根据线性分组码的性质提出了一种新型数据矩阵模型,用于对线性分组码进行盲识别,并将该方法推广应用到系统卷积码盲识别,取得了很好的效果。     

Performance of Unequally Punctured Convolutional Codes

In practical applications, some coded symbols are unequally punctured for rate matching of terminated convolutional codes. In this letter, performance upper bounds are proposed for a terminated convolutional code punctured with an arbitrary pattern. To obtain the upper bounds, a weight enumerator is defined to represent the relation between the Hamming weight of the coded outputs and that of the selected input information bits. A method is presented to compute the weight enumerator based on a modified trellis diagram. Simulation and numerical analysis show that the proposed bounds are tight to the performance of terminated convolutional codes.     

LDPC卷积码的快速收敛译码

采用串行消息传递策略,文中提出了LDPC卷积码的一种改进的流水线式译码器.分析和仿真结果均表明改进的译码器在不增加单个处理器计算复杂度的前提下,仅通过改变消息传递方式就能够大大加速译码收敛速率,与原译码器相比大约可以节省一半的处理器.     

Quaternary Convolutional Codes From Linear Block Codes Over Galois Rings

From a linear block code B over the Galois ring GR(4, m) with a k times n generator matrix and minimum Hamming distance d, a rate-k/n convolutional code over the ring Z₄ with squared Euclidean free distance at least 2d and a nonrecursive encoder with memory at most m - 1 is constructed. When the generator matrix of B is systematic, the convolutional encoder is systematic, basic, noncatastrophic and minimal. Long codes constructed in this manner are shown to satisfy a Gilbert-Varshnmov bound.     

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.     

Real-Time Minimal-Bit-Error Probability Decoding of Convolutional Codes

A recursive procedure is derived for decoding of rateR = 1/nbinary convolutional codes which minimizes the probability of the individual decoding decisions for each information bit, subject to the constraint that the decoding delay be limited to Δ branches. This new decoding algorithm is similar to, but somewhat more complex than, the Viterbi decoding algorithm. A "real-time," i.e., fixed decoding delay, version of the Viterbi algorithm is also developed and used for comparison to the new algorithm on simulated channels. It is shown that the new algorithm offers advantages over Viterbi decoding in soft-decision applications, such as in the inner coding system for concatenated coding.     

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%     

运用删截卷积码实现不等错误保护

在数字通信系统中，发送的数据序列中的比特往往具有不等的重要性。为了寻求更可靠的信息传输，人们提出了一些不等错误保护（UEP）编码方案。本文介绍了一种通过删截卷积码（CC）实现UEP编码的方案，并通过仿真分析了该UEP编码的性能。仿真结果表明，运用删截卷积码实现的UEP编码能获得较好的性能。     

Pseudocodeword Performance Analysis for LDPC Convolutional Codes

Message-passing iterative decoders for low-density parity-check (LDPC) block codes are known to be subject to decoding failures due to so-called pseudocodewords. These failures can cause the large signal-to-noise ratio (SNR) performance of message-passing iterative decoding to be worse than that predicted by the maximum-likelihood (ML) decoding union bound.      

级联卷积码的性能评估

本文给出了三个采用卷积码的数字通信系统,并对其性能进行了评估.其中两个系统采用了用两个短的卷积码进行级联的方式(称为级联系统). 而另一个则是现在普遍使用的卷积编码方式,它采用一个长的卷积码(称为基联系统),三个系统的编码效率和约束长度分别采用R=2/3和K=3,R=3/4和K=2,以及R=1/2和K=7.前两个系统在Viterbi译码器进行硬件判决之前采用了软判决.两个级联系统中最为突出的特点是它们的译码器的复杂程度被大大降低,整个系统的复杂程度比基联系统改变了25%到50%.     

高编码率维特比译码器的设计

本文提出了一种高编码维特比译码器设计方案，并采用单片机加以实现。因此方案具有一定的实用性。     

1／n卷积码盲识别

在未知情况下如何仅仅根据接收的数据识别出信道纠错码的参数,目前还是个很难解决的问题.本文根据线性分组码的性质提出了一种新型数据矩阵模型,用于对线性分组码进行盲识别;并将该方法推广应用到1/n卷积码盲识别,取得了很好的效果.