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。     

Performance Bounds for Nonbinary Linear Block Codes Over Memoryless Symmetric Channels

The performance of nonbinary linear block codes is studied in this paper via the derivation of new upper bounds on the block error probability under maximum-likelihood (ML) decoding. The transmission of these codes is assumed to take place over a memoryless and symmetric channel. The new bounds, which are based on the Gallager bounds and their variations, are applied to the Gallager ensembles of nonbinary and regular low-density parity-check (LDPC) codes. These upper bounds are also compared with sphere-packing lower bounds. This study indicates that the new upper bounds are useful for the performance evaluation of coded communication systems which incorporate nonbinary coding techniques.      

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.     

LDPC Codes Over Rings for PSK Modulation

This paper describes the design and analysis of low-density parity-check (LDPC) codes over rings and shows how these codes, when mapped onto appropriate signal constellations, can be used to effect bandwidth-efficient modulation. Specifically, LDPC codes are constructed over the integer rings$BBZ_m$and$BBG_m^2$and mapped onto phase-shift keying (PSK)-type signal sets to yield geometrically uniform signal space codes. This paper identifies and addresses the design issues that affect code performance. Examples of codes over$BBZ_8$and$BBG_64$mapped onto$8$-ary and$64$-ary signal sets at a spectral efficiency of 1.5 and 2.0 bits per second per hertz (b/s/Hz) illustrate the approach; simulation of these codes over the additive white Gaussian noise (AWGN) channel demonstrates that this approach is a good alternative to bandwidth-efficient techniques based on binary LDPC codes—e.g., bit-interleaved coded modulation.     

闭环模式的线性空时分组码

介绍了正交空时分组码的模型,自干扰,性能;并由此提出了一种高速率准正交空时分组码的闭环模式,保证MIMO系统获得较高的速率,同时减少由于正交性减弱而引起的性能下降.其中反馈的方法就是根据发射端能够获得部分信道状态信息而提出的,这种自适应模式的性能在瑞利衰落信道下通过仿真得到了验证.     

Efficient Linear Homomorphic Encryption from LWE Over Rings

As the basis for secure public-key encryption under various cases, the learning with errors (LWE) problem has proved to be versatile for encryption schemes. Unfortunately, it tends not to be efficient enough for practical applications. For improving the efficiency issues and quickening the practical applications of the lattice-based public-key cryptosystems, an efficient homomorphic encryption scheme is presented in this paper, which is based on the learning with errors over rings (R-LWE) assumption, and its security is reducible to the hardness of the shortest vector problem in the worst case on ideal lattices. Furthermore, the scheme possesses homomorphism feature that encryption operations are consistent with message operations. The security analysis shows that the proposed encryption scheme is secure against chosen-plaintext attacks in the standard model. At the same time, the efficiency analysis and simulation results indicate that the scheme is much more efficient than previous lattice-based cryptosystems.     

线性分组码的神经网络译码

介绍了神经网络与线性分组码之间的关系，并在文献[1]的基础上证明了软判决译码与求解能量函数最大值之间的等价性，然后以(7，4，3)汉明码为例介绍了神经网络在循环码硬判决、软判决译码中的应用。     

线性分组码与时空分组码级联的迭代译码

提出了线性分组码与时空分组码的级联编码方案,推导了时空分组码在比特级上的软输入软输出译码算法,进而给出了在线性分组码和时空分组码之间进行迭代译码的算法。仿真结果表明这种方案与现有方案相比在能够获得最大分集增益的同时还能获得更大的编码增益。     

Bounds on the Minimum Homogeneous Distance of the pr-ary Image of Linear Block Codes Over the Galois Ring GR(pr,m)

In this correspondence, bounds are derived on the minimum homogeneous distance of the image of a linear block code over the Galois ring GR(p^r,m), with respect to any basis of GR(p^r,m). These bounds depend on the parameters of GR(p^r ,m), the minimum Hamming distance of the block code, and the average value of the homogeneous weight applied on the base ring Zopf _p ^r. Examples are given of Galois ring codes that meet these bounds     

A New Linear Programming Approach to Decoding Linear Block Codes

In this paper, we propose a new linear programming formulation for the decoding of general linear block codes. Different from the original formulation given by Feldman, the number of total variables to characterize a parity-check constraint in our formulation is less than twice the degree of the corresponding check node. The equivalence between our new formulation and the original formulation is proven. The new formulation facilitates to characterize the structure of linear block codes, and leads to new decoding algorithms. In particular, we show that any fundamental polytope is simply the intersection of a group of the so-called minimum polytopes, and this simplified formulation allows us to formulate the problem of calculating the minimum Hamming distance of any linear block code as a simple linear integer programming problem with much less auxiliary variables. We then propose a branch-and-bound method to compute a lower bound to the minimum distance of any linear code by solving a corresponding linear integer programming problem. In addition, we prove that, for the family of single parity-check (SPC) product codes, the fractional distance and the pseudodistance are both equal to the minimum distance. Finally, we propose an efficient algorithm for decoding SPC product codes with low complexity and maximum-likelihood (ML) decoding performance.      

Area-Efficient Parallel Syndrome Generators for Linear Block Codes

The common subexpression elimination (CSE) method has been applied to reduce the computational cost of the parallel syndrome generators, which are essential components for decoding of linear block codes. In this work, we present an alternative expression for the parallel syndrome generation formula, with which CSE is able to search redundant computations in a maximally expanded space to achieve a significantly higher optimization efficiency. In particular, two search space expansion schemes are studied for syndrome generators of BCH and RS codes. Experiments demonstrate at most 81 % of area savings using the proposed optimization schemes, and the post-layout results show the power saving of 41 ～ 45 % compared to a straightforward design.     

空时分组码与线性分组码相结合的

空时分组码能够实现MIMO系统的完全发射分集,但不能实现任何的编码增益.对此,提出了线性分组码与空时分组码级联的MIMO系统,该系统能够同时实现完全发射分集和编码增益.仿真结果表明,在比特误码率为10-5时,与未进行前向纠错的空时分组码系统相比,该系统能提供了大约2.7dB的编码增益.     

基于VHDL的线性分组码编译码器设计

数字信号在传输过程中受到干扰的影响,降低了其传输的可靠性,线性分组码作为一种常用的信道编码,在通信传输系统中应用广泛。在对线性分组码的编译码规则研究基础上,讨论了生成矩阵、监督矩阵与错误图样集之间的关系,在Max＋PlusⅡ开发环境中,用VHDL语言设计线性分组码编译码器,对其各项设计功能进行了仿真和验证。结果表明,该设计正确,其功能符合线性分组码编译码器的要求。     

Perfect Codes From Cayley Graphs Over Lipschitz Integers

The search for perfect error-correcting codes has received intense interest since the seminal work by Hamming. Decades ago, Golomb and Welch studied perfect codes for the Lee metric in multidimensional torus constellations. In this work, we focus our attention on a new class of four-dimensional signal spaces which include tori as subcases. Our constellations are modeled by means of Cayley graphs defined over quotient rings of Lipschitz integers. Previously unexplored perfect codes of length one will be provided in a constructive way by solving a typical problem of vertices domination in graph theory. The codewords of such perfect codes are constituted by the elements of a principal (left) ideal of the considered quotient ring. The generalization of these techniques for higher dimensional spaces is also considered in this work by modeling their signal sets through Cayley-Dickson algebras.     

A Comparison of Block and Convolutional Codes in ARQ Error Control Schemes

ARQ methods of error control can considerably improve the reliablity of data transmission in such areas as satellite communications, computer networks, etc. A number of ARQ schemes using both block and convolutional codes have appeared in the literature. In this paper, the following problem is addressed. Given two different implementations of an ARQ scheme, one using a block code and the other using a convolutional code, such that the bit error probability of both implementations does not exceed some specific value, which implementation has the higher throughput and under what conditions will it be attained? The comparison is made for three basic retransmission schemes using both hybrid and pure ARQ: stop-and-wait, go-back-N, and selective repeat. Numerical estimates of the throughput were obtained using approximate theoretical expressions for BCH codes and simulation results for sequential decoding of rate 1/2 convolutional codes. Parameters optimizing the performance of both block and convolutional codes for different channel conditions and round trip delays were found and were used to obtain these numerical estimates. Comparison of the quantitative results indicates a trend toward preferring convolutional codes as delay and/or block length increases. A binary symmetric channel with noiseless feedback was assumed. Possible implications for the Gaussian channel are also discussed.     

一种线性分组码参数的盲识别方法

针对线性分组码参数的盲识别问题,根据实际序列与随机序列码重分布相似度差异最大的特性,提出一种基于码重相似度识别码字长度和码字同步点的方法,在此基础上,利用一种新的特征——深度分布,识别生成矩阵,利用高斯消去法产生典型生成矩阵,实现了线性分组码的盲识别。码重相似度识别方法简单易行,理论分析及仿真实验表明该方法的容错性较强,误码率为0.01条件下识别效果较好。     

一种线性分组码的查表译码法及其应用

针对纠正两个随机错误的线性分组码,采用重复查表译码法,通过多次查询含一个错误的伴随式与错误图样的译码表,实现了一种占有很少存储空间的查表译码算法。该算法在码长较短时译码的计算量较少,可适用于利用单片机等低运算能力情况下的通信应用中。文中对纠正2个错误的（26,16）缩短循环码的译码进行了实现,验证了算法的可行性。     

两类新的线性分组码的译码

本文推广了Ｐｌｅｓｓ由四元线性分组码构造Ｇｏｌａｙ码和由三元（４，２，３）线性分组码构造三元（１２，６，６）Ｇｏｌａｙ码的投影方法，给出了由四元（ｎ，ｋ，ｄ）线性分组码构造的二元（４ｎ，ｎ＋２ｋ，≥ｍｉｎ（８，ｎ，２ｄ）线性分组码和由三元（ｎ，ｋ，ｄ）线性分组码构造的三元（３ｎ，ｎ＋ｋ，≥ｍｉｎ（ｎ，２ｄ，６）线性分组码，并根据所得码的结构给出了有效的最大似然译码算法。     

On the Coding Gain of Linear Binary Block Codes

The coding gain of linear binary block codes on the AWGN channel is studied. Antipodal signaling and hard decision demodulation are assumed. Simple asymptotic expressions for the gain at high and low energy to noise spectral density ratios are derived. Monotonicity of the coding gain is also discussed.     

低码率二进制线性分组码的盲识别

针对信息截获领域中的低码率二进制分组码的盲识别问题,提出了根据码重分布距离估计码长的方法,进而通过改进传统的矩阵化简方法获得生成矩阵,实现了对低码率二进制线性分组码的盲识别。理论推算和数据仿真都表明,本算法在较高误码率的情况下,也可以得到很好的识别效果。