Hybrid ARQ scheme using interleaved Reed-Solomon codes in apower-controlled DS-CDMA cellular system

A new hybrid automatic repeat request (ARQ) scheme is proposed for data transmission in a power-controlled direct sequence (DS) code division multiple access (CDMA) system cellular system. The data frame is composed of interleaved Reed-Solomon codes. The depth of interleaving is determined by a power-control interval. After decoding each codeword with algebraic decoding, the post-decoding processor decides whether to accept the codeword or to discard it by using channel state information from the power-control processor. The proposed hybrid ARQ scheme significantly reduces the probability of undetected error among accepted codewords without significantly reducing the throughput     

A Decoding Algorithm for Turbo Product Codes Using Optimality Test and Amplitude Clipping

This paper presents an iterative soft-input/soft-output (SISO) decoderfor product code using optimality test and amplitude clipping. A modifiedexpression for computing the soft-output of SISO decoder is proposed.The correlation discrepancy is employed to provide an optimality teston the decision codeword. The optimality test is performed in rowand column decoding to evaluate the reliability of row and columndecision codewords. Based on the optimality test, the variable reliabilityfactor is introduced for optimization of turbo decoding. A stoppingcriterion with very little performance degradation is also designedfor turbo decoding of product codes by using the optimality test.Besides, the amplitude clipping is employed to improve the performanceof turbo product code. Simulation results on the performance of theintroduced SISO decoder are presented.     

Variable-rate coding for meteor-burst communications

The performance of variable-rate Reed-Solomon error-control coding for meteor-burst communications is considered. The code rate is allowed to vary from codeword to codeword within each packet, and the optimum number of codewords per packet and optimum rates for the codewords are determined as a function of the length of the message and the decay rate for the meteor trail. The resulting performance is compared to that obtained from, fixed-rate coding. Of central importance is the derivation of tractable expressions for the probability of correct decoding for bounded-distance decoding on a memoryless channel with a time-varying symbol error probability. A throughout measure is developed that is based on the probability distribution of the initial signal-to-noise ratio     

Permuted M-matrices for the reduction of phase-induced intensity noise in optical CDMA network

Two codeword families and the corresponding encoder/decoder schemes are present for spatial/frequency optical code-division multiple-access communications. These 2-D codewords have multiple weights per row and can be encoded/decoded via compact hardware. With the proposed decoding mechanism, the intended user will reject interfering users and multiple-access interference is fully eliminated. In addition, the power of the same wavelength contributed by all interfering codewords is split and detected by distinct photodiodes in the decoder. Thus the performance degradation due to the beat noise arising in the photodetecting process is improved, as compared with the traditional 1-D coding scheme, and a larger number of active users is supported under a given bit-error rate.     

纠正随机错误与长突发删除的多进制乘积码研究

考虑多进制LDPC码的符号特性，以及对其残留错误和删除的分析，本文采用多进制LDPC码作为内码，相同Galois域下的高码率RS码作为外码来构造多进制乘积码；并提出了一种低复杂度的迭代译码方案，减少信息传输的各类错误。在译码时，只对前一次迭代中译码失败的码字执行译码，并对译码正确码字所对应的比特初始概率信息进行修正，增强下一次迭代多进制LDPC译码符号先验信息的准确性，减少内码译码后的判决错误，从而充分利用外码的纠错能力。仿真结果显示，多进制乘积码相较于二进制LDPC乘积码有较大的编码增益，并通过迭代进一步改善了性能，高效纠正了信道中的随机错误和突发删除。对于包含2%突发删除的高斯信道，在误比特率为10-6时，迭代一次有0.4 dB左右的增益。      

Multiple-symbol parallel decoding for variable length codes

In this paper, a multiple-symbol parallel variable length decoding (VLD) scheme is introduced. The scheme is capable of decoding all the codewords in an N-bit block of encoded input data stream. The proposed method partially breaks the recursive dependency related to the VLD. First, all possible codewords in the block are detected in parallel and lengths are returned. The procedure results redundant number of codeword lengths from which incorrect values are removed by recursive selection. Next, the index for each symbol corresponding the detected codeword is generated from the length determining the page and the partial codeword defining the offset in symbol table. The symbol lookup can be performed independently from symbol table. Finally, the sum of the valid codeword lengths is provided to an external shifter aligning the encoded input stream for a new decoding cycle. In order to prove feasibility and determine the limiting factors of our proposal, the variable length decoder has been implemented on an field-programmable gate-array (FPGA) technology. When applied to MPEG-2 standard benchmark scenes, on average 4.8 codewords are decoded per cycle resulting in the throughput of 106 million symbols per second.     

Design and analysis of transmitter diversity using intentionalfrequency offset for wireless communications

Coded modulation (usually with interleaving) is used in fading channel communications to achieve a good error performance. The major benefit from using coded modulation in fading channels is achieved if each code symbol of a codeword (or coded sequence) suffers statistically different fading (preferably independent fading). However, in many applications of mobile communications (e.g., in a metropolitan environment), a low vehicle speed (and hence, a small Doppler spread, f _D) is very common. With a small Doppler spread, ideal or close-to-ideal interleaving is no longer feasible and all code symbols of a codeword would suffer highly correlated fading especially in stationary fading (f_D≈0). Coded modulations will thus suffer seriously degraded performance. Previous performance analyses based on ideal interleaving are not accurate when a small Doppler spread is encountered and the much used union bound error probability analysis is loose for small Doppler spreads. To rectify this situation, this paper presents an improved performance analysis of coded modulations with correlated fading and pilot-symbol-assisted modulation (PSAM). Transmitter diversity can generate the necessary time-varying fading to maintain the effectiveness of a coded signaling scheme which this paper examines in detail using an intentional frequency offset between antennas. This work found that proper selections of the intentional frequency offset and interleaving depth can lead to good performance with traditional coded modulations (if enough antennas are used) using essentially the same simple demodulation structure as used in the traditional single-antenna PSAM     

Improved upper bound for the redundancy of fix-free codes

A variable-length code is a fix-free code if no codeword is a prefix or a suffix of any other codeword. In a fix-free code, any finite sequence of codewords can be decoded in both directions, which can improve the robustness to channel noise and speed up the decoding process. In this paper, we prove a new sufficient condition of the existence of fix-free codes and improve the upper bound on the redundancy of optimal fix-free codes.     

Reliability-based code-search algorithms for maximum-likelihooddecoding of block codes

Efficient code-search maximum-likelihood decoding algorithms, based on reliability information, are presented for binary Linear block codes. The codewords examined are obtained via encoding. The information set utilized for encoding comprises the positions of those columns of a generator matrix G of the code which, for a given received sequence, constitute the most reliable basis for the column space of G. Substantially reduced computational complexity of decoding is achieved by exploiting the ordering of the positions within this information set. The search procedures do not require memory; the codeword to be examined is constructed from the previously examined codeword according to a fixed rule. Consequently, the search algorithms are applicable to codes of relatively large size. They are also conveniently modifiable to achieve efficient nearly optimum decoding of particularly large codes     

Collaborative Decoding of Interleaved Reed–Solomon Codes and Concatenated Code Designs

Interleaved Reed-Solomon codes are applied in numerous data processing, data transmission, and data storage systems. They are generated by interleaving several codewords of ordinary Reed-Solomon codes. Usually, these codewords are decoded independently by classical algebraic decoding methods. However, by collaborative algebraic decoding approaches, such interleaved schemes allow the correction of error patterns beyond half the minimum distance, provided that the errors in the received signal occur in bursts. In this work, collaborative decoding of interleaved Reed-Solomon codes by multisequence shift-register synthesis is considered and analyzed. Based on the framework of interleaved Reed-Solomon codes, concatenated code designs are investigated, which are obtained by interleaving several Reed-Solomon codes, and concatenating them with an inner code.     

Parallel lookahead algorithms for pruned interleavers

In this letter, the design of efficient parallel pruned channel and turbo interleavers for Ultra Mobile Broadband (UMB) physical layer standard [1] is addressed. Channel interleaving is based on a bit-reversal algorithm in which addresses are mapped from linear order into bit-reversed order. Turbo interleaving is based on filling a 2D array row by row, interleaving each row independently using a linear congruential sequence (LCS), bit-reversing the order of the rows, and then reading the interleaved addresses column by column. To accommodate for flexible codeword lengths L, interleaving is done using a mother interleaver of length M = 2ⁿ, where n is the smallest integer such that L ⩽ M, such that outlier interleaved addresses greater than L - 1 get pruned away. This pruning operation creates a serial bottleneck since the interleaved address of a linear address χ is now a function of the interleaving operation as well as the number of pruned addresses up to χ. A generic parallel lookahead pruned interleaving scheme that breaks this dependency is proposed. The efficiency of the proposed scheme is demonstrated in the context of both UMB interleavers. An iterative pruned bit-reversal algorithm that interleaves any address in O(log L) steps is presented. Moreover, an iterative pruned turbo interleaving algorithm based on LCSs that interleaves any address in O(log² L) steps is presented.     

Composition bounds for channel block codes

The performance of Channel block codes for a general channel is studied by examining the relationship between the rate of a code, the joint composition of pairs of codewords, and the probability of decoding error. At fixed rate, lower bounds and upper bounds, both on minimum Bhattacharyya distance between codewords and on minimum equivocation distance between codewords, are derived. These bounds resemble, respectively, the Gilbert and the Elias bounds on the minimum Hamming distance between codewords. For a certain large class of channels, a lower bound on probability of decoding error for low-rate channel codes is derived as a consequence of the upper bound on Bhattacharyya distance. This bound is always asymptotically tight at zero rate. Further, for some channels, it is asymptotically tighter than the straight line bound at low rates. Also studied is the relationship between the bounds on codeword composition for arbitrary alphabets and the expurgated bound for arbitrary channels having zero error capacity equal to zero. In particular, it is shown that the expurgated reliability-rate function for blocks of letters is achieved by a product distribution whenever it is achieved by a block probability distribution with strictly positive components.     

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     

迭代译码的级联Reed-Solomon乘积码与卷积码

该文提出用Reed Solomon(RS)乘积码作为外码,卷积码作为内码的级联码方案并且内外码间用Congruential向量生成的交织图案对RS码符号进行重排列。对此级联码采用的迭代译码基于成员码的软译码算法。当迭代次数达到最大后,通过计算RS码的校正子,提出一种纠正残余错误的方法,进一步提高了系统的误比特性能。仿真结果表明,在AWGN信道中与迭代译码的级联RS/卷积码相比,当误比特率为1e-5时,新系统的编码增益大约有0.4 dB。     

IEEE802.16e中的BTC码编译码方案

介绍了BTC码的基本概念以及IEEE802.16e协议中的BTC编码方案,给出BTC迭代译码、每次行/列SISO译码以及扩展Hamming子码的硬判决译码方案,给出基于该译码方案的仿真结果.     

数字全息数据存储系统中的格雷映射等重调制码的设计

在数字全息数据存储系统的记录通道中,使用二进制映射等重调制码有利于信号的检测.本文作者提出了6:8格雷映射等重调制码的编码方案,将每6比特数据视为一个格雷码字,而相应的等重码设计为具有2单位距离特性.当检测到的8比特码字中发生一个2码元交换错误时,该方案具有一定的容错能力.误码性能的仿真结果表明,在系统的信噪比较低时6:8格雷映射等重调制码优于6:8二进制映射等重调制码.     

Computing upper bounds to error probability of soft-decision decoding of Reed-Solomon codes based on the ordered statistics algorithm

This correspondence presents performance analysis of symbol-level soft-decision decoding of q-ary maximum-distance-separable (MDS) codes based on the ordered statistics algorithm. The method we present is inspired by the one recently proposed by Agrawal and Vardy (2000), who approximately evaluate the performance of generalized minimum-distance decoding. The correspondence shows that in our context, the method allows us to compute the exact value of the probability that the transmitted codeword is not one of the candidate codewords. This leads to a close upper bound on the performance of the decoding algorithm. Application of the ordered statistics algorithm to MDS codes is not new. Nevertheless, its advantages seem not to be fully explored. We show an example where the decoding algorithm is applied to singly extended 16-ary Reed-Solomon (RS) codes in a 128-dimensional multilevel coded-modulation scheme that approaches the sphere lower bound within 0.5 dB at the word error probability of 10/sup -4/ with manageable decoding complexity.     

Differential Distributed Space-Time Modulation for Cooperative Networks

In this paper, we develop a protocol for the construction of cooperative networks when the channel state information is not available at the transmitters and the receivers. In the proposed protocol, differential space-time codewords are generated at the source terminal. In the broadcast phase, each row of the differential space-time codeword is transmitted to a different relay, whereas in the relay phase, the relaying terminals retransmit the codeword through simple amplify-and-forward algorithm. The performance of the cooperative diversity system is analyzed for a two-user case for different channel environments in. terms of the diversity gain and the diversity product. The optimization of the power allocation between source and relay terminals is considered for the maximization of the diversity product. When the same modulation scheme is used, the performance of differential detection is degraded by 3 dB noise enhancement compared with coherent detection     

Implementation of a High Throughput 3GPP Turbo Decoder on GPU

Turbo code is a computationally intensive channel code that is widely used in current and upcoming wireless standards. General-purpose graphics processor unit (GPGPU) is a programmable commodity processor that achieves high performance computation power by using many simple cores. In this paper, we present a 3GPP LTE compliant Turbo decoder accelerator that takes advantage of the processing power of GPU to offer fast Turbo decoding throughput. Several techniques are used to improve the performance of the decoder. To fully utilize the computational resources on GPU, our decoder can decode multiple codewords simultaneously, divide the workload for a single codeword across multiple cores, and pack multiple codewords to fit the single instruction multiple data (SIMD) instruction width. In addition, we use shared memory judiciously to enable hundreds of concurrent multiple threads while keeping frequently used data local to keep memory access fast. To improve efficiency of the decoder in the high SNR regime, we also present a low complexity early termination scheme based on average extrinsic LLR statistics. Finally, we examine how different workload partitioning choices affect the error correction performance and the decoder throughput.     

Iterative decoding with a hamming threshold for block turbo codes

This work introduces a novel approach to increase the performance of block turbo codes (BTCs). The idea is based on using a Hamming threshold to limit the search for the maximum-likelihood (ML) codeword within only those codewords that lie within this threshold. The proposed iterative decoding approach is shown to offer both significant coding gain and complexity reduction over the standard iterative decoding methods.