Joint Source and Channel Coding using Punctured Ring Convolutional Coded CPM

In this paper, a novel trellis source encoding scheme based on punctured ring convolutional codes is presented. Joint source and channel coding (JSCC) using trellis coded continuous phase modulation (CPM) with punctured convolutional codes over rings is investigated. The channels considered are the additive white gaussian noise (AWGN) channel and the Rayleigh fading channel. Optimal soft decoding for the proposed JSCC scheme is studied. The soft decoder is based on the a posteriori probability (APP) algorithm for trellis coded CPM with punctured ring convolutional codes. It is shown that these systems with soft decoding outperform the same systems with hard decoding especially when the systems operate at low to medium signal-to-noise ratio (SNR). Furthermore, adaptive JSCC approaches based on the proposed source coding scheme are investigated. Compared with JSCC schemes with fixed source coding rates, the proposed adaptive approaches can achieve much better performance in the high SNR region. The novelties of this work are the development of a trellis source encoding method based on punctured ring convolutional codes, the use of a soft decoder, the APP algorithm for the combined systems and the adaptive approaches to the JSCC problem.     

Complexity Reduction in SISO Decoding of Block Codes

SISO decoding for block codes can be carried out based on a trellis representation of the code. However, the complexity entailed by such decoding is most often prohibitive and thus prevents practical implementation. This paper examines a new decoding scheme based on the soft-output Viterbi algorithm (SOVA) applied to a sectionalized trellis for linear block codes. The computational complexities of the new SOVA decoder and of the conventional SOVA decoder, based on a bit-level trellis, are theoretically analyzed and derived for different linear block codes. These results are used to obtain optimum sectionalizations of a trellis for SOVA. For comparisons, the optimum sectionalizations for Maximum A Posteriori (MAP) and Maximum Logarithm MAP (Max-Log-MAP) algorithms, and their corresponding computational complexities are included. The results confirm that the new SOVA decoder is the most computationally efficient SISO decoder, in comparisons to MAP and Max-Log-MAP algorithms. The simulation results of the bit error rate (BER) performance, assuming binary phase -- shift keying (BPSK) and additive white Gaussian noise (AWGN) channel, demonstrate that the performance of the new decoding scheme is not degraded. The BER performance of iterative SOVA decoding of serially concatenated block codes shows no difference in the quality of the soft outputs of the new decoding scheme and of the conventional SOVA.     

Iterative decoding of serially concatenated arithmetic and channel codes with JPEG 2000 applications.

In this paper, an innovative joint-source channel coding scheme is presented. The proposed approach enables iterative soft decoding of arithmetic codes by means of a soft-in soft- out decoder based on suboptimal search and pruning of a binary tree. An error-resilient arithmetic coder with a forbidden symbol is used in order to improve the performance of the joint source/channel scheme. The performance in the case of transmission across the AWGN channel is evaluated in terms of word error probability and compared to a traditional separated approach. The interleaver gain, the convergence property of the system, and the optimal source/channel rate allocation are investigated. Finally, the practical relevance of the proposed joint decoding approach is demonstrated within the JPEG 2000 coding standard. In particular, an iterative channel and JPEG 2000 decoder is designed and tested in the case of image transmission across the AWGN channel.     

RS码与LDPC码的联合迭代译码

针对RS码与LDPC码的串行级联结构,提出了一种基于自适应置信传播(ABP)的联合迭代译码方法.译码时,LDPC码置信传播译码器输出的软信息作为RS码ABP译码器的输入;经过一定迭代译码后,RS码译码器输出的软信息又作为LDPC译码器的输入.软输入软输出的RS译码器与LDPC译码器之间经过多次信息传递,译码性能有很大提高.码长中等的LDPC码采用这种级联方案,可以有效克服短环的影响,消除错误平层.仿真结果显示:AWGN信道下这种基于ABP的RS码与LDPC码的联合迭代译码方案可以获得约0.8 dB的增益.     

Soft-decision COVQ for turbo-coded AWGN and Rayleigh fadingchannels

A robust soft-decision channel-optimized vector quantization (COVQ) scheme for turbo coded additive white Gaussian noise (AWGN) and Rayleigh fading channels is proposed, The log likelihood ratio (LLR) generated by the turbo decoder is exploited via the use of a q-bit scalar soft-decision demodulator. The concatenation of the turbo encoder, modulator, AWGN channel or Rayleigh fading channel, turbo decoder, and q-bit soft-decision demodulator is modeled as an expanded discrete memoryless channel (DMC). A COVQ scheme for this expanded discrete channel is designed. Numerical results indicate substantial performance improvements over traditional tandem coding systems, COVQ schemes designed for hard-decision demodulated turbo coded channels (q=1), as well as performance gains over a recent soft decoding COVQ scheme by Ho (see IEEE Commun. Lett., vol.3, p.208-10, 1999)     

Lattice coding and decoding achieve the optimal diversity-multiplexing tradeoff of MIMO channels

This paper considers communication over coherent multiple-input multiple-output (MIMO) flat-fading channels where the channel is only known at the receiver. For this setting, we introduce the class of LAttice Space-Time (LAST) codes. We show that these codes achieve the optimal diversity-multiplexing tradeoff defined by Zheng and Tse under generalized minimum Euclidean distance lattice decoding. Our scheme is based on a generalization of Erez and Zamir mod-/spl Lambda/ scheme to the MIMO case. In our construction the scalar "scaling" of Erez-Zamir and Costa Gaussian "dirty-paper" schemes is replaced by the minimum mean-square error generalized decision-feedback equalizer (MMSE-GDFE). This result settles the open problem posed by Zheng and Tse on the construction of explicit coding and decoding schemes that achieve the optimal diversity-multiplexing tradeoff. Moreover, our results shed more light on the structure of optimal coding/decoding techniques in delay-limited MIMO channels, and hence, open the door for novel approaches for space-time code constructions. In particular, 1) we show that MMSE-GDFE plays a fundamental role in approaching the limits of delay-limited MIMO channels in the high signal-to-noise ratio (SNR) regime, unlike the additive white Gaussian noise (AWGN) channel case and 2) our random coding arguments represent a major departure from traditional space-time code designs based on the rank and/or mutual information design criteria.     

A soft-output decoding algorithm for concatenated systems

In order to fully utilize the SDD (soft-decision decoding) capacity of the outer codes in a concatenated system, reliability information on the inner decoder outputs (called soft outputs) needs to be provided to the outer decoder. This paper shows that a modified MAP algorithm can be effectively and accurately used to generate such information. In the course of the presentation, a metric based on the reliability information is proposed for the outer decoder. This metric has the Euclidean metric on AWGN channels as its special case, which leads to the concept of generalized SDD (GSDD). Several practical concerns regarding the proposed soft-output decoder are addressed through theoretical analysis and simulation: the effect of finite decoding depth, computational complexity, range overflow, and scaling. Comparisons to previous work on soft-output decoders are made     

Performance evaluation of superorthogonal turbo codes in AWGN andflat Rayleigh fading channels

Turbo codes are parallel concatenated codes whose performance in the additive white Gaussian noise (AWGN) channel has been shown to be near the theoretical limit. In this paper, we describe a low-rate superorthogonal turbo code that combines the principles of low-rate convolutional coding and that of parallel concatenation. Due to the bandwidth expansion, this code outperforms the ordinary turbo code both in AWGN and especially in fading channels. Thus, superorthogonal turbo codes are suited mainly for spread-spectrum applications. For the purposes of iterative decoding, we concisely describe the connection between the optimal maximum a posteriori symbol estimation and suboptimal soft-output decoding based on sequence estimation. The suboptimal decoder produces outputs that can directly be used as additive metrics at successive decoding iterations, without the need for estimating channel noise variance. Simulation results in AWGN and flat Rayleigh fading channels are also presented, along with analytical upper bounds of bit- and frame-error probabilities     

Improved Turbo Decoding Using Soft Combining Principle

One great challenge in wireless communication systems is to ensure reliable communications. Turbo codes are known by their interesting capabilities to deal with transmission errors. In this paper, we present a novel turbo decoding scheme based on soft combining principle. Our method improves decoding performance using soft combining technique inside the turbo decoder. Working on Max-Log-Maximum a Posteriori (Max-Log-MAP) turbo decoding algorithm and using an Additive White Gaussian Noise (AWGN) channel model and 16 Quadrature Amplitude Modulation (16QAM), simulation results show that the suggested solution is efficient and outperforms the conventional Max-Log-MAP algorithm in terms of Bit Error Rate (BER). The performance analysis is carried out in terms of BER by varying parameters such as the Energy per bit to Noise power spectral density ratio ( \(\text {E}_{\text {b}}/\text {N}_{\text {o}}\) ), and decoding iterations number. We call our proposed solution Soft Combined Turbo Codes.     

一种低译码复杂度的Turbo架构LDPC码

针对低密度奇偶校验(LDPC)码较大的译码复杂度和RAM占用,该文提出了一种低译码复杂度的Turbo架构LDPC码并行交织级联Gallager码 (Parallel Interleaved Concatenated Gallager Code,PICGC)。该文给出了PICGC的设计方法和编译码算法,并分析比较了PICGC译码器与LDPC译码器所需的RAM存储量,推导出RAM节省比的上界。理论分析和仿真结果表明,PICGC以纠错性能略微降低为代价,有效地降低译码复杂度和RAM存储量,且译码时延并未增加,是一种有效且易于实现的信道编码方案。     

Quantization loss in convolutional decoding

The loss in quantizing coded symbols in the additive white Gaussian noise (AWGN) channel with binary phase-shift keying (BPSK) or quadrature phase-shift keying (QPSK) modulation is discussed. A quantization scheme and branch metric calculation method are presented. For the uniformly quantized AWGN channel, cutoff rate is used to determine the step size and the smallest number of quantization bits needed for a given bit-signal-to-noise ratio (E_b/N₀) loss. A nine-level quantizer is presented, along with 3-b branch metrics for a rate-1/2 code, which causes an E_b/N₀ loss of only 0.14 dB. These results also apply to soft-decision decoding of block codes. A tight upper bound is derived for the range of path metrics in a Viterbi decoder. The calculations are verified by simulations of several convolutional codes, including the memory-14, rate-1/4 or -1/6 codes used by the big Viterbi decoders at JPL     

Generalization of chase algorithms for soft decision decoding of binary linear codes

Soft decision decoding of binary linear block codes transmitted over the additive white Gaussian channel (AWGN) using antipodal signaling is considered. A set of decoding algorithms called generalized Chase algorithms is proposed. In contrast to Chase algorithms, which require alfloor (d- 1)/2 rfloorbinary error-correcting decoder for decoding a binary linear block code of minimum distanced, the generalized Chase algorithms can use a binary decoder that can correct less thanlfloor ( d - 1)/2 rfloorhard errors. The Chase algorithms are particular cases of the generalized Chase algorithms. The performance of all proposed algorithms is asymptotically optimum for high signal-to-noise ratio (SNR). Simulation results for the(47, 23)quadratic residue code indicate that even for low SNR the performance level of a maximum likelihood decoder can be approached by a relatively simple decoding procedure.     

基于重复累积码的BICM系统译码算法

重复累积码(RA)由于其编译码复杂度低、性能接近香农限的优点,目前得到学术界的广泛关注。文中研究了RA码及其译码算法,并将其应用于比特交织编码调制(BICM)系统。针对低信噪比下基于RA码的编码调制系统误码率较高的问题,提出了一种改进算法,该算法通过在解调器和译码器之间引入迭代处理,利用译码器输出的外信息改善解映射结果,从而降低了系统误码率。仿真结果表明,在加性高斯白噪声(AWGN)信道、瑞利(Rayleigh)衰落信道下,BICM系统使用迭代的译码算法与原算法相比,误码性能有较明显提高。     

On coding without restrictions for the AWGN channel

Many coded modulation constructions, such as lattice codes, are visualized as restricted subsets of an infinite constellation (IC) of points in the n-dimensional Euclidean space. The author regards an IC as a code without restrictions employed for the AWGN channel. For an IC the concept of coding rate is meaningless and the author uses, instead of coding rate, the normalized logarithmic density (NLD). The maximum value C_∞ such that, for any NLD less than C_∞, it is possible to construct an PC with arbitrarily small decoding error probability, is called the generalized capacity of the AWGN channel without restrictions. The author derives exponential upper and lower bounds for the decoding error probability of an IC, expressed in terms of the NLD. The upper bound is obtained by means of a random coding method and it is very similar to the usual random coding bound for the AWGN channel. The exponents of these upper and lower bounds coincide for high values of the NLD, thereby enabling derivation of the generalized capacity of the AWGN channel without restrictions. It is also shown that the exponent of the random coding bound can be attained by linear ICs (lattices), implying that lattices play the same role with respect to the AWGN channel as linear-codes do with respect to a discrete symmetric channel     

Performance of sphere decoding of block codes

A sphere decoder searches for the closest lattice point within a certain search radius. The search radius provides a tradeoff between performance and complexity. We focus on analyzing the performance of sphere decoding of linear block codes. We analyze the performance of soft-decision sphere decoding on AWGN channels and a variety of modulation schemes. A hard-decision sphere decoder is a bounded distance decoder with the corresponding decoding radius. We analyze the performance of hard-decision sphere decoding on binary and q-ary symmetric channels. An upper bound on the performance of maximum-likelihood decoding of linear codes defined over F_q (e.g. Reed- Solomon codes) and transmitted over q-ary symmetric channels is derived and used in the analysis.We then discuss sphere decoding of general block codes or lattices with arbitrary modulation schemes. The tradeoff between the performance and complexity of a sphere decoder is then discussed.     

On acceptance criterion for efficient successiveerrors-and-erasures decoding of Reed-Solomon and BCH codes

We describe an efficient algorithm for successive errors-and-erasures decoding of BCH codes. The decoding algorithm consists of finding all necessary error locator polynomials and errata evaluator polynomials, choosing the most appropriate error locator polynomial and errata evaluator polynomial, using these two polynomials to compute a candidate codeword for the decoder output, and testing the candidate for optimality via an originally developed acceptance criterion. Even in the most stringent case possible, the acceptance criterion is only a little more stringent than Forney's (1966) criterion for generalised minimum distance (GMD) decoding. We present simulation results on the error performance of our decoding algorithm for binary antipodal signals over an AWGN channel and a Rayleigh fading channel. The number of calculations of elements in a finite field that are required by our algorithm is only slightly greater than that required by hard-decision decoding, while the error performance is almost as good as that achieved with GMD decoding. The presented algorithm is also applicable to efficient decoding of product RS codes     

A robust Viterbi decoder and its application to terrestrial HDTVbroadcasting

The conventional Viterbi (1967) decoder employing the Euclidean distance has been widely used and considered as the optimum one in the sense of maximum likelihood sequence decoding under the hypothesis of additive white Gaussian noise (AWGN). However, what will happen if the noise distributions of actual channels deviate from the assumed AWGN? A robust Viterbi decoder utilizing absolute distance is carefully examined. Analytical and numerical results show that this Viterbi decoder is more advantageous than the conventional Viterbi decoder for actual channels with various kinds of interference, particularly in the presence of impulsive noise. Finally the robust Viterbi decoder is applied to TCM-8VSB terrestrial HDTV broadcasting, achieving 0.5-1.0 dB SNR gains over the conventional Viterbi decoder on contaminated AWGN channels     

Adaptive multidimensional coded modulation over flat fadingchannels

We introduce a general adaptive coding scheme for Nakagami multipath fading channels. An instance of the coding scheme utilizes a set of 2L-dimensional (2L-D) trellis codes originally designed for additive white Gaussian noise (AWGN) channels. Any set of 2L-D trellis codes for AWGN channels can be used, Sets for which all codes can be generated by the same encoder and decoded by the same decoder are of particular interest. A feedback channel between the transmitter and receiver makes it possible to transmit at high spectral efficiencies under favorable channel conditions and respond to channel degradation through a smooth reduction of the spectral efficiency. We develop a general technique to determine the average spectral efficiency of the coding scheme for any set of 2L-D trellis codes. As an illustrative example, we calculate the average spectral efficiency of an adaptive codec utilizing eight 4-D trellis codes. The example codec is based on the International Telecommunications Union's ITU-T V.34 modem standard     

An FPGA Implementation of High‐Speed Flexible 27‐Mbps 8‐StateTurbo Decoder

In this paper, we propose a flexible turbo decoding algorithm for a high order modulation scheme that uses a standard half‐rate turbo decoder designed for binary quadrature phase‐shift keying (B/QPSK) modulation. A transformation applied to the incoming I‐channel and Q‐channel symbols allows the use of an off‐the‐shelf B/QPSK turbo decoder without any modifications. Iterative codes such as turbo codes process the received symbols recursively to improve performance. As the number of iterations increases, the execution time and power consumption also increase. The proposed algorithm reduces the latency and power consumption by combination of the radix‐4, dual‐path processing, parallel decoding, and early‐stop algorithms. We implement the proposed scheme on a field‐programmable gate array and compare its decoding speed with that of a conventional decoder. The results show that the proposed flexible decoding algorithm is 6.4 times faster than the conventional scheme.     

基于LDPC码的BICM系统性能分析

低密度校验码(LDPC)由于其编码增益高、译码速度快、性能接近香农限的优点,目前得到学术界的广泛关注.文中简单介绍了LDPC码及其译码算法,在此基础上结合比特交织编码调制(BICM)系统,并在算法上作出了相应改进.仿真结果表明,在高斯信道、充分交织瑞利信道、相关瑞利衰落信道下,此算法正确有效.