三维TPC译码器的设计及FPGA实现

Turbo乘积码（TPC）是一种性能优秀的纠错编码方法,它具有译码复杂度低、译码延时小等优点,且在低信噪比下可以获得近似最优的性能。介绍了基于Chase算法的三维TPC软输入软输出（SISO）迭代译码算法,提出了三维TPC译码器硬件设计方案并在FPGA芯片上进行了仿真和验证。测试结果表明,该译码器具有较高的纠错能力,满足移动通信误码率的要求。     

Iterative Decoding of Multiple-Step Majority Logic Decodable Codes

We investigate the performance of iterative decoding algorithms for multistep majority logic decodable (MSMLD) codes of intermediate length. We introduce a new bit-flipping algorithm that is able to decode these codes nearly as well as a maximum-likelihood decoder on the binary-symmetric channel. We show that MSMLD codes decoded using bit-flipping algorithms can outperform comparable Bose-Chaudhuri-Hocquenghem (BCH) codes decoded using standard algebraic decoding algorithms, at least for high bit-flip rates (or low and moderate signal-to-noise ratios (SNRs)).     

Near-optimum decoding of product codes: block turbo codes

This paper describes an iterative decoding algorithm for any product code built using linear block codes. It is based on soft-input/soft-output decoders for decoding the component codes so that near-optimum performance is obtained at each iteration. This soft-input/soft-output decoder is a Chase decoder which delivers soft outputs instead of binary decisions. The soft output of the decoder is an estimation of the log-likelihood ratio (LLR) of the binary decisions given by the Chase decoder. The theoretical justifications of this algorithm are developed and the method used for computing the soft output is fully described. The iterative decoding of product codes is also known as the block turbo code (BTC) because the concept is quite similar to turbo codes based on iterative decoding of concatenated recursive convolutional codes. The performance of different Bose-Chaudhuri-Hocquenghem (BCH)-BTCs are given for the Gaussian and the Rayleigh channel. Performance on the Gaussian channel indicates that data transmission at 0.8 dB of Shannon's limit or more than 98% (R/C>0.98) of channel capacity can be achieved with high-code-rate BTC using only four iterations. For the Rayleigh channel, the slope of the bit-error rate (BER) curve is as steep as for the Gaussian channel without using channel state information     

A low-complexity receiver for iterative parallel interference cancellation and decoding in MIMO–OFDM systems

A novel low-complexity iterative receiver for coded multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems is proposed in this letter. The soft-in soft-out (SISO) detector is simply a parallel interference cancellation (PIC)–maximum ratio combining (MRC) operation. However, system performance would be degraded because of ignoring the existence of the residual interference from other transmit antennas. In our scheme, the log likelihood ratios (LLRs) of encoded bits after channel decoding are multiplied by a constant factor to achieve a performance gain. The constant factor is optimized according to the extrinsic information transfer (EXIT) chart. Simulation results show that the proposed iterative receiver can significantly improve the system performance and converge to the matched filter bound (MFB) with low computational complexity at high signal-to-noise ratios (SNRs).     

一种低复杂度软入软出迭代检测方案

在MIMO系统中,以软输入软输出方式为基础的迭代检测方式,性能要明显优于基于硬判决的迭代方案。因此基于软信息传递的迭代检测理论具有广泛的应用。但是,其复杂度较高,特别是应用于MIMO系统时,复杂度的限制尤为明显。球形译码是一种近似最大似然检测的低复杂度方案,在这里,引入一种低复杂度的软入软出（SISO）球形译码迭代方案,并给出球形译码中搜索树的删减简化方案。     

Iterative turbo decoder analysis based on density evolution

We track the density of extrinsic information in iterative turbo decoders by actual density evolution, and also approximate it by symmetric Gaussian density functions. The approximate model is verified by experimental measurements. We view the evolution of these density functions through an iterative decoder as a nonlinear dynamical system with feedback. Iterative decoding of turbo codes and of serially concatenated codes is analyzed by examining whether a signal-to-noise ratio (SNR) for the extrinsic information keeps growing with iterations. We define a “noise figure” for the iterative decoder, such that the turbo decoder will converge to the correct codeword if the noise figure is bounded by a number below zero dB. By decomposing the code's noise figure into individual curves of output SNR versus input SNR corresponding to the individual constituent codes, we gain many new insights into the performance of the iterative decoder for different constituents. Many mysteries of turbo codes are explained based on this analysis. For example, we show why certain codes converge better with iterative decoding than more powerful codes which are only suitable for maximum likelihood decoding. The roles of systematic bits and of recursive convolutional codes as constituents of turbo codes are crystallized. The analysis is generalized to serial concatenations of mixtures of complementary outer and inner constituent codes. Design examples are given to optimize mixture codes to achieve low iterative decoding thresholds on the signal-to-noise ratio of the channel     

基于SSCANL译码器的联合迭代检测译码算法

为了提升基于极化码的稀疏码多址接入（sparse code multiple access,SCMA）系统接收机性能,提出了基于简化软消除列表（simplify soft cancellation list,SSCANL）译码器的循环冗余校验（cyclic redundancy check,CRC）辅助联合迭代检测译码接收机方案。该方案中极化码译码器使用SSCANL译码算法,采用译码节点删除技术对软消除列表（soft cancellation list,SCANL）算法所需要的L次软消除译码（soft cancellation, SCAN）进行简化,通过近似删除冻结位节点,简化节点间软信息更新计算过程,从而降低译码算法的计算复杂度。仿真结果表明,SSCANL算法可获得与SCANL算法一致的性能,其计算复杂度与SCANL算法相比有所降低,码率越低,算法复杂度降低效果越好;且基于SSCANL译码器的CRC 辅助联合迭代检测译码接收机方案相较基于SCAN译码器的联合迭代检测译码（joint iterative detection and decoding based on SCAN decoder, JIDD-SCAN）方案、基于SCAN译码器的CRC辅助联合迭代检测译码（CRC aided joint iterative detection and decoding based on SCAN decoder,C-JIDD-SCAN）方案,在误码率为10^-4时,性能分别提升了约0.65 dB、0.59 dB。     

Dynamics and performance analysis of analog iterative decoding for low-density parity-check (LDPC) codes

Conventional iterative decoding with flooding or parallel schedule can be formulated as a fixed-point problem solved iteratively by a successive substitution (SS) method. In this paper, we investigate the dynamics of a continuous-time (asynchronous) analog implementation of iterative decoding, and show that it can be approximated as the application of the well-known successive relaxation (SR) method for solving the fixed-point problem. We observe that SR with the optimal relaxation factor can considerably improve the error-rate performance of iterative decoding for short low-density parity-check (LDPC) codes, compared with SS. Our simulation results for the application of SR to belief propagation (sum-product) and min-sum algorithms demonstrate improvements of up to about 0.7 dB over the standard SS for randomly constructed LDPC codes. The improvement in performance increases with the maximum number of iterations, and by accordingly reducing the relaxation factor. The asymptotic result, corresponding to an infinite maximum number of iterations and infinitesimal relaxation factor, represents the steady-state performance of analog iterative decoding. This means that under ideal circumstances, continuous-time (asynchronous) analog decoders can outperform their discrete-time (synchronous) digital counterparts by a large margin. Our results also indicate that with the assumption of a truncated Gaussian distribution for the random delays among computational modules, the error-rate performance of the analog decoder, particularly in steady state, is rather independent of the variance of the distribution. The proposed simple model for analog decoding, and the associated performance curves, can be used as an "ideal analog decoder" benchmark for performance evaluation of analog decoding circuits.     

Turbo processing for an OFDM-based MIMO system

We consider improving the overall system performance of an orthogonal frequency-division multiplexing-based multiple-input multiple-output (MIMO) wireless local area network system. We use a combined iterative detection/decoding and channel updating method, referred to herein as turbo processing, to improve performance. First, we improve a recently proposed list sphere decoder-based iterative MIMO soft-detector by constraining the value of the a priori information from a soft-in soft-out channel decoder. Second, we propose a channel updating scheme using the decoded packet data to improve the channel estimation accuracy. Simulation results show that turbo processing can be used to significantly improve the performance of the system considered.     

Iterative joint source–channel decoding of H.264 compressed video

This paper proposes an Iterative Joint Source–Channel Decoding (IJSCD) scheme for error resilient transmission of H.264 compressed video over noisy channels by using the available H.264 compression, e.g., Context-based Adaptive Binary Arithmetic Coding (CABAC), and channel coding, i.e., rate-1/2 Recursive Systematic Convolutional (RSC) code, in transmission. At the receiver, the turbo decoding concept is explored to develop a joint source–channel decoding structure using a soft-in soft-out channel decoder in conjunction with the source decoding functions, e.g., CABAC-based H.264 semantic verification, in an iterative manner. Illustrative designs of the proposed IJSCD scheme for an Additive White Gaussian Noise (AWGN) channel, including the derivations of key parameters for soft information are discussed. The performance of the proposed IJSCD scheme is shown for several video sequences. In the examples, for the same desired Peak Signal-to-Noise Ratio (PSNR), the proposed IJSCD scheme offers a savings of up to 2.1 dB in required channel Signal-to-Noise Ratio (SNR) as compared to a system using the same RSC code alone. The complexity of the proposed scheme is also evaluated. As the number of iterations is controllable, a tradeoff can be made between performance improvement and the overall complexity.     

Turbo multiuser detection for differentially modulated CDMA

In this letter, we study differentially modulated, iteratively decoded CDMA. The iterative multiuser receiver proposed consists of an additional soft-input soft-output (SISO) differential decoder, when compared to turbo multiuser detectors for absolutely modulated systems. Algorithms for iterative decoding with and without phase information at the receiver are developed. The resulting turbo receivers with differential modulation outperform coherent receivers with absolute modulation at moderate to high signal to noise ratios due to the interleaver gain associated with recursive inner encoders in serially concatenated encoding structures.     

Novel approaches to signal transmission based on chaotic signalsand artificial neural networks

A novel chaotic-based coding/decoding strategy that exploits radial basis function (RBF) artificial neural networks (ANNs) in a dynamic feedback (DF) configuration is reported. The ANNs are used as pseudochaotic carrier generators and as estimators for the received signal. The dynamics approximated were those of the logistic map (LM). This approach is compared with established methods that employ inversion, dynamic feedback, and least mean square (LMS) and recursive least squares (RLS) estimation. Our RBF-ANN-DF approach is shown to outperform these methods in terms of the recovered signal SNR at various channel SNRs with a speech information signal used as an example. In particular, the RBF-ANN-DF method is shown to outperform DF approaches by about 33 dB at all channel SNRs. Moreover, the proposed RBF-ANN-DF approach offers a recovered signal SNR improvement between about 15.1 and 27.4 dB for channel SNRs between 10 and 50 dB as compared to an LMS-based chaotic receiver. As a by-product, we have also shown that, for the logistic map, LMS- and RLS-based chaotic receivers are equivalent and, hence, the use of LMS-based receivers can result in implementation savings     

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.     

Reduced Complexity Decoding of Space Time Trellis Codes in the Frequency Selective Channel

An iterative approach is developed for decoding Space Time Trellis Codes (STTCs) in frequency selective Multiple Input Multiple Output (MIMO) channels. The method uses the Partitioned Viterbi Algorithm (PVA) as an equaliser for the MIMO system. It is used iteratively with a STTC decoder that provides soft outputs using the Soft Output Viterbi Algorithm (SOVA). It is shown through simulation that the iterative procedure achieves a performance within 2.0dB of Maximum Likelihood (ML) decoding, at a FER of 10^?2, but suffers a small diversity loss. It is also shown that the complexity of the iterative approach is lower than that of ML decoding.     

Serial concatenated coding scheme with minimum shift keying

A novel serially concatenated coding scheme for use with minimum shift keying (MSK) is proposed. The novelty is to use a mixture of recursive and non-recursive realisations for the MSK modulator. It is shown that this improves the performance of iterative demodulation and decoding of convolutionally encoded MSK signals with a slight decrease in the decoder complexity     

Adaptive Channel Estimation Aided Log-Map Turbo Decoder Implementation for DS-CDMA Based Mobile Systems

Practical implementation of convolutional turbo codec is impeded by the difficulty of real-time execution in high transmission rate communication systems due to high computational complexity, iterative block decoding structure, as well as the requirement of accurate on-line channel reliability estimation for maximum-likelihood decoding. Relying on innovative channel estimation techniques involving DS-CDMA specific noise/interference variance estimation and fading channel variation tracking, this paper provides a low-complexity all-digital design of an iterative SISO log-MAP turbo decoder for DS-CDMA based mobile communication systems. The issues of quantization and data flow in both pre-decoder processing module and iterative trellis decoding module are prudently addressed to ensure highly efficient hardware implementation. The efficient design strategies applied confine the decoding complexity while leading to an excellent performance within 0.2 dB of the software decoder.     

OFDM系统中低复杂度联合译码和信道估计方法研究

本文针对OFDM(Orthogonal Frequency Division Multiplexing)系统提出了一种低复杂度联合译码和信道估计算法的接收机。接收机首先通过导频对信道进行估计，然后使用Turbo码译码输出判决信息对信道参数进行稳健的估计。仿真结果表明，即使系统误码率大于10^-2，经过3次迭代估计，系统性能提高仍有0．5-1dB；在高信噪比下，可显著地降低系统的误码底限。本文同时还给出了译码迭代次数对系统性能的影响。     

Approaching Shannon's capacity limit by 0.2 dB using simple Hammingcodes

The authors show that the Shannon capacity limit for the additive white Gaussian noise (AWGN) channel can be approached within 0.27 dB at a bit error rate (BER) of 10^-5 by applying long but simple Hamming codes as component codes to an iterative turbo-decoding scheme. In general, the complexity of soft-in/soft-out decoding of binary block codes is rather high. However, the application of a neurocomputer in combination with a parallelization of the decoding rule facilitates an implementation of the decoding algorithm in the logarithmic domain which requires only matrix additions and multiplications. But the storage requirement might still be quite high depending on the interleavers used     

Turbo multiuser detection for coded DMT VDSL systems

In recent years, iterative processing techniques with soft-in/soft-out components have received considerable attention. Such techniques, based on the so-called turbo principle, are exemplified through turbo decoding, turbo equalization, and turbo multiuser detection. Turbo multiuser detection is applied to a discrete multitone (DMT) very-high-rate digital subscriber line system to combat crosstalk signals and to obtain substantial coding gain. The proposed iterative DMT receiver is shown to achieve an overall 7.0 dB gain over the uncoded optimum receiver at a bit error rate of 10^-7 for a channel with severe intersymbol interference and additive white Gaussian noise and with one dominant crosstalk signal. Impulse noise is detrimental to the proposed scheme but can be overcome through erasure decoding techniques, as is shown by example     

一种改善Turbo乘积编码OFDM系统性能的新方法

本文提出一种利用对译码器软信息限幅来改善多径衰落信道中Turbo乘积编码OFDM(TPC-OFDM)系统性能的新方法。通过对不同多径衰落信道中QPSK映射和16QAM映射的TPC-OFDM系统性能的数值仿真，结果表明在10^-5误比特率下，这种新方法比传统的迭代译码大约有6～10dB的改进，对严重多径环境下TPC-OFDM系统的错误平底也有明显的改进。