IRA码在远程光纤通信系统中的应用

前向纠错码 (FEC)是光纤通信系统提高系统容量的一项关键技术。在远程光纤信道中 ,放大器自发辐射 (ASE)噪声是主要噪声源。FEC在光纤通信系统应用时 ,通常用高斯分布估计ASE噪声。本文提出用x平方律分布模型代替高斯信道模型 ,并将高性能的不规则重复累积 (IRA)码应用于远程光纤通信系统。仿真结果表明 :IRA码的性能优于RS码、Turbo码等 ,而且x平方律信道的性能优于高斯信道。     

Comparison of turbo-code decoders applied to short frametransmission systems

A novel class of binary parallel concatenated recursive systematic convolutional codes termed turbo-codes, having amazing error correcting capabilities, has previously been proposed. However, the decoding of turbo-codes relies on the application of soft input/soft output decoders. Such decoders can be realized either using maximum a posteriori (MAP) symbol estimators or MAP sequence estimators, e.g., the a priori soft output Viterbi algorithm (APRI-SOVA). In this paper, the structure of turbo-code encoders as well as of turbo-code decoders is described. In particular, four different decoder structures are illustratively characterized and their error rate performance capabilities compared in both additive white Gaussian noise (AWGN) as well as flat Rayleigh-fading channels based on extensive simulation results for short frames used for speech transmission in the uplink of a digital mobile radio system applying code division multiple access and joint detection. The decoders are investigated as follows: 1) the MAP symbol estimator-based approach used by Berrou et al. [1993], 2) the MAP symbol estimator-based approach used by Robertson [1994], 3) a new reduced complexity MAP symbol estimator-based approach [Jung 1995], and 4) an APRI-SOVA based approach used by Hagenauer et al. [1994]     

Turbo decoding of simple product codes in a two user binary adder channel employing the Bahl–Cocke–Jelinek–Raviv algorithm

The main goal in this paper is an investigation of the Bahl–Cocke–Jelinek–Raviv (BCJR) algorithm applied in a turbo decoding scheme. Binary product codes are employed in a turbo coding scheme and the channel model considered is the two user binary adder channel (2-BAC) with additive white Gaussian noise. A trellis for two users is constructed for a pair of product codes tailored for use in the 2-BAC in order to employ the BCJR decoding algorithm. Computer simulation is employed to show that product codes on the 2-BAC, employing low-complexity component codes, produces considerable gain with few iterations under iterative BCJR decoding.     

Performance evaluation of list sequence MAP decoding

List-sequence (LS) decoding has the potential to yield significant coding gain additional to that of conventional single-sequence decoding, and it can be implemented with full backward compatibility in systems where an error-detecting code is concatenated with an error-correcting code. LS maximum-likelihood (ML) decoding provides a list of estimated sequences in likelihood order. For convolutional codes, this list can be obtained with the serial list Viterbi algorithm (SLVA). Through modification of the metric increments of the SLVA, an LS maximum a posteriori (MAP) probability decoding algorithm is obtained that takes into account bitwise a priori probabilities and produces an ordered list of sequence MAP estimates. The performance of the resulting LS-MAP decoding algorithm is studied in this paper. Computer simulations and approximate analytical expressions, based on geometrical considerations of the decision domains of LS decoders, are presented. We focus on the frame-error performance of LS-MAP decoding, with genie-assisted error detection, on the additive white Gaussian noise channel. It is concluded that LS-MAP decoding exploits a priori information more efficiently, in order to achieve performance improvements, than does conventional single-sequence MAP decoding. Interestingly, LS-MAP decoding can provide significant improvements at low signal-to-noise ratios, compared with LS-ML decoding. In this environment, it is furthermore observed that feedback convolutional codes offer performance improvements over their feedforward counterparts. Since LS-MAP decoding can be implemented in existing systems at a modest complexity increase, it should have a wide area of applications, such as joint source-channel decoding and other kinds of iterative decoding.     

Coded overlapped code division multiplexing system with Turbo product structure

Coded overlapped code division multiplexing system with Turbo product structure (TPC-OVCDM) is introduced, and trellis coded modulation (TCM) code is employed as error correcting code for uncoded overlapped code division multiplexing (OVCDM) system. In such a scheme, row code and column code are TCM and OVCDM spreading code, respectively. Data bits are only encoded directly by TCM and transformed into a matrix. Each column of this matrix is then permuted by symbol interleaver before being encoded by OVCDM spreading code. During iterative decoding process in the receiver, two constituent decoders use symbol by symbol BCJR algorithm in the log domain. The order of decoding two sub-codes is determined by the encoding order. The proportion of TCM coding and OVCDM coding affects system performance. For fixed coding structure and symbol interleaver, the performance of TPC-OVCDM systems of different proportions of additive white Gaussian noise (AWGN) channel have been simulated. The results show that TPC-OVCDM system of reasonable proportion can achieve significant coding gain, compared with uncoded OVCDM system under the condition of same spectral efficiency at bit error rate (BER) level of 10-5 .     

On the capacity loss due to separation of detection and decoding

The performance loss due to separation of detection and decoding on the binary-input additive white Gaussian noise (AWGN) channel is quantified in terms of mutual information. Results are reported for both the code-division multiple-access (CDMA) channel in the large system limit and the intersymbol interference (ISI) channel. The results for CDMA rely on the replica method developed in statistical mechanics. It is shown that a previous result of Shamai and Verdu found for Gaussian input alphabet holds also for binary input alphabets. For the ISI channel, the performance loss is calculated via the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. Comparisons are made to the capacity of separate detection and decoding using suboptimum detectors such as a decision-feedback equalizer.     

High-Speed Recursion Architectures for MAP-Based Turbo Decoders

The maximum a posterior probability (MAP) algorithm has been widely used in Turbo decoding for its outstanding performance. However, it is very challenging to design high-speed MAP decoders because of inherent recursive computations. This paper presents two novel high-speed recursion architectures for MAP-based Turbo decoders. Algorithmic transformation, approximation, and architectural optimization are incorporated in the proposed designs to reduce the critical path. Simulations show that neither of the proposed designs has observable decoding performance loss compared to the true MAP algorithm when applied in Turbo decoding. Synthesis results show that the proposed Radix-2 recursion architecture can achieve comparable processing speed to that of the state-of-the-art recursion (Radix-4) architecture with significantly lower complexity while the proposed Radix-4 architecture is 32% faster than the best existing design     

Blind turbo multiuser detection for long-code multipath CDMA

We consider the problem of demodulating and decoding multiuser information symbols in an uplink asynchronous coded code-division multiple-access (CDMA) system employing long (aperiodic) spreading sequences, in the presence of unknown multipath channels, out-cell multiple-access interference (OMAI), and narrow-band interference (NBI). A blind turbo multiuser receiver, consisting of a novel blind Bayesian multiuser detector and a bank of MAP decoders, is developed for such a system. The effect of OMAI and NBI is modeled as colored Gaussian noise with some unknown covariance matrix. The main contribution of this paper is to develop blind Bayesian multiuser detectors for long-code multipath CDMA systems under both white and colored Gaussian noise. Such detectors are based on the Bayesian inference of all unknown quantities. The Gibbs sampler, a Markov chain Monte Carlo procedure, is then used to calculate the Bayesian estimates of the unknowns. The blind Bayesian multiuser detector computes the a posteriori probabilities of the channel coded symbols, which are differentially encoded before being sent to the channel. Being soft-input soft-output in nature, the proposed blind Bayesian multiuser detectors and the MAP decoders can iteratively exchange the extrinsic information to successively refine the performance, leading to the so-called blind turbo multiuser receiver     

Iterative multiuser detection for turbo-coded synchronous CDMA inGaussian and non-Gaussian impulsive noise

We develop an iterative multiuser receiver for decoding turbo-coded synchronous code-division multiple-access signals in both Gaussian and non-Gaussian noise. A soft-input soft-output nonlinear multiuser detector is combined with a set of single-user channel decoders in an iterative detection/decoding structure. The nonlinear multiuser detector utilizes the prior probabilities of each user's bits to form soft estimates used for multiple-access interference cancellation. The channel decoders perform turbo-code decoding and produce posterior probabilities which are fed back to the multiuser detector for use as prior probabilities. Simulation results show that the proposed multiuser receiver performs well in both Gaussian and non-Gaussian noise. In particular, single-user turbo-code performance can be approached within a few iterations with medium to low cross correlation (ρ⩽0.5)     

累加交叉并行级联单奇偶校验码的低复杂度译码算法

累加交叉并行级联单奇偶校验(A-CPSPC)码是一种新的纠错编码,其编码结构简单并具有较好的误比特率性能。该文针对A-CPSPC码的局部编码结构提出了一种低复杂度的最大后验(MAP)局部译码算法,该方法利用基于双向消息传递原则的和积算法(SPA)进行局部译码,消除了短环对局部译码性能的影响。分析及仿真表明,传统的置信传播算法并不适用于A-CPSPC码,该文提出的局部译码算法与基于BCJR算法的局部译码算法的性能一致,且复杂度更低。     

Rate-1/2 component codes for nonbinary turbo codes

The iterative decoding structure and component maximum a posteriori decoders used for decoding binary concatenated codes can be extended to the nonbinary domain. This paper considers turbo codes over nonbinary rings, specifically ternary, quaternary, penternary, hexernary, and octernary codes. The best rate-1/2 component codes are determined using a practical search algorithm. The performance of the resulting rate-1/3 turbo codes on an additive white Gaussian noise channel using q-ary phase-shift keying modulation is given.     

Performance of turbo equalizers for optical PMD channels

This paper investigates the performance of iterative (turbo) equalization to mitigate the effects of a polarization-mode dispersion (PMD) in nonreturn-to-zero (NRZ) intensity-modulated optical-fiber transmission systems. A PMD can lead to severe distortions in the received electrical signal and is a key limiter for the development of high-bit-rate transmission over currently used fibers. In order to reduce the distortions due to a PMD, the performance of symbol-by-symbol maximum a posteriori (sbs-MAP) soft-in/soft-out (SISO) decoders is studied. The SISO algorithms are adapted to the noise statistics of the optical channel where the photo detector leads to a non-Gaussian signal-dependent noise at the receiver side. The modified SISO algorithms are successfully employed for turbo equalization and results show that iterative (turbo) equalization and decoding for the compensation of a PMD can lead to a tremendous reduction in the bit error ratio (BER). Moreover, it is shown that, due to the robustness of mutual information, the extrinsic information transfer (EXIT) chart can be applied for the design of iterative receivers in optical transmission systems even with a non-Gaussian noise.     

AWGN信道下Turbo码解码算法的选择

在加性高斯白噪声（AWGN）信道下,采用最大后验概率(MAP)算法的Turbo码解码是误比特率最低的算法。为了降低运算量实现快速解码,Log-MAP算法、Max-Log-Map算法和线性Max-Log-Map算法分别对MAP算法进行了不同程度的简化。本文简单介绍了基于MAP算法的Turbo码解码原理,从纠正函数的角度出发归纳和比较了三种MAP类简化算法,通过纠正函数从理论上对算法性能以及对信噪比估计误差的敏感度进行了分析,对分析结果进行了仿真验证。综合解码性能和运算量,提出了Turbo码解码的算法选择方案,以及实用,简易的Turbo码解码参数设置建议。      

On maximum-likelihood detection and the search for the closest lattice point

Maximum-likelihood (ML) decoding algorithms for Gaussian multiple-input multiple-output (MIMO) linear channels are considered. Linearity over the field of real numbers facilitates the design of ML decoders using number-theoretic tools for searching the closest lattice point. These decoders are collectively referred to as sphere decoders in the literature. In this paper, a fresh look at this class of decoding algorithms is taken. In particular, two novel algorithms are developed. The first algorithm is inspired by the Pohst enumeration strategy and is shown to offer a significant reduction in complexity compared to the Viterbo-Boutros sphere decoder. The connection between the proposed algorithm and the stack sequential decoding algorithm is then established. This connection is utilized to construct the second algorithm which can also be viewed as an application of the Schnorr-Euchner strategy to ML decoding. Aided with a detailed study of preprocessing algorithms, a variant of the second algorithm is developed and shown to offer significant reductions in the computational complexity compared to all previously proposed sphere decoders with a near-ML detection performance. This claim is supported by intuitive arguments and simulation results in many relevant scenarios.     

High performance, high throughput turbo/SOVA decoder design

Two efficient approaches are proposed to improve the performance of soft-output Viterbi (1998) algorithm (SOVA)-based turbo decoders. In the first approach, an easily obtainable variable and a simple mapping function are used to compute a target scaling factor to normalize the extrinsic information output from turbo decoders. An extra coding gain of 0.5 dB can be obtained with additive white Gaussian noise channels. This approach does not introduce extra latency and the hardware overhead is negligible. In the second approach, an adaptive upper bound based on the channel reliability is set for computing the metric difference between competing paths. By combining the two approaches, we show that the new SOVA-based turbo decoders can approach maximum a posteriori probability (MAP)-based turbo decoders within 0.1 dB when the target bit-error rate (BER) is moderately low (e.g., BER<10/sup -4/ for 1/2 rate codes). Following this, practical implementation issues are discussed and finite precision simulation results are provided. An area-efficient parallel decoding architecture is presented in this paper as an effective approach to design high-throughput turbo/SOVA decoders. With the efficient parallel architecture, multiple times throughput of a conventional serial decoder can be obtained by increasing the overall hardware by a small percentage. To resolve the problem of multiple memory accesses per cycle for the efficient parallel architecture, a novel two-level hierarchical interleaver architecture is proposed. Simulation results show that the proposed interleaver architecture performs as well as random interleavers, while requiring much less storage of random patterns.     

High-throughput LDPC decoders

A high-throughput memory-efficient decoder architecture for low-density parity-check (LDPC) codes is proposed based on a novel turbo decoding algorithm. The architecture benefits from various optimizations performed at three levels of abstraction in system design-namely LDPC code design, decoding algorithm, and decoder architecture. First, the interconnect complexity problem of current decoder implementations is mitigated by designing architecture-aware LDPC codes having embedded structural regularity features that result in a regular and scalable message-transport network with reduced control overhead. Second, the memory overhead problem in current day decoders is reduced by more than 75% by employing a new turbo decoding algorithm for LDPC codes that removes the multiple checkto-bit message update bottleneck of the current algorithm. A new merged-schedule merge-passing algorithm is also proposed that reduces the memory overhead of the current algorithm for low to moderate-throughput decoders. Moreover, a parallel soft-input-soft-output (SISO) message update mechanism is proposed that implements the recursions of the Balh-Cocke-Jelinek-Raviv (BCJR) algorithm in terms of simple "max-quartet" operations that do not require lookup-tables and incur negligible loss in performance compared to the ideal case. Finally, an efficient programmable architecture coupled with a scalable and dynamic transport network for storing and routing messages is proposed, and a full-decoder architecture is presented. Simulations demonstrate that the proposed architecture attains a throughput of 1.92 Gb/s for a frame length of 2304 bits, and achieves savings of 89.13% and 69.83% in power consumption and silicon area over state-of-the-art, with a reduction of 60.5% in interconnect length.     

Turbo decoding of quantized data

Much of the work on turbo decoding assumes that the decoder has access to infinitely soft (unquantized) channel data. In practice, however, a quantizer is used at the receiver and the turbo decoder must operate on finite precision, quantized data. Hence, the maximum a posteriori (MAP) component decoder which was designed assuming infinitely soft data is not necessarily optimum when operating on quantized data. We modify the well-known normalized MAP algorithm taking into account the presence of the quantizer. This algorithm is optimum given any quantizer and is no more complex than quantized implementations of the MAP algorithm derived based on unquantized data. Simulation results on an additive white Gaussian noise channel show that, even with four bits of quantization, the new algorithm based on quantized data achieves a performance practically equal to the MAP algorithm operating on infinite precision data     

A pattern recognition framework to blind audio watermark decoding

Conventional blind audio watermark (WM) decoders use matched-filtering techniques because of their simplicity. In these methods, WM decoding and WM detection are often considered as separate problems and the WM signal embedded by spreading a secret key through the spectrum of a host signal is extracted by maximizing correlation between the secret key and the received audio. Conventionally decoding is achieved by using a pre-defined decoding/detection threshold and tradeoff between the false rejection ratio and false acceptance ratio constitutes main drawback of the conventional decoders. Unlike the conventional methods, this paper introduces a pattern recognition (PR) framework to WM extraction and integrates WM decoding and detection problems into a unique classification problem that eliminates thresholding. The proposed method models statistics of watermarked and original audio signals by a Gaussian mixture model (GMM) with K components. Learning of the embedded WM data is achieved in a principal component analysis (PCA) transformed wavelet space and a maximum likelihood (ML) classifier is designed for WM decoding. Robustness of the proposed method is evaluated under compression, additive noise and Stirmark benchmark attacks. It is shown that both WM decoding and detection performances of the introduced decoder outperform the conventional decoders.     

Robust decoding of variable-length encoded Markov sources using a three-dimensional trellis

In this letter, we present an improved index-based a-posteriori probability (APP) decoding approach for the error-resilient transmission of packetized variable-length encoded Markov sources. The proposed algorithm is based on a novel two-dimensional (2D) state representation which leads to a three-dimensional trellis with unique state transitions. APP decoding on this trellis is realized by employing a 2D version of the BCJR algorithm where all available source statistics can be fully exploited in the source decoder. For an additional use of channel codes the proposed approach leads to an increased error-correction performance compared to a one-dimensional state representation.     

Simple MAP decoding of first-order Reed-Muller and Hamming codes

A maximum a posteriori (MAP) probability decoder of a block code minimizes the probability of error for each transmitted symbol separately. The standard way of implementing MAP decoding of a linear code is the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm, which is based on a trellis representation of the code. The complexity of the BCJR algorithm for the first-order Reed-Muller (RM-1) codes and Hamming codes is proportional to n/sup 2/, where n is the code's length. In this correspondence, we present new MAP decoding algorithms for binary and nonbinary RM-1 and Hamming codes. The proposed algorithms have complexities proportional to q/sup 2/n log/sub q/n, where q is the alphabet size. In particular, for the binary codes this yields complexity of order n log n.