Turbo Code译码方法的改进

在文章中，首先介绍Turbo码的基本编译码结构和它的译码算法MAP。在此基础上，尝试对MAP算法的循环译码的后向递推的起点以及循环译码结构的最终判决条件根据实际应用情况进行改进。将译码的后向递推的起点定义为译码的前向递推的终点，并且将每一轮译码结果进行加权相加，得到最后系统输出。最后，根据MATLAB仿真的结果论证改进后的算法能减少系统的误码率。     

Reduced-Complexity Turbo Equalization for Turbo Coded MIMO/OFDM Systems

1IntroductionTowards wireless systems Beyondthe3G(B3G),it isa great challenge for the physical layer to support high-speed transmissioninthe mobile environment to providecomfortable Internet access.Multiple Input MultipleOutput(MI MO)technique is effectiv…     

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     

Turbo decoder SNR estimation with RAKE reception

The joint performance of a turbo decoder and RAKE receiver using the MAP algorithm depends on the accuracy of the channel reliability factor. In a high data rate/low processing gain environment, inherent interference that results from non-idealities of the RAKE receiver complicate the estimation of the channel reliability factor. The combined performance of a turbo decoder and RAKE receiver is analyzed in a timedispersive and time-varying channel with distinct multipath components. Approaches are examined for estimating the channel reliability factor using the limited information that is known by the RAKE receiver. The sensitivity of performance to SNR mismatches is computed. The impact of the processing gain and the number of multipath components on BER performance is analyzed along with the effect of the channel time coherence. By accounting for the non-ideal RAKE interference effects, improvements in the channel reliability factor calculation result in BER performance improvements on the order of 0.5-2 dB.     

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。     

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     

迭代结构的信源信道联合解码及其简化算法

信源信道联合解码算法中的迭代信道解码需要进行比特似然值和概率值转换,以及联乘、累加运算,增加了信道解码的计算复杂度,该文针对这一问题,直接利用信道解码的比特硬判决值和参数的先验概率,估计比特的外信息,用于迭代信道解码。基于高斯-马尔可夫信源参数的仿真实验表明,该简化算法大大降低了迭代信道解码算法的计算复杂度。与独立解码算法相比,简化的联合解码算法明显改善了接收参数的信噪比,同时不会明显降低原迭代结构解码算法的性能。     

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     

Carrier Synchronization for Very Low SNR

The Turbo decoding performance will suffer serious degradation under low signal-to-noise ratios (SNR) conditions for the reason of residual frequency and phase offset in the carrier. In this paper, an improved residual carrier frequency offset estimation algorithm based on u priori probability aided (APPA) phase estimation is proposed. A carrier synchronization loop that combines the iterative turbo decoder and the phase estimator together is constructed, where the extrinsic information obtained from the Turbo decoder is used to aid an iterative phase estimation process. The simulation results show that the algorithm performs successfully under very low SNR conditions (for example, less than -7.4 dB) with large frequency offset and phase error and the performance of this algorithm is very close to the optimally synchronized system.     

Comparative study of turbo decoding techniques: an overview

We provide an overview of the novel class of channel codes referred to as turbo codes, which have been shown to be capable of performing close to the Shannon limit. We commence with a discussion on turbo encoding, and then move on to describing the form of the iterative decoder most commonly used to decode turbo codes. We then elaborate on various decoding algorithms that can be used in an iterative decoder, and give an example of the operation of such a decoder using the so-called soft output Viterbi (1996) algorithm (SOVA). Lastly, the effect of a range of system parameters is investigated in a systematic fashion, in order to gauge their performance ramifications     

A parallel MAP algorithm for low latency turbo decoding

To reduce the computational decoding delay of turbo codes, we propose a parallel algorithm for maximum a posteriori (MAP) decoders. We divide a whole noisy codeword into sub-blocks and use multiple processors to perform sub-block MAP decoding in parallel. Unlike the previously proposed approach with sub-block overlapping, we utilize the forward and backward variables computed in the previous iteration to provide boundary distributions for each sub-block MAP decoder. Our scheme depicts asymptotically optimal performance in the sense that the BER is the same as that of the regular turbo decoder     

Memory-Reduced Maximum A Posteriori Probability Decoding for High-Throughput Parallel Turbo Decoders

Wireless communication standards make use of parallel turbo decoder for higher data rate at the cost of large hardware resources. This paper presents a memory-reduced back-trace technique, which is based on a new method of estimating backward-recursion factors, for the maximum a posteriori probability (MAP) decoding. Mathematical reformulations of branch-metric equations are performed to reduce the memory requirement of branch metrics for each trellis stage. Subsequently, an architecture of MAP decoder and its scheduling based on the proposed back trace as well as branch-metric reformulation are presented in this work. Comparative analysis of bit-error-rate (BER) performances in additive white Gaussian noise channel environment for MAP as well as parallel turbo decoders are carried out. It has shown that a MAP decoder with a code rate of 1/2 and a parallel turbo decoder with a code rate of 1/3 have achieved coding gains of 1.28 dB at a BER of 10\(^{-5}\) and of 0.4 dB at a BER of 10\(^{-4}\), respectively. In order to meet high-data-rate benchmarks of recently deployed wireless communication standards, very large scale integration implementations of parallel turbo decoder with 8–64 MAP decoders have been reported. Thereby, savings of hardware resources by such parallel turbo decoders based on the suggested memory-reduced techniques are accounted in terms of complementary metal oxide semiconductor transistor count. It has shown that the parallel turbo decoder with 32 and 64 MAP decoders has shown hardware savings of 34 and 44 % respectively.     

Bandwidth-efficient turbo trellis-coded modulation using puncturedcomponent codes

We present a bandwidth-efficient channel coding scheme that has an overall structure similar to binary turbo codes, but employs trellis-coded modulation (TCM) codes (including multidimensional codes) as component codes. The combination of turbo codes with powerful bandwidth-efficient component codes leads to a straightforward encoder structure, and allows iterative decoding in analogy to the binary turbo decoder. However, certain special conditions may need to be met at the encoder, and the iterative decoder needs to be adapted to the decoding of the component TCM codes. The scheme has been investigated for 8-PSK, 16-QAM, and 64-QAM modulation schemes with varying overall bandwidth efficiencies. A simple code choice based on the minimal distance of the punctured component code has also been performed. The interset distances of the partitioning tree can be used to fix the number of coded and uncoded bits. We derive the symbol-by-symbol MAP component decoder operating in the log domain, and apply methods of reducing decoder complexity. Simulation results are presented and compare the scheme with traditional TCM as well as turbo codes with Gray mapping. The results show that the novel scheme is very powerful, yet of modest complexity since simple component codes are used     

Iterative multiuser detection, macrodiversity combining, anddecoding for the TDMA cellular uplink

A soft-input soft-output (SISO) multiuser detector (MUD) suitable for inclusion in iterative processing architectures is presented and applied to the detection of the coded time division multiple access (TDMA) cellular uplink. A SISO-MUD processor is located at each base station in the network, and adjacent base stations share information concerning the mobiles they serve. Because the MUD outputs are soft, they are suitable for postdetection macrodiversity combining. The combined signals are then passed to a SISO forward error correction (FEC) decoder, and the soft outputs are fed back to the multiuser detectors. Processing continues in an iterative fashion in accordance with the turbo principle. Simulation results are presented that indicate that use of such a scheme enables cellular systems to be overloaded with more than just one cochannel user per cell at the price of a minimal loss in signal-to-noise ratio (SNR). The proposed implementation assumes the availability of both perfect channel state information and a high capacity backhaul     

Turbo equalization of serially concatenated turbo codes using a predictive DFE-based receiver

This paper investigates the performance of various “turbo” receivers for serially concatenated turbo codes transmitted through intersymbol interference (ISI) channels. Both the inner and outer codes are assumed to be recursive systematic convolutional (RSC) codes. The optimum turbo receiver consists of an (inner) channel maximum a posteriori (MAP) decoder and a MAP decoder for the outer code. The channel MAP decoder operates on a “supertrellis” which incorporates the channel trellis and the trellis for the inner error-correcting code. This is referred to as the MAP receiver employing a SuperTrellis (STMAP). Since the complexity of the supertrellis in the STMAP receiver increases exponentially with the channel length, we propose a simpler but suboptimal receiver that employs the predictive decision feedback equalizer (PDFE). The key idea in this paper is to have the feedforward part of the PDFE outside the iterative loop and incorporate only the feedback part inside the loop. We refer to this receiver as the PDFE-STMAP. The complexity of the supertrellis in the PDFE-STMAP receiver depends on the inner code and the length of the feedback part. Investigations with Proakis B, Proakis C (both channels have spectral nulls with all zeros on the unit circle and hence cannot be converted to a minimum phase channel) and a minimum phase channel reveal that at most two feedback taps are sufficient to get the best performance. A reduced-state STMAP (RS-STMAP) receiver is also derived which employs a smaller supertrellis at the cost of performance.     

Turbo codes for image transmission-a joint channel and sourcedecoding approach

This paper studies an application of turbo codes to compressed image/video transmission and presents an approach to improving error control performance through joint channel and source decoding (JCSD). The proposed approach to JCSD includes error-free source information feedback, error-detected source information feedback, and the use of channel soft values (CSV) for source signal postprocessing. These feedback schemes are based on a modification of the extrinsic information passed between the constituent maximum a posteriori probability (MAP) decoders in a turbo decoder. The modification is made according to the source information obtained from the source signal processor. The CSVs are considered as reliability information on the hard decisions and are further used for error recovery in the reconstructed signals. Applications of this joint decoding technique to different visual source coding schemes, such as spatial vector quantization, JPEG coding, and MPEG coding, are examined. Experimental results show that up to 0.6 dB of channel SNR reduction can be achieved by the joint decoder without increasing computational cost for various channel coding rates     

An iterative receiver for turbo-coded pilot-assisted modulation infading channels

We introduce an iterative joint channel and data estimation receiver that exploits both the power of pilot-symbol assisted modulation (PSAM) and turbo coding for fading channels. The key innovation is a low-complexity soft channel estimator which divides a processing block into overlapped cells and performs maximum a posteriori (MAP) sequence estimation and MMSE filtering based on the received signal and extrinsic information delivered by the soft channel decoder. Simulation results show that for turbo-coded PSAM systems under time-variant fading the proposed receiver offers significant performance gains over a non-iterative receiver and two other cancellation schemes     

Effect of mismatched SNR on the performance of log-MAP turbo detector

The effect of signal-to-noise ratio (SNR) mismatch on the bit error rate (BER) performance of log-MAP turbo detector is studied. It is shown that the sensitivity to the mismatched SNR depends on the channel loss and the encoder memory length. In particular, the sensitivity is more important for a "difficult-to-equalize" channel or, in other words, a high-loss channel. In fact, by affecting the equalizer and the decoder, a mismatched SNR (with an offset with respect to the true SNR) affects the convergence of the turbo detector. Using the asymptotic analysis tool of extrinsic information transfer (EXIT) charts, the effect of a positive or a negative SNR offset on the convergence of the log-MAP turbo detector is studied. When no information is available at the receiver on SNR, an online estimation of SNR is necessary in order to not lose the advantage of the log-MAP turbo detector over other suboptimal turbo detectors. In this view, a relatively simple SNR estimation method is proposed, which offers satisfying results.     

Joint iterative channel estimation and decoding in flat correlatedRayleigh fading

This paper addresses the design and performance evaluation with respect to capacity of M-PSK turbo-coded systems operating in frequency-flat time-selective Rayleigh fading. The receiver jointly performs channel estimation and turbo decoding, allowing the two processes to benefit from each other. To this end, we introduce a suitable Markov model with a finite number of states, designed to approximate both the values and the statistical properties of the correlated flat fading channel phase, which poses a more severe challenge to PSK transmission than amplitude hiding. Then, the forward-backward algorithm determines both the maximum a posteriori probability (MAP) value for each symbol in the data sequence and the MAP channel phase in each iteration. Simulations show good performance in standard correlated Rayleigh fading channels. A sequence of progressively tighter upper bounds to the capacity of a simplified Markov-phase channel is derived, and performance of a turbo code with joint iterative channel estimation and decoding is demonstrated to approach these capacity bounds     

A Two-Stage Capacity-Achieving Demodulation/Decoding Method for Random Matrix Channels

Iterative processing for linear matrix channels, aka turbo equalization, turbo demodulation, or turbo code-division multiple access (CDMA), has traditionally been addressed as the concatenation of conventional error control codes with the linear (matrix) channel. However, in several situations, such as CDMA, multiple-input–multiple-output (MIMO) channels, orthogonal frequency-division multiplexing (OFDM), and intersymbol–interference (ISI) channels, the channel itself either contains inherent signal redundancy or such redundancy can readily be introduced at the transmitter. For such systems, iterative demodulation of the linear channel exploiting this redundancy using simple iterative cancellation demodulators, followed by conventional feedforward error control decoding, provides a low-complexity, but extremely efficient decoding alternative. This two-stage demodulator/decoder outperforms more complex turbo CDMA methods for equal power modes (users). Furthermore, it is shown that arbitrary numbers of modes can be supported if an unequal power distribution is adopted. These power distributions are nested, which means that additional modes can be added without disturbing an existing mode population. The main result shows that these nested power distributions enable the two-stage receiver to approach the Shannon capacity of the channel to within less than one bit for any signal-to-noise ratio (SNR).