Noncoherent iterative (turbo) decoding

Previously, noncoherent sequence detection schemes for coded linear and continuous phase modulations have been proposed, which deliver hard decisions by means of a Viterbi algorithm. The current trend in digital transmission systems toward iterative decoding algorithms motivates an extension of these schemes. In this paper, we propose two noncoherent soft-output decoding algorithms. The first solution has a structure similar to that of the well-known algorithm by Bahl et al. (1974), whereas the second is based on noncoherent sequence detection and a reduced-state soft-output Viterbi algorithm. Applications to the combined detection and decoding of differential or convolutional codes are considered. Further applications to noncoherent iterative decoding of turbo codes and serially concatenated interleaved codes are also considered. The proposed noncoherent detection schemes exhibit moderate performance loss with respect to corresponding coherent schemes and are very robust to phase and frequency instabilities     

Iterative demodulation and decoding of frequency-hopped PSK in partial-band jamming

This paper considers the problem of developing and utilizing side information in a frequency-hopped communication system using phase-shift keying (PSK) and operating in an environment with partial-band jamming. Two aspects of side information are studied. The first deals with estimating the unknown random carrier phase that varies from hop to hop. The second aspect is the detection of jamming signals. We use a serially concatenated convolutional code structure with differential M-ary PSK as the inner code. The iterative receiver uses an expanded trellis in the inner decoder to resolve the phase ambiguity and is augmented by a ratio-threshold test for detecting jammer energy. Performance is compared for different dwell interval lengths and both log-APP and max-log-APP decoding algorithms. This paper also considers the effect of different thresholds on the false alarm and detection probabilities of the ratio-threshold test.     

Improving the spectral efficiency of FDM‐CPM systems through packing and multiuser processing

In frequency division multiplexed (FDM) systems, spectral efficiency (SE) can be increased by reducing the spacing between two adjacent channels, thus increasing the relevant interference and possibly accounting for it at the receiver. In this paper, we consider a FDM system where each user employs a continuous phase modulation, serially concatenated with an outer code through an interleaver, and iterative detection/decoding. We show that, by taking into account the increased interference using properly designed multiuser detection and synchronization schemes, it is possible to implement transmission schemes with unprecedented SE at a price of a limited complexity increase with respect to a classical single‐user receiver which neglects the interference. Copyright © 2012 John Wiley & Sons, Ltd.     

满速率串行级联空时分组MTCM编码方法研究

该文研究了级联空时编码系统在编码增益,分集增益和传输能量效率的限定下最大化传输速率的问题,提出了一种在保留TCM编码方法校验位冗余的同时,还可获得满速率串行级联空时分组TCM编码方法。新方法通过引入具有不同功率分集因子的正交发射码字矩阵,并给出新的译码算法,从而使得新的编码方法在获得满速率的同时还可以获得满分集增益。分析和MATLAB仿真结果表明,在相同的编码状态数下,新方法在编码增益上比现有的满速率超正交空时分组编码方法提高1dB左右。     

Performance of trellis-coded CPM with iterative demodulation anddecoding

Interleaved trellis-coded systems with full response continuous-phase modulation (CPM) are considered. Upper bounds on the bit-error rate performance are derived for coherent detection on the additive white Gaussian noise and flat Rayleigh fading channels by considering the trellis code, interleaver, and CPM modulator as a serially concatenated convolutional code. A coherent receiver that performs iterative demodulation and decoding is shown to provide good bit error performance. Finally, a noncoherent iterative receiver is proposed and is shown to perform close to the coherent iterative receiver     

Performance of coded OQPSK and MIL-STD SOQPSK with iterative decoding

We show that military standard (MIL-STD) shaped-offset quadrature phase-shift keying (SOQPSK), a highly bandwidth-efficient constant-envelope modulation, can be represented in the form of a cross-correlated trellis-coded quadrature modulation. Similarly, we show that offset QPSK (OQPSK) can be decomposed into a "degraded" trellis encoder and a memoryless mapper. Based on the representations of OQPSK and MIL-STD SOQPSK as trellis-coded modulations (TCMs), we investigate the potential coding gains achievable from the application of simple outer codes to form a concatenated coding structure with iterative decoding. For MIL-STD SOQPSK, we describe the optimum receiver corresponding to its TCM form and then propose a simplified receiver. The bit-error rate (BER) performances of both receivers for uncoded and coded MIL-STD SOQPSK are simulated and compared with that of OQPSK and Feher-patented QPSK (FQPSK). The asymptotic BER performance of MIL-STD SOQPSK is also analyzed and compared with that of OQPSK and FQPSK. Simulation results show that, compared with their uncoded systems, there are significant coding gains for both OQPSK and MIL-STD SOQPSK, obtained by applying iterative decoding to either the parallel concatenated coding scheme or the serial one, even when very simple outer codes are used.     

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.     

Iterative semiblind multiuser receivers for a space-time block-coded MC-CDMA uplink system

Iterative multiuser detection and space-time coding are two promising techniques to improve the capacity and performance of coded multiuser systems in wireless channels. In this paper, we present iterative multiuser detection schemes for a space-time block-coded multicarrier code-division multiple-access system with multiple transmit and receive antennas. We consider a more general case of an uplink system in the presence of both intra- and intercell interferences. We propose two types of iterative semiblind space-time receivers for such an uplink environment. The first is based on the minimum mean-square error criterion and the second is a hybrid scheme based on a combination of parallel interference cancellation and linear multiuser detection. These iterative receivers are derived, using a subspace approach, which utilizes known users' information for the computation of log-likelihood ratios (LLRs) while blindly suppressing the unknown interference. The LLRs are refined successively during the iterative process by using the extrinsic information available through decoding of all known users. A turbo code is used for channel coding. Simulation results in a frequency-selective Rayleigh-fading environment are presented to verify the performance of the proposed schemes.     

迭代检测算法在比特交织编码调制系统中的比较研究

迭代检测技术不仅局限于在传统的级联码系统中的应用,还可用于解决现代数字通信中的许多检测／译码问题。随着Turbo码的出现,人们对迭代译码算法进行深入研究,并提出一些简化译码算法。比特交织编码调制及迭代检测（bit—interleaved coded modulation with iterative decoding,BICMID）是一种高效数据传输系统。比特交织和迭代译码是BICM—ID系统具有卓越性能的关键因素,译码算法的选择不仅影响接收机的性能,也决定了系统的复杂度。文中研究迭代译码算法对BICM—ID系统性能的影响,分析各种译码算法的计算复杂度。仿真结果表明log-APP算法有好的性能同时复杂度也高,简化的译码算法能降低译码器的复杂度,但会带来一定的性能损失;随着信道条件的改善,算法简化带来的性能损失也随之减小。     

Concatenated multilevel block coded modulation

Encoding and decoding schemes for concatenated multilevel block codes are presented. By one of these structures, a real coding gain of 5.6-7.4 dB for the bit error range of 10^-6 to 10^-9 is achieved for transmission through the additive white Gaussian noise channel. Also, a rather large asymptotic coding gain is obtained. The new coding schemes have very low decoding complexity and increased coding gain in comparison with the conventional block and trellis coded modulation structures. A few design rules for concatenated (single and) multilevel block codes with large coding gain are also provided     

M-ary phase coding for the noncoherent AWGN channel

This work considers coded M-ary phase-shift keying (MPSK) schemes with noncoherent detection. A class of block codes called module-phase codes is described. The algebraic framework used for describing these codes relies on elements from module theory which are discussed along with a method for constructing such codes for noncoherent detection. It is shown that differential encoding may be viewed as a specific code from a particular class of module-phase codes. Two classes of codes that achieve significant coding gain with respect to coherent detection of uncoded MPSK are presented. In the first class of module-phase codes, the coding gain is achieved at the expense of bandwidth expansion. In the second class, however, the coding gain is achieved at the expense of signal constellation expansion without expanding bandwidth. Finally, an integrated demodulation/decoding technique based on a modification of information set decoding is presented. It Is shown that this reduced-complexity, suboptimal decoding strategy performs nearly as well as maximum-likelihood decoding     

A RAKE-based iterative receiver for space-time block-coded multipath CDMA

A turbo multiuser receiver is proposed for space-time block and channel-coded code division multiple access (CDMA) systems in multipath channels. The proposed receiver consists of a first stage that performs detection, space-time decoding, and multipath combining followed by a second stage that performs the channel decoding. A reduced complexity receiver suitable for systems with large numbers of transmitter antennas is obtained by performing the space-time decoding along each resolvable multipath component and then diversity combining the set of space-time decoded outputs. By exchanging the soft information between the first and second stages, the receiver performance is improved via iteration. Simulation results show that while in some cases a noniterative space-time coded system may have inferior performance compared with a system without space-time coding in a multipath channel, proposed iterative schemes significantly outperform systems without space-time coding, even with only two iterations. Furthermore, the performance loss in the reduced-complexity receiver due to decoupling of interference suppression, space-time decoding, and multipath combining is very small for error rates of practical interest.     

Soft-Output Decoding of Rotationally Invariant Codes Over Channels With Phase Noise

We consider rotationally invariant (RI) trellis-coded modulations (TCMs) transmitted over channels affected by phase noise. To describe the main ideas of this paper, we first concentrate, as a case study, on the simplest RI scheme, namely the differentially encoded M-ary phase-shift keying (M-PSK) signal. For this problem, we use the framework based on factor graphs (FGs) and the sum-product algorithm (SPA), to derive the exact maximum a posteriori (MAP) symbol detection algorithm. By analyzing its properties, we demonstrate that it can be implemented by a forward-backward estimator of the phase probability density function, followed by a symbol-by-symbol completion to produce the a posteriori probabilities of the information symbols. To practically implement the forward-backward phase estimator, we propose a couple of schemes with different complexity. The resulting algorithms exhibit an excellent performance and, in one case, only a limited complexity increases with respect to the algorithm that perfectly knows the channel phase. The properties of the optimal decoder and the proposed practical decoding schemes are then extended to the case of a generic RI code. The proposed soft-output algorithms can also be used in iterative decoding schemes for concatenated codes employing RI inner components. Among them, in the numerical results, we consider repeat-accumulate (RA) codes and other serially concatenated schemes recently proposed in the technical literature.     

Sequence MAP decoding of trellis codes for Gaussian and Rayleighchannels

This paper considers the use of sequence maximum a posteriori (MAP) decoding of trellis codes. A MAP receiver can exploit any “residual redundancy” that may exist in the channel encoded signal in the form of memory and/or a nonuniform distribution, thereby providing enhanced performance over very noisy channels, relative to maximum likelihood (ML) decoding. The paper begins with a first-order two-state Markov model for the channel encoder input. A variety of different systems with different source parameters, different modulation schemes, and different encoder complexities are simulated. Sequence MAP decoding is shown to substantially improve performance under very noisy channel conditions for systems with low-to-moderate redundancy, with relative gain increasing as the rate increases. As a result, coding schemes with multidimensional constellations are shown to have higher MAP gains than comparable schemes with two-dimensional (2-D) constellations. The second part of the paper considers trellis encoding of the code-excited linear predictive (CELP) speech coder's line spectral parameters (LSPs) with four-dimensional (4-D) QPSK modulation. Two source LSP models are used. One assumes only intraframe correlation of LSPs while the second one models both intraframe and interframe correlation. MAP decoding gains (over ML decoding) as much as 4 dB are achieved. Also, a comparison between the conventionally designed codes and an I-Q QPSK scheme shows that the I-Q scheme achieves better performance even though the first (sampler) LSP model is used     

On the design of space-time and space-frequency codes for MIMO frequency-selective fading channels

The authors introduced an algebraic design framework for space-time coding in flat-fading channels . We extend this framework to design algebraic codes for multiple-input multiple-output (MIMO) frequency-selective fading channels. The proposed codes strive to optimally exploit both the spatial and frequency diversity available in the channel. We consider two design approaches: The first uses space-time coding and maximum likelihood decoding to exploit the multi-path nature of the channel at the expense of increased receiver complexity. Within this time domain framework, we also propose a serially concatenated coding construction which is shown to offer a performance gain with a reasonable complexity iterative receiver in some scenarios. The second approach utilizes the orthogonal frequency division multiplexing technique to transform the MIMO multipath channel into a MIMO flat block fading channel. The algebraic framework is then used to construct space-frequency codes (SFC) that optimally exploit the diversity available in the resulting flat block fading channel. Finally, the two approaches are compared in terms of decoder complexity, maximum achievable diversity advantage, and simulated frame error rate performance in certain representative scenarios.     

Low-complexity iterative joint source-channel decoding for variable-length encoded Markov sources

In this paper, we present a novel packetized bit-level decoding algorithm for variable-length encoded Markov sources, which calculates reliability information for the decoded bits in the form of a posteriori probabilities (APPs). An interesting feature of the proposed approach is that symbol-based source statistics in the form of the transition probabilities of the Markov source are exploited as a priori information on a bit-level trellis. This method is especially well-suited for long input blocks, since in contrast to other symbol-based APP decoding approaches, the number of trellis states does not depend on the packet length. When additionally the variable-length encoded source data is protected by channel codes, an iterative source-channel decoding scheme can be obtained in the same way as for serially concatenated codes. Furthermore, based on an analysis of the iterative decoder via extrinsic information transfer charts, it can be shown that by using reversible variable-length codes with a free distance of two, in combination with rate-1 channel codes and residual source redundancy, a reliable transmission is possible even for highly corrupted channels. This justifies a new source-channel encoding technique where explicit redundancy for error protection is only added in the source encoder.     

Iterative receivers for multiuser space-time coding systems

Space-time coding (STC) techniques, which combine antenna array signal processing and channel coding techniques, are very promising approaches to substantial capacity increase in wireless channels. Multiuser detection techniques are powerful signal processing methodologies for interference suppression in CDMA systems. In this paper, by drawing analogies between a synchronous CDMA system and an STC multiuser system, we study the applications of some multiuser detection methods to STC multiuser systems. Specifically, we show that the so-called “turbo multiuser detection” technique, which performs soft interference cancellation and decoding iteratively, can be applied to STC multiuser systems in flat-fading channels. An iterative multiuser receiver and its projection-based variants are developed for both the space-time block coding (STBC) system and the space-time trellis coding (STTC) system. During iterations, extrinsic information is computed and exchanged between a soft multiuser demodulator and a bank of MAP decoders, to achieve successively refined estimates of the users' signals. Computer simulations demonstrate that the proposed iterative receiver techniques provide significant performance improvement over conventional noniterative methods in both single-user and multiuser STC systems. Furthermore, the performance of the proposed iterative multiuser receiver approaches that of the iterative single-user receiver in both STBC and STTC systems     

线性分组码与时空分组码级联的迭代译码

提出了线性分组码与时空分组码的级联编码方案,推导了时空分组码在比特级上的软输入软输出译码算法,进而给出了在线性分组码和时空分组码之间进行迭代译码的算法。仿真结果表明这种方案与现有方案相比在能够获得最大分集增益的同时还能获得更大的编码增益。     

MAP decoding of convolutional codes using reciprocal dual codes

A new symbol-by-symbol maximum a posteriori (MAP) decoding algorithm for high-rate convolutional codes using reciprocal dual convolutional codes is presented. The advantage of this approach is a reduction of the computational complexity since the number of codewords to consider is decreased for codes of rate greater than 1/2. The discussed algorithms fulfil all requirements for iterative (“turbo”) decoding schemes. Simulation results are presented for high-rate parallel concatenated convolutional codes (“turbo” codes) using an AWGN channel or a perfectly interleaved Rayleigh fading channel. It is shown that iterative decoding of high-rate codes results in high-gain, moderate-complexity coding     

A close-to-capacity dirty paper coding scheme

The "writing on dirty paper"-channel model offers an information-theoretic framework for precoding techniques for canceling arbitrary interference known at the transmitter. It indicates that lossless precoding is theoretically possible at any signal-to-noise ratio (SNR), and thus dirty-paper coding may serve as a basic building block in both single-user and multiuser communication systems. We design an end-to-end coding realization of a system materializing a significant portion of the promised gains. We employ multidimensional quantization based on trellis shaping at the transmitter. Coset decoding is implemented at the receiver using "virtual bits." Combined with iterative decoding of capacity-approaching codes we achieve an improvement of 2dB over the best scalar quantization scheme. Code design is done using the EXIT chart technique.