Iterative decoding and channel parameter estimation algorithms for repeat-accumulate codes

The sensitivity of the iterative decoder for repeat-accumulate (RA) codes to carrier phase and channel signal-to-noise ratio estimation errors is investigated, and efficient algorithms to estimate and correct these errors are developed. The behavior of RA codes with imperfect channel estimation is different from that of turbo codes, and correction algorithms specific to RA codes must be formulated. The proposed algorithms use the soft information generated within the iterative decoder, and thus, are not only hardware-efficient, but also offer excellent performance.     

Embedding carrier phase recovery into iterative decoding of turbo-coded linear modulations

In this paper, we introduce a low-complexity carrier phase estimation algorithm to be integrated into the data decoder of a turbo-coded modem employing a linear modulation. The estimator is based on a pseudo-maximum-likelihood approach and makes iterative use of soft decisions provided by the soft-in/soft-out decoders within the overall turbo-decoding scheme. In doing so, iterative decoding and carrier phase recovery go together iteration after iteration in a "soft decision-directed" mode. This allows performing reliable blind phase estimation and almost ideal coherent detection for values of the signal-to-noise ratio down to a few decibels only, and without the need to resort to narrowband phase-locked loops with large acquisition time. Performance in terms of mean estimated value, root mean-squared estimation error, and overall decoder bit-error rate as derived by simulation are also reported.     

Turbo decoder

We propose an adaptive channel SNR estimation algorithm required for the iterative MAP decoding of turbo decoders. The proposed algorithm uses the extrinsic values generated within the iterative MAP decoder to update the channel SNR estimate toward its optimum value per each decoder iteration or per each turbo code frame     

Carrier phase recovery for turbo‐coded systems with pre‐coded GMSK modulation

A carrier phase recovery scheme suited for turbo‐coded systems with pre‐coded Gaussian minimum shift keying (GMSK) modulation is proposed and evaluated in terms of bit‐error‐rate (BER) performance. This scheme involves utilizing the extrinsic information obtained from the turbo‐decoder to aid an iterative carrier phase estimation process, based on a maximum‐likelihood (ML) strategy. The phase estimator works jointly with the turbo‐decoder, using the updated extrinsic information from the turbo‐decoder in every iterative decoding. A pre‐coder is used to remove the inherent differential encoding of the GMSK modulation. Two bandwidths of GMSK signals are considered: BT=0.5 and 0.25, which are recommended by the European Cooperation for Space Standardization (ECSS). It is shown that the performance of this technique is quite close to the perfect synchronized system within a wide range of phase errors. This technique is further developed to recover nearly any phase error in [?π,+π] by increasing the number of phase estimators and joint decoding units. This, however, will increase the complexity of the system. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

基于Turbo码迭代的低信噪比载波同步技术

针对低信噪比短突发通信系统的载波恢复问题,研究了一种基于迭代思想的载波相位估计算法.该算法首先利用导频进行初始的载波相位估计,然后再利用Turbo译码器输出的软信息进行载波相位细估计,进而实现有效的载波同步.仿真结果表明,该算法仅利用11个QPSK导频符号就能校正较大范围的相位偏移,进而达到理想的误比特性能.     

Innovations-based MAP estimation with application to phase synchronization for serially concatenated CPM

A novel adaptive soft-input soft-output (A-SISO) module is developed for maximum a posteriori (MAP) symbol detection with parameter uncertainty. In contrast to the existing A-SISO algorithms that use linear prediction, the parameter estimation in the proposed structure is operated in a more general least-squares sense. Based on this scheme, a family of fixed-interval A-SISO (FI-A-SISO) algorithms is utilized to implement blind iterative phase synchronization for serially concatenated continuous phase modulation (SCCPM). For SCCPM systems, the forward-only FI-A-SISO algorithms are shown to be much more robust than the forward-backward FI-A-SISO algorithms in acquiring and tracking a time-varying carrier phase. The reason has to do with rotational invariance of CPM signals. This result can be extended to any rotationally invariant convolutional coded system with an unknown carrier phase.     

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.     

On turbo decoding of nonbinary codes

Symbol-by-symbol maximum a posteriori (MAP) decoding algorithms for nonbinary block and convolutional codes over an extension field GF(p ^a) are presented. Equivalent MAP decoding rules employing the dual code are given which are computationally more efficient for high-rate codes. It is shown that these algorithms meet all requirements needed for iterative decoding as the output of the decoder can be split into three independent estimates: soft channel value, a priori term and extrinsic value. The discussed algorithms are then applied to a parallel concatenated coding scheme with nonbinary component codes in conjunction with orthogonal signaling     

Low Complexity Carrier Phase Tracking Decoders for Continuous Phase Modulations

Phase tracking capability is incorporated into two sequence estimation decoders for continuous phase modulations. One decoder employs the Viterbi algorithm; the other uses a reduced-survivor approach proposed earlier by one of the authors [11] for the more bandwidth efficient of these modulations. Computational complexity with the simplest of the joint data/phase algorithms is only marginally greater than that required for the equivalent decoding algorithm employing an externally derived carrier phase reference as supplied by a conventional carrier recovery circuit. Simulations with representative partial response modulations demonstrate the phase synchronization and tracking capabilities of the decoders. High SNR losses relative to an optimal receiver having perfect phase knowledge are found to be small (∼ 1 dB).     

CMOS analog MAP decoder for (8,4) Hamming code

Design and test results for a fully integrated translinear tail-biting MAP error-control decoder are presented. Decoder designs have been reported for various applications which make use of analog computation, mostly for Viterbi-style decoders. MAP decoders are more complex, and are necessary components of powerful iterative decoding systems such as turbo codes. Analog circuits may require less area and power than digital implementations in high-speed iterative applications. Our (8, 4) Hamming decoder, implemented in an AMI 0.5-/spl mu/m process, is the first functioning CMOS analog MAP decoder. While designed to operate in subthreshold, the decoder also functions above threshold with a small performance penalty. The chip has been tested at bit rates up to 2 Mb/s, and simulations indicate a top speed of about 10 Mb/s in strong inversion. The decoder circuit size is 0.82 mm/sup 2/, and typical power consumption is 1 mW at 1 Mb/s.     

一种应用CPM扩频调制的Turbo CDMA系统

本文首先介绍了连续相位调制CPM (Continuous Phase Modulation) 的分解模型^[1],得到CPM调制可以分解为一个线性连续相位编码CPE (Continuous Phase Encoder)和无记忆调制的组合;接着基于CPM的错误事件和递归特性,推出了采用CPM扩频调制的Turbo CDMA系统模型,这里CPM扩频调制作为递归内码,与外编码器及交织器级连构成Turbo迭代系统,该系统有明显的交织增益.利用系统的迭代解调解扩和解码的特点,设计了软输入输出的接收机,接收机中解调器采用MAP(Maximum A Posterior)和SOVA(Soft Output Viterbi Algorithm)算法,解码器采用MAP算法.仿真结果表明CPM调制器作为内码形成级连迭代系统交织增益非常明显.     

Code-aided iterative carrier phase estimation using selective soft decision feedback

A code-aided iterative carrier phase estimator using selective soft decision feedback is proposed. Based on the reliability metric defined, soft decisions provided by the soft-in/soft-out channel decoder with higher reliabilities are selected to perform carrier phase estimation iteratively. Simulation results demonstrate the performance improvement of the proposed algorithm in both the unbiased estimation range and the estimation precision. The overall bit error rate performance of the coded systems with different phase estimators is also compared.     

Adaptive Bayesian and EM-based detectors for frequency-selective fading channels

The problems of adaptive maximum a posteriori (MAP) symbol detection for uncoded transmission and of adaptive soft-input soft-output (SISO) demodulation for coded transmission of data symbols over time-varying frequency-selective channels are explored within the framework of the expectation-maximization (EM) algorithm. In particular, several recursive forms of the classical Baum-Welch (BW) algorithm and its Bayesian counterpart (often referred to a Bayesian EM algorithm) are derived in an unified way. In contrast to earlier developments of the BW and BEM algorithms, these formulations lead to computationally attractive algorithms which avoid matrix inversions while using sequential processing over the time and trellis branch indices. Moreover, it is shown how these recursive versions of the BW and BEM algorithms can be integrated with the well-known forward-backward processing SISO algorithms resulting in adaptive SISOs with embedded soft decision directed (SDD) channel estimators. An application of the proposed algorithms to iterative "turbo-processing" receivers illustrates how these SDD channel estimators can efficiently exploit the extrinsic information obtained as feedback from the SISO decoder in order to enhance their estimation accuracy.     

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.     

A New Iterative Decoder of Space-Time Data in Time Selective MIMO Channels

In this paper we present a new iterative decoder of Space-Time Block Coded data in the presence of carrier offsets. This decoder starts the iteration with a small amount of training data to find the initial estimate of carrier offset, channel and noise co-variance. Subsequently it attempts to find the estimate of the STBC data by an alternating maximization (AM) technique. In this way better estimates of Space–Time data are achieved after the final iteration as compared to those found without an iterative method. Thus the new decoder reduces the training overhead required by the conventional data-aided (DA) estimators for efficient estimates of carrier offsets and S–T data, and provides higher data rate.     

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。     

Multiuser SCCPM with iterative decoding

The recent technique of serially concatenated continuous phase modulation (SCCPM) is extended to a multiuser system with a carrier frequency offset between the users. Simulation results for up to five users with an iterative decoder show that the performance loss is small considering the substantial spectral overlap. Consequently, power/bandwidth efficiencies which are better than for SCCPM are achievable     

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.     

Soft input soft output Kalman equalizer for MIMO frequency selective fading channels

We consider the Kalman filter for equalization of a multiple-input multiple-output (MIMO), frequency selective, quasi-static fading channel. More specifically, we consider a coded system, where the incoming bit stream is convolutionally encoded, interleaved and then spatially multiplexed across the transmit antennas. Each substream is modulated into M-ary symbols before being transmitted over a frequency selective channel. At the receiver, we propose to use the Kalman filter as a low complexity MIMO equalizer, as opposed to the trellis based maximum a-posteriori (MAP) equalizer whose computational complexity grows exponentially with the channel memory, the number of transmit antennas and the spectral efficiency (bits/s/Hz) of the system. We modify the structure of the Kalman filter and enable it to process the a-priori (soft) information provided by the channel decoder, thereby allowing us to perform iterative (turbo) equalization on the received sequence. The iterative equalizer structure is designed for general M-ary constellations. We also propose a low complexity version of the above algorithm whose performance is comparable to its full complexity counterpart, but which achieves a significant complexity reduction. We demonstrate via simulations that for higher order constellations, when sufficient number of receive antennas are available (e.g. for a 2 transmitter, 3 receiver system, QPSK), the performance of the proposed algorithms after 4 iterations is within 1.5 dB of the non-iterative MAP algorithm with close to an order of magnitude complexity reduction. By objectively quantifying the complexity of all the considered algorithms we show that the complexity reduction for the proposed schemes becomes increasingly significant for practical systems with moderate to large constellation sizes and a large number of transmit antennas