Iterative turbo decoder analysis based on density evolution

We present a new adaptive approach for iterative turbo decoding using a pseudorandom training sequence with the distribution patterns known by both the transmitter and receiver, which can be adaptively sent to the receiver whenever the channel status changes. The branch detector computes the conditional distributions of extrinsic values produced by both arms at each iterative decoding with the aid of the training sequence. These updated probabilities are obtained instead of the traditional Gaussian law for further iterative decoding of information bits over additive white Gaussian noise and various fading channels. Such an adaptive decoding has considerable gains, investigated by the numerical simulation, over the traditional approach under the same conditions.

In this paper, we propose three categories of iterative decoding structures of three-dimensional(3-D) turbo product code(TPC), which is based on soft-input-soft-output(SISO) iterative decoding algorithm. Then by weighing the bit-error-rate(BER) curves of the 3-D TPC serial iterative decoder, a hybrid form of serial and parallel decoder and the parallel iterative decoder, and an optimal iterative decoding scheme is emerged. Furthermore, via adjusting the iterative weighing coefficient of the extrinsic information and equilibrating the proportion between the extrinsic information and the received information while decoding, the soft information of each bit is continuously modified to increase its reliability, delivering better decoding performance. Moreover, based on the enhanced structure of the 3-D TPC parallel iterative algorithm, we test different kinds of combinations of weighing coefficient, and pick out the best choice to achieve the lowest BER. Simulation results show that the performance of the modified 3-D TPC parallel decoder is substantially augmented under the circumstance of 3dB signal noise ratio(SNR) and 0.706 code rate, where the BER is quite close to the Shannon limit. under where its BER is almost approaching 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−6</sup> , which meets the BER requirements in modern wireless communication systems.

An iterative detection and decoding (IDD) receiver which combines a soft-input soft-output (SISO) detector and a SISO double binary (DB) turbo decoder improves the bit-error rate performance. However, the amount of the extrinsic information sent from the DB turbo decoder to the detector is much different from the amount of the extrinsic information sent from the detector to the decoder. Herein, a parity-enhanced DB turbo decoder is designed to provide the bit-level extrinsic information of systematic and parity bits for the WiMAX-based turbo-coded IDD receiver. Compared to the conventional turbo decoder, the proposed decoder achieves ~0.3 dB coding gain with a 6.06% area overhead.

In this paper, we propose a low complexity turbo coded BICM-ID (Bit-Interleaved Coded Modulation with Iterative Decoding) scheme. To increase the spectral efficiency, capacity approaching turbo codes can be combined with high order modulations and form a turbo coded modulation (CM) or a turbo-BICM (Bit-Interleaved Coded Modulation). On the other hand, it is also well known that the performance of turbo-BICM can be further improved by performing iterative demodulation and decoding between demodulator and turbo decoder which known as turbo-BICM-ID. However, compared to turbo-BICM, the decoding complexity of turbo-BICM-ID is highly increased. To reduce the required complexity of turbo-BICM-ID, we propose a low complexity turbo-BICM-ID scheme which offers virtually identical performance compared to turbo-BICM-ID.

Iterative or Turbo decoding of parallel concatenated binary error control codes in Binary Phase Shift Keyed (BPSK) Communication System corrupted by both Additive White Gaussian Noise (AWGN) and oscillator phase noise is discussed. As an example of application of the discussed theory, iterative decoding technique of Parallel Concatenated block Codes (PCBC) is applied to a coherent Optical Code Division Multiple Access (OCDMA) network in the presence of Multiple Access Interference (MAI), detector shot noise and laser phase noise. Remarkable improvement in performance resulting from the use of turbo decoding in the OCDMA network is also discussed.

A novel receiver is proposed for CDMA links with recursive turbo coding, based on a soft-input soft-output multistage interference canceler (IC) and an iterative turbo decoder (TD). After performing IC and TD a first time, the coder state estimates available from the two soft-output Viterbi algorithms in the last TD iteration are exploited to calculate the data bits and the redundancy bits. These are employed for preliminary hard cancellation in the first iteration of a supplementary IC run, and then the TD is run again. An alternative solution with soft feedback is obtained by approximating the reliabilities of the redundancy bits with those of the coder state estimates, and using them for preliminary soft cancellation. Simulation results show the effectiveness of the proposed solutions.

In iterative decoding it is well accepted that extrinsic information is to be exchanged between full-complexity soft-input, soft-output constituent decoder components. It is, however, still an open problem to determine the optimal information for exchange between reduced complexity decoder components that are only approximating posterior probabilities. In this paper we investigate the use of weighted extrinsic feedback in iterative multiuser decoding for coded code-division multiple-access (CDMA) systems. The case of no extrinsic feedback corresponds to the conventional approach of exchanging extrinsic information, while full extrinsic feedback corresponds to exchanging a posteriori information. Weighted extrinsic feedback offers a trade-off between the two extreme cases, which can provide significant improvements. These improvements are demonstrated through simulation of an iterative multiuser decoder using parallel interference cancellation as the soft-input, soft-output multiuser detector.

A more robust version of the nonlinear M-decorrelating detector through iterative (turbo) decoding is proposed. The turbo code performance in the linear decorrelating detector is also studied. Simulation results indicate that combined nonlinear signal processing and turbo decoding can achieve highly robust performance in impulsive noise.

We propose a novel class of provably good codes which are a serial concatenation of a single-parity-check (SPC)-based product code, an interleaver, and a rate-1 recursive convolutional code. The proposed codes, termed product accumulate (PA) codes, are linear time encodable and linear time decodable. We show that the product code by itself does not have a positive threshold, but a PA code can provide arbitrarily low bit-error rate (BER) under both maximum-likelihood (ML) decoding and iterative decoding. Two message-passing decoding algorithms are proposed and it is shown that a particular update schedule for these message-passing algorithms is equivalent to conventional turbo decoding of the serial concatenated code, but with significantly lower complexity. Tight upper bounds on the ML performance using Divsalar's (1999) simple bound and thresholds under density evolution (DE) show that these codes are capable of performance within a few tenths of a decibel away from the Shannon limit. Simulation results confirm these claims and show that these codes provide performance similar to turbo codes but with significantly less decoding complexity and with a lower error floor. Hence, we propose PA codes as a class of prospective codes with good performance, low decoding complexity, regular structure, and flexible rate adaptivity for all rates above 1/2.

For space-time bit-interleaved coded modulation (ST-BICM) systems with iterative decoding, the overall perfor- mance is affected by the chosen mapping. In bit error rate (BER) curves, one mapping reaches an error floor at a low signal- to-noise ratio (SNR), while other mappings result in a lower error floor at a higher SNR. The constellation mappings are divided into groups where each group exhibits a distinctive BER curve. We show that the convergence abscissa of the system depends on the average total bit errors and the harmonic mean of the minimum squared Euclidean distance. In this paper, we characterize all mapping groups for ST-BICM with 8PSK and present the optimal selection for each mapping group over independent fading channels. I. INTRODUCTION Space-time coding techniques significantly improve trans- mission efficiency in radio channels by using multiple transmit and/or receive antennas and coordination of the signaling over these antennas. Bit-interleaved coded modulation with iterative decoding (BICM-ID) gives good diversity gains and Euclidean distance property with higher order modulation schemes using well known binary convolutional codes (1). Tonello (2) combined these two schemes as space-time BICM (ST-BICM) with Gray mapping. In this paper, we will first show that the asymptotic BER performance of ST-BICM system is equivalent to the single antenna BICM-ID case even when the throughput of ST-BICM is higher. This indicates that the total data rate of ST-BICM can be increased linearly with the number of transmit antennas while maintaining the same error probability as BICM-ID. This demonstrates the superior performance of ST-BICM. Motivated by the fact that the ST-BICM performance can be characterized by BICM-ID with the same code and mapping, we optimize the ST-BICM mappings based on the BICM-ID parameters. While the error floor (EF) bound (1) offers a good match for an error floor region, a heuristic analysis is still needed to study BER curve behaviors of BICM-ID for the water fall region. Thus, we derive design considerations based on both

An iterative detection and decoding (IDD) technique has recently received much attention due to its capacity approaching performance and manageable complexity for (parallel) turbo-coded systems. The existing IDD receivers process indiscriminately the a priori information of the systematic bits and the parity bits generated by the turbo decoder in the front-end detection. In this paper, we first show that the parity bits of the parallel turbo codes are inherently less protected than the systematic bits, which leads to suboptimality for the IDD receivers. Based on this observation, we then propose an unequal-error-correcting-capability-aware technique to mitigate the associated performance loss. As an illustrative example, the minimum-mean-square-error (MMSE) filtering and soft interference cancelation (MMSE-SIC)-aided iterative receiver for parallel-turbo-coded multiple-input-multiple-output (MIMO) systems is employed in this paper. Numerical results manifest that the MMSE-SIC-aided iterative receiver based on the proposed paradigm achieves noticeable performance gains over the conventional unequal-error-correcting-capability-agnostic one even with reduced computational complexity. The extension of the proposed principle to other iterative algorithms for parallel-turbo-coded data transmission is straightforward.

Iterative probabilistic inference, popularly dubbed the soft-iterative paradigm, has found great use in a wide range of communication applications, including turbo decoding and turbo equalization. The classic approach of analyzing the iterative approach inevitably use the statistical and information-theoretical tools that bear ensemble-average flavors. This paper consider the per-block error rate performance, and analyzes it using nonlinear dynamical theory. By modeling the iterative processor as a nonlinear dynamical system, we report a universal "Z-crease phenomenon:" the zig-zag or up-and-down fluctuation -- rather than the monotonic decrease -- of the per-block errors, as the number of iteration increases. Using the turbo decoder as an example, we also report several interesting motion phenomenons which were not previously reported, and which appear to correspond well with the notion of "pseudo codewords" and "stopping/trapping sets." We further propose a heuristic stopping criterion to control Z-crease and identify the best iteration. Our stopping criterion is most useful for controlling the worst-case per-block errors, and helps to significantly reduce the average-iteration numbers.

We propose the signal-to-noise ratio (SNR) transfer characteristic band (TCB) chart of extrinsic information (EI) as a basic tool for the probabilistic convergence analysis of iterative decoding. The proposed SNR TCB chart is a general version of the widely used SNR transfer chart, and it can model the behavior of EI in iterative decoding with any blocklength. We propose an algorithm using the SNR TCB chart to obtain the information, which is both quantitative and qualitative, on the probabilistic convergence behavior of iterative decoding. We also propose the bit-error rate (BER) estimate, in the form of a lower bound, of turbo codes over an additive white Gaussian noise channel. The proposed estimate is especially useful in estimating the BER of finite-length turbo codes in a waterfall region, while it is meaningful for all blocklengths and all E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub>

In this contribution we investigate the performance of the UMTS Long Term Evolution (LTE) physical layer using turbo coding and 64QAM with Gray mapping. We show how the mapping of systematic and parity bits to the six different bit positions defining one complex 64QAM symbol influences the convergence of the turbo decoder and thereby the bit error rate (BER) performance as well as number of necessary decoding iterations. Exploiting the unequal error protection (UEP) property of Gray mapped 64QAM results in an SNR performance gain of approximately 2 dB for the non-iterative system and in addition leads to a significant reduction of the necessary decoding iterations when iterative decoding is performed.

The partial response channel can be viewed as a rate-1 encoder in which the output alphabet differs from the input alphabet. In serially concatenated coding schemes, the partial response channel can serve as the inner encoder. Recent work has focused on convolutional codes and parity-check codes as the outer code in such serial concatenation schemes. This work focuses instead on the use of product codes as the outer code. Systems using both hard and soft decoding, with both iterative and non-iterative decoding, are presented. Simulation results are presented comparing performance of product codes which use Reed-Solomon and BCH codes as the constituent codes.