Exchange Of Extrinsic Information Research Articles

Protograph-Based Interleavers for Punctured Turbo Codes

A method to design efficient puncture-constrained interleavers for turbo codes (TCs) is introduced. Resulting TCs profit from a joint optimization of puncturing pattern and interleaver to achieve an improved error rate performance. First, the puncturing pattern is selected based on the constituent code Hamming distance spectrum and on the TC extrinsic information exchange under uniform interleaving. Then, the interleaver function is defined via a layered design process taking account of several design criteria, such as minimum span, correlation girth, and puncturing constraints. We show that applying interleaving with a periodic cross connection pattern that can be assimilated to a protograph improves error-correction performance when compared to the state-of-the-art TCs. An application example is elaborated and compared with the long-term evolution standard: a significant gain in performance can be observed. An additional benefit of the proposed technique resides in the important reduction of the search space for the different interleaver parameters.

Performance analysis and optimisation for edge connection of JSCC system based on double protograph LDPC codes

For a joint source-channel coding system based on double protograph low-density parity-check codes, the exchange of extrinsic information through edge connection between the source code and channel code is essential for good performance. In this study, the relationship between the performance and edge connection in the tanner graph is analysed and it has never been seen in the literature to the authors' knowledge. Both the joint protograph extrinsic information transfer and simulation results indicate that the edge connection should be optimised in practical applications since it plays an important role in the bit error rate performance and an optimisation scheme for the edge connection is put forward to enhance performance.

Dynamic iteration stopping algorithm for non-binary LDPC-coded high-order PRCPM in the Rayleigh fading channel

This paper mainly studies the association between non-binary low-density parity-check codes and high-order partial response continuous phase modulation, which prevents information loss in the mutual conversion of bit and symbol probabilities. Although the iterative detection and decoding technique applied in this system can obtain good performance/complexity tradeoff, the iterative process still encounters the problems of positive feedback and relatively large decoding delay, similar to other iterative coded modulation systems. The inhibitory effects of different extrinsic information exchange methods on positive feedback under different signal-to-noise ratio (SNR) conditions are investigated in this work to address this issue. Two dynamic iterative stopping algorithms, namely, cross entropy and hard decision aided combined with weighted extrinsic information exchange for cases with medium and high SNRs, are then proposed. Extrinsic information exchange between the demodulator and the decoder is conducted in the two algorithms through weighted processing. Iterative detection is subsequently performed based on two stopping criteria of dynamic iterative decoding. Theoretic analysis and simulation results for the Rayleigh fading channel show that the combination of weighted extrinsic information exchange and the two dynamic iterative stopping algorithms effectively resists positive feedback and improves the convergence of iterative detection and bit error rate performance. Such a combination also reduces the average iteration number to improve the real-time performance of iterative detection and decoding.

Joint Detection and Decoding in LDPC-Based Space-Time Coded MIMO-OFDM Systems via Linear Programming

This work proposes a novel linear programming approach for the joint detection and decoding of LDPC-based space-time (ST) coded signals in multi-antenna orthogonal frequency division multiplexing (OFDM) systems. While traditional receivers typically decouple the detection and decoding processes as two disjunctive blocks or require iterative turbo exchange of extrinsic information between the soft detector and decoder, we formulate a joint linear program (LP) by exploiting the constraints imposed on the data symbols, training symbols, noise subspace as well as channel code. In consideration of the vast amount of LDPC parity check inequalities, we further present an adaptive procedure to significantly reduce the complexity of the joint LP receiver. Our LP-based receivers outperform existing receivers with substantial performance gains. Moreover, the proposed joint LP receiver demonstrates strong robustness when pilot symbols are sparsely arranged on subcarriers.

Reconfigurable Parallel Turbo Decoder Design for Multiple High-Mobility 4G Systems

For high-mobility 4G applications of LTE-A and WiMAX-2 systems, this paper presents a dual-standard turbo decoder design with the following three techniques. 1) Circular parallel decoding reduces decoding latency and improves throughput rate. 2) Collision-free vectorizable dual-standard parallel interleaver enhances hardware utilization of the interleaving address generator. 3) One-bank extrinsic buffer design with bit-level extrinsic information exchange reduces size of the extrinsic buffer compared with the two-bank extrinsic buffer design. Furthermore, a multi-standard turbo decoder chip is fabricated in a core area of 3.38 mm2 by 90 nm CMOS process. This chip is maximally measured at 152 MHz with 186.1 Mbps for LTE-A standard and 179.3 Mbps for WiMAX-2 standard.

Immediate Exchange of Extrinsic Information for High-Throughput Turbo Decoding

To increase the throughput of turbo decoding, a new decoding method is proposed in this letter. The proposed method performs two decoding phases, in-ordered and interleaved ones, simultaneously by using two SISO decoders, which is completely contrast to the conventional decoding approach that conducts one of the two phases alternatively. The two SISO decoders exchange their outputs immediately to accelerate the update of extrinsic information and in turn to reduce the overall decoding latency, increasing the throughput by almost two times. Moreover, the proposed decoding method can be applied to any turbo code specified in communication standards, because it is not necessary to modify the encoding process. The effectiveness of the proposed method is verified from intensive simulations conducted for 3GPP LTE-Advanced codes.

Adaptive Linear Turbo Equalization Over Doubly Selective Channels

Over the last decade, tremendous gains, leading to near-capacity achieving performance, have been shown for a variety of communication systems through the application of the turbo principle, i.e., the exchange of extrinsic information between constituent algorithms for tasks such as channel decoding, equalization, and multiple-input–multiple-output (MIMO) detection. In this paper, we study the practical application of such an iterative detection and decoding (IDD) framework to underwater acoustic communications. We explore complexity and performance tradeoffs of a variety of turbo equalization (TEQ)-based receiver architectures. First, we elaborate on two popular but suboptimal turbo equalization techniques: a channel-estimate-based minimum mean-square error TEQ (CE-based MMSE-TEQ) and a direct-adaptive TEQ (DA-TEQ). We study the behavior of both TEQ approaches in the presence of channel estimation errors and adaptive filter adjustment errors. We confirm that after a sufficient number of iterations, the performance gap between these two TEQ algorithms becomes small. Next, we demonstrate that an underwater receiver architecture built upon the least mean squares (LMS) DA-TEQ technique can leverage and dramatically improve the performance of the conventional implementation based on the decision-feedback equalizer at a feasible complexity. To maintain performance gains over time-varying channels, the slow convergence speed of the LMS algorithm has been improved via two methods: 1) repeating the weight update for the same set of data with decreasing step size and 2) reducing the dimensionality of the equalizer by capturing sparse channel structure. This receiver architecture was used to process collected data from the SPACE 08 experiment (Martha's Vineyard, MA). Receiver performance for different modulation orders, channel codes, and hydrophone configurations is examined at a variety of distance, up to 1 km from the transmitters. Experimental results show great promise for this approach, as data rates in excess of 15 kb/s could readily be achieved without error.

Joint iterative decoding for pragmatic irregular LDPC-coded multi-relay cooperations

In this article, a new kind of pragmatic simple-encoding irregular systematic low-density parity-check (LDPC) code for multi-relay coded cooperation is designed, where the introduced joint iterative decoding is performed in the destination based on a proposed joint Tanner graph for all the constituent LDPC codes used by the source and relays in multi-relay cooperation. The theoretical analysis and numerical results show that the coded cooperations outperform the coded non-cooperation under the same code rate, and also achieve a good trade-off between the performance and the decoding complexity associated with the number of relays. This performance gain can be credited to the additional exchange of extrinsic information from the LDPC codes used by the source and the relays in both ideal and non-ideal cooperations.

Iterative Receiver Design With Joint Doubly Selective Channel and CFO Estimation for Coded MIMO-OFDM Transmissions

This paper is concerned with the problem of turbo (iterative) processing for joint channel and carrier frequency offset (CFO) estimation and soft decoding in coded multiple-input-multiple-output (MIMO) orthogonal frequency-division-multiplexing (OFDM) systems over time- and frequency-selective (doubly selective) channels. In doubly selective channel modeling, a basis expansion model (BEM) is deployed as a fitting parametric model to reduce the number of channel parameters to be estimated. Under pilot-aided Bayesian estimation, CFO and BEM coefficients are treated as random variables to be estimated by the maximum a posteriori technique. To attain better estimation performance without sacrificing spectral efficiency, soft bit information from a soft-input-soft-output (SISO) decoder is exploited in computing soft estimates of data symbols to function as pilots. These additional pilot signals, together with the original signals, can help to enhance the accuracy of channel and CFO estimates for the next iteration of SISO decoding. The resulting turbo estimation and decoding performance is enhanced in a progressive manner by benefiting from the iterative extrinsic information exchange in the receiver. Both extrinsic information transfer chart analysis and numerical results show that the iterative receiver performance is able to converge fast and close to the ideal performance using perfect CFO and channel estimates.

Near-capacity iterative decoding of binary self-concatenated codes using soft decision demapping and 3-D EXIT charts

In this paper 3-D Extrinsic Information Transfer (EXIT) charts are used to design binary Self-Concatenated Convolutional Codes employing Iterative Decoding (SECCC-ID), exchanging extrinsic information with the soft-decision demapper to approach the channel capacity. Recursive Systematic Convolutional (RSC) codes are selected as constituent codes, an interleaver is used for randomising the extrinsic information exchange of the constituent codes, while a puncturer helps to increase the achievable bandwidth efficiency. The convergence behaviour of the decoder is analysed with the aid of bit-based 3-D EXIT charts, for accurately calculating the operating EbN0 threshold, especially when SP based soft demapper is employed. Finally, we propose an attractive system configuration, which is capable of operating within about 1 dB from the channel capacity.

Three-Stage Irregular Convolutional Coded Iterative Center-Shifting $K$-Best Sphere Detection for Soft-Decision SDMA–OFDM

The iterative exchange of extrinsic information between the K-best sphere detector (SD) and the channel decoder is appealing since it is capable of achieving a near maximum a posteriori (MAP) performance at a moderate complexity. However, the computational complexity imposed by the K-best SD significantly increases when using a large value of K for the sake of maintaining a near-MAP performance in a high-throughput uplink spatial-division multiple access (SDMA) orthogonal frequency-division multiplexing (OFDM) system supporting a large number of users and/or a high number of bits/symbol. This problem is further aggravated when the number of users/mobile stations (MSs) U exceeds that of the receive antennas N at the base station (BS), namely, in the challenging scenario of rank-deficient systems. We demonstrate that the iterative decoding convergence of this two-stage system may be improved by incorporating a unity rate code (URC) having an infinite impulse response, which improves the efficiency of the extrinsic information exchange. Although this results in a slightly more complex three-stage system architecture, it allows us to use a low-complexity SD having a significantly reduced candidate list size N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cand</sub> . Alternatively, a reduced signal-to-noise ratio (SNR) is required. For example, given a target bit error ratio (BER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> and N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cand</sub> = 32 for the SD, the three-stage receiver is capable of achieving a performance gain of 2.5 dB over its two-stage counterpart in a rank-deficient SDMA/OFDM 4-quadratic-amplitude modulation (4-QAM) system supporting U = 8 cochannel users and employing N = 4 receive antennas at the BS, namely, in an (8 x 4) system. For the sake of further enhancing the three-stage concatenated receiver, the proposed iterative center-shifting SD scheme and the irregular convolutional codes (IrCCs) are intrinsically amalgamated, which leads to an additional performance gain of 2 dB.

Semi-Iterative Analog Turbo Decoding

Based on multiple-slice turbo codes, a novel semi-iterative analog turbo decoding algorithm and its corresponding decoder architecture are presented. This work paves the way for integrating flexible analog decoders dealing with frame lengths over thousands of bits. The algorithm benefits from a partially continuous exchange of extrinsic information to improve decoding speed and correction performance. The proposed algorithm and architecture are applied to design an analog decoder for double-binary codes. Taking full advantage of multiple slice codes, the on-chip area is shown to be reduced by ten when compared to a conventional fully parallelized analog slice turbo decoder. The reconfigurable analog core area for frames of 40 bits up to 2432 bits is 37 nm2 in a 0.25-mum BiCMOS process.

A LOW-COMPLEXITY ITERATIVE RECEIVER FOR MULTIUSER SPACE-TIME BLOCK CODING SYSTEMS

In an iterative receiver of a bandwidth-efficient multiuser space-time block coding (STBC) system, the extrinsic information is iteratively exchanged among the soft-input soft-output (SISO) channel decoders, the soft-output multiuser detector and the soft-output M-ary demodulators. Error performance, complexity and efficiency of the extrinsic information exchange are the most important properties of an iterative receiver. Taking these factors into account, sigma mapping is first applied to M-QAM constellations to yield a low-complexity soft-output minimum mean squared error (MMSE) demodulator to be used in the iterative receiver. Then a low-complexity two-loop iterative receiver is proposed for the multiuser STBC systems. It is shown that by running an additional inner iteration (between the channel decoders and the M-ary demodulators) for every outer iteration (between the channel decoders and the multiuser detector), the proposed receiver is superior to the conventional one, in which only one inner iteration is executed per one outer iteration. The results in this paper are therefore useful for wireless applications that employ space-time coding and require a very high bandwidth efficiency.

Bandwidth reduction of extrinsic information exchange in turbo decoding

Besides computations and decoding delay, iterations in turbo decoding imply intensive and random extrinsic information exchange between component decoders. This high data exchange rate needs huge communication and routing resources to support the required bandwidth. Proposed is a novel symbol-based criterion to reduce the extrinsic information bandwidth in turbo decoding. The proposed criterion measures each symbol&apos;s contribution to the convergence of the iterative process and inhibits unnecessary extrinsic information exchange according to an appropriate threshold. Simulation results demonstrate a 20–25% mean extrinsic information exchange rate reduction with negligible error-rate degradation. This significant bandwidth reduction can directly alleviate communication and routing architecture.

Combined turbo detection and decoding for unknown isi channels

We present two decoding structures which combine turbo detection and decoding, allowing communication in the presence of intersymbol interference (ISI). The first one treats the ISI as another constituent decoder which participates in the exchange of extrinsic information, and performs slightly worse than the second structure, which combines the trellis representing each one of the constituent encoders with the ISI trellis. We show that for both methods, it is possible to obtain good performance, even when no a priori information about the ISI channel is available to the decoder.

Code characteristic matching for iterative decoding of serially concatenated codes

The design of serially concatenated codes has yet been dominated by optimizing asymptotic slopes of error probability curves. We propose mutual information transfer characteristics for soft in/soft out decoders to design serially concatenated codes based on the convergence behavior of iterative decoding. The exchange of extrinsic information is visualized as a decoding trajectory in the Extrinsic Information Transfer Chart (exit chart). By finding matching pairs of inner and outer decoder transfer characteristics we are able to construct serially concatenated codes whose iterative decoder converges towards low bit error rate at signal- to- noise ratios close to the theoretical limits.

Convergence behavior of iteratively decoded parallel concatenated codes

Mutual information transfer characteristics of soft in/soft out decoders are proposed as a tool to better understand the convergence behavior of iterative decoding schemes. The exchange of extrinsic information is visualized as a decoding trajectory in the extrinsic information transfer chart (EXIT chart). This allows the prediction of turbo cliff position and bit error rate after an arbitrary number of iterations. The influence of code memory, code polynomials as well as different constituent codes on the convergence behavior is studied for parallel concatenated codes. A code search based on the EXIT chart technique has been performed yielding new recursive systematic convolutional constituent codes exhibiting turbo cliffs at lower signal-to-noise ratios than attainable by previously known constituent codes.

Convergence of iterative decoding

A novel method for visualising the convergence behaviour of iterative decoding schemes is proposed. Each constituent decoder is represented by a mutual information transfer characteristic which describes the flow of extrinsic information through the soft in/soft out decoder. The exchange of extrinsic information between constituent decoders is plotted in an extrinsic information transfer chart. The concepts are illustrated for an iterative demapping and decoding scheme.