Iterative Soft-input Soft-output Research Articles

Reliability Level List Based Iterative SISO Decoding Algorithm for Block Turbo Codes

An iterative Reliability Level List (RLL) based soft-input soft-output (SISO) decoding algorithm has been proposed for Block Turbo Codes (BTCs). The algorithm ingeniously adapts the RLL based decoding algorithm for the constituent block codes, which is a soft-input hard-output algorithm. The extrinsic information is calculated using the reliability of these hard-output decisions and is passed as soft-input to the iterative turbo decoding process. RLL based decoding of constituent codes estimate the optimal transmitted codeword through a directed minimal search. The proposed RLL based decoder for the constituent code replaces the Chase-2 based constituent decoder in the conventional SISO scheme. Simulation results show that the proposed algorithm has a clear advantage of performance improvement over conventional Chase-2 based SISO decoding scheme with reduced decoding latency at lower noise levels.

Turbo Coded OFDM Combined with MIMO Antennas Based on Matched Interleaver for Coded-Cooperative Wireless Communication

A turbo coded cooperative orthogonal frequency division multiplexing (OFDM) with multiple-input multiple-output (MIMO) antennas scheme is considered, and its performance over a fast Rayleigh fading channel is evaluated. The turbo coded OFDM incorporates MIMO (2 × 2) Alamouti space-time block code. The interleaver design, and its placement always plays a vital role in the performance of a turbo coded cooperation scheme. Therefore, a code-matched interleaver (CMI) is selected as an optimum choice of interleaver and is placed at the relay node. The performance of the CMI is evaluated in a turbo coded OFDM system over an additive white Gaussian noise (AWGN) channel. Moreover, the performance of the CMI is also evaluated in the turbo coded OFDM system with MIMO antennas over a fast Rayleigh fading channel. The modulation schemes chosen are Binary Phase shift keying (BPSK), Quadrature phase shift keying (QPSK) and 16-Quadrature amplitude modulation (16QAM). Soft-demodulators are employed along with joint iterative soft-input soft-output (SISO) turbo decoder at the destination node. Monte Carlo simulated results reveal that the turbo coded cooperative OFDM system with MIMO antennas scheme incorporates coding gain, diversity gain and cooperation gain successfully over the direct transmission scheme under identical conditions.

Efficient Decoding Technique for Block Product Turbo Codes

In this paper, we propose an efficient technique for an iterative soft input soft output (SISO) decoding algorithm of block turbo codes with constituent Hamming codes. Pyndiah’s iterative decoding algorithm for block turbo codes supports various code rates by using concatenation, and shows high bit error rate (BER) performance in an additive white Gaussian noise channel (AWGN) environment as the iterative decoding progresses. However, one disadvantage of this code is that the delay increases during decoding with an increasing number of iterations. By employing syndrome-based iterative SISO decoding and iterative SISO decoding using an alpha value, we could obtain high BER performance. In addition, we propose a SISO-hybrid maximum likelihood decoding (SISO-H-MLD) algorithm which achieves almost the same performance as SISO decoding while reducing the number of iterations.

Stochastic Decoding of Linear Block Codes With High-Density Parity-Check Matrices

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This correspondence extends the application of the recently proposed stochastic decoding approach to decode linear block codes with high-density parity-check matrices and discusses its hardware complexity. Results demonstrate decoding performance close to floating-point iterative soft-input soft-output (SISO) decoding while offering nodes with considerably lower complexity compared to fixed-point SISO decoding. </para>

Generalized Low-Density Parity-Check Codes Based on Hadamard Constraints

In this paper, we consider the design and analysis of generalized low-density parity-check (GLDPC) codes in AWGN channels. The GLDPC codes are specified by a bipartite Tanner graph, as with standard LDPC codes, but with the single parity-check constraints replaced by general coding constraints. In particular, we consider imposing Hadamard code constraints at the check nodes for a low-rate approach, termed LDPC-Hadamard codes. We introduce a low-complexity message-passing based iterative soft-input soft-output (SISO) decoding algorithm, which employs the a posteriori probability (APP) fast Hadamard transform (FHT) for decoding the Hadamard check codes at each decoding iteration. The achievable capacity with the GLDPC codes is then discussed. A modified LDPC-Hadamard code graph is also proposed. We then optimize the LDPC-Hadamard code ensemble using a low-complexity optimization method based on approximating the density evolution by a one-dimensional dynamic system represented by an extrinsic mutual information transfer (EXIT) chart. Simulation results show that the optimized LDPC-Hadamard codes offer better performance in the low-rate region than low-rate turbo-Hadamard codes, but also enjoy a fast convergence rate. A rate-0.003 LDPC-Hadamard code with large block length can achieve a bit-error-rate (BER) performance of 10-5 at -1.44 dB, which is only 0.15 dB away from the ultimate Shannon limit (-1.592 dB) and 0.24 dB better than the best performing low-rate turbo-Hadamard codes

Iterative Soft-Input Soft-Output Decoding of Reed–Solomon Codes by Adapting the Parity-Check Matrix

An iterative algorithm is presented for soft-input soft-output (SISO) decoding of Reed-Solomon (RS) codes. The proposed iterative algorithm uses the sum-product algorithm (SPA) in conjunction with a binary parity-check matrix of the RS code. The novelty is in reducing a submatrix of the binary parity-check matrix that corresponds to less reliable bits to a sparse nature before the SPA is applied at each iteration. The proposed algorithm can be geometrically interpreted as a two-stage gradient descent with an adaptive potential function. This adaptive procedure is crucial to the convergence behavior of the gradient descent algorithm and, therefore, significantly improves the performance. Simulation results show that the proposed decoding algorithm and its variations provide significant gain over hard-decision decoding (HDD) and compare favorably with other popular soft-decision decoding methods

On the Application of Factor Graphs and the Sum–Product Algorithm to ISI Channels

In this paper, based on the application of the sum-product (SP) algorithm to factor graphs (FGs) representing the joint a posteriori probability (APP) of the transmitted symbols, we propose new iterative soft-input soft-output (SISO) detection schemes for intersymbol interference (ISI) channels. We have verified by computer simulations that the SP algorithm converges to a good approximation of the exact marginal APPs of the transmitted symbols if the FG has girth at least 6. For ISI channels whose corresponding FG has girth 4, the application of a stretching technique allows us to obtain an equivalent girth-6 graph. For sparse ISI channels, the proposed algorithms have advantages in terms of complexity over optimal detection schemes based on the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. They also allow a parallel implementation of the receiver and the possibility of a more efficient complexity reduction. The application to joint detection and decoding of low-density parity-check (LDPC) codes is also considered and results are shown for some partial-response magnetic channels. Also in these cases, we show that the proposed algorithms have a limited performance loss with respect to that can be obtained when the optimal "serial" BCJR algorithm is used for detection. Therefore, for their parallel implementation, they represent a favorable alternative to the modified "parallel" BCJR algorithm proposed in the literature for the application to magnetic channels.

Adaptive Iterative Soft-Input Soft-Output Parallel Decision-Feedback Detectors for Asynchronous Coded DS-CDMA Systems

The optimum and many suboptimum iterative soft-input soft-output (SISO) multiuser detectors require a priori information about the multiuser system, such as the users' transmitted signature waveforms, relative delays, as well as the channel impulse response. In this paper, we employ adaptive algorithms in the SISO multiuser detector in order to avoid the need for this a priori information. First, we derive the optimum SISO parallel decision-feedback detector for asynchronous coded DS-CDMA systems. Then, we propose two adaptive versions of this SISO detector, which are based on the normalized least mean square (NLMS) and recursive least squares (RLS) algorithms. Our SISO adaptive detectors effectively exploit the a priori information of coded symbols, whose soft inputs are obtained from a bank of single-user decoders. Furthermore, we consider how to select practical finite feedforward and feedback filter lengths to obtain a good tradeoff between the performance and computational complexity of the receiver.