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.Comment: 10 pages, 10 figures, final version accepted by IEEE Trans. on Information Theor

Adaptive and Iterative Multi-Branch MMSE Decision Feedback Detection Algorithms for MIMO Systems

In this work, decision feedback (DF) detection algorithms based on multiple processing branches for multi-input multi-output (MIMO) spatial multiplexing systems are proposed. The proposed detector employs multiple cancellation branches with receive filters that are obtained from a common matrix inverse and achieves a performance close to the maximum likelihood detector (MLD). Constrained minimum mean-squared error (MMSE) receive filters designed with constraints on the shape and magnitude of the feedback filters for the multi-branch MMSE DF (MB-MMSE-DF) receivers are presented. An adaptive implementation of the proposed MB-MMSE-DF detector is developed along with a recursive least squares-type algorithm for estimating the parameters of the receive filters when the channel is time-varying. A soft-output version of the MB-MMSE-DF detector is also proposed as a component of an iterative detection and decoding receiver structure. A computational complexity analysis shows that the MB-MMSE-DF detector does not require a significant additional complexity over the conventional MMSE-DF detector, whereas a diversity analysis discusses the diversity order achieved by the MB-MMSE-DF detector. Simulation results show that the MB-MMSE-DF detector achieves a performance superior to existing suboptimal detectors and close to the MLD, while requiring significantly lower complexity.Comment: 10 figures, 3 tables; IEEE Transactions on Wireless Communications, 201

Iterative Algebraic Soft-Decision List Decoding of Reed-Solomon Codes

In this paper, we present an iterative soft-decision decoding algorithm for Reed-Solomon codes offering both complexity and performance advantages over previously known decoding algorithms. Our algorithm is a list decoding algorithm which combines two powerful soft decision decoding techniques which were previously regarded in the literature as competitive, namely, the Koetter-Vardy algebraic soft-decision decoding algorithm and belief-propagation based on adaptive parity check matrices, recently proposed by Jiang and Narayanan. Building on the Jiang-Narayanan algorithm, we present a belief-propagation based algorithm with a significant reduction in computational complexity. We introduce the concept of using a belief-propagation based decoder to enhance the soft-input information prior to decoding with an algebraic soft-decision decoder. Our algorithm can also be viewed as an interpolation multiplicity assignment scheme for algebraic soft-decision decoding of Reed-Solomon codes.Comment: Submitted to IEEE for publication in Jan 200

Approximate MIMO Iterative Processing with Adjustable Complexity Requirements

Targeting always the best achievable bit error rate (BER) performance in iterative receivers operating over multiple-input multiple-output (MIMO) channels may result in significant waste of resources, especially when the achievable BER is orders of magnitude better than the target performance (e.g., under good channel conditions and at high signal-to-noise ratio (SNR)). In contrast to the typical iterative schemes, a practical iterative decoding framework that approximates the soft-information exchange is proposed which allows reduced complexity sphere and channel decoding, adjustable to the transmission conditions and the required bit error rate. With the proposed approximate soft information exchange the performance of the exact soft information can still be reached with significant complexity gains.Comment: The final version of this paper appears in IEEE Transactions on Vehicular Technolog

A Suboptimal Receiver with Turbo Block Coding for Ultra-Wideband Communications

In this paper, the performance of adaptive equalization and turbo product coding is investigated for pulse-based UWB communications in short-range indoor environments. The sensitivity of adaptive LMS linear and nonlinear (decision-feedback) equalizers with respect to the number of training symbols and number of taps is considered. To reduce the error performance variation with respect to changing channel conditions, a turbo product code (TPC) with two component (31,26,3) Hamming codes is proposed. We report simulation results showing that channel coding not only improves error performance, but also reduces significantly the sensitivity of UWB systems in short-range indoor wireless communications