Abstract-In this work we present a low-complexity implementation of Chase-type decoding of Reed-Solomon Codes. In such, we first use the soft-information available at the channel output to construct a test-set of 2 η vectors, equivalent in all except the η << n least reliable coordinate positions. We then give an interpolation procedure to construct a set of 2 η bivariate polynomials, with the roots of each specified by its corresponding test-vector. Here, test-vector similarity is exploited to share much of the required computation. Finally, we obtain the candidate message from the single z-linear factor of each bivariate polynomial. Although we provide an expression for the direct computation of each candidate message, the complexity of repeating this computation for each interpolation polynomial is prohibitive. We, thus, also present a reduced-complexity factorization (RCF) method to select a single polynomial that, with high probability, contains the correctly decoded message in its z-linear factor. Although suboptimal, the loss in performance of RCF decreases rapidly with increasing code length. We provide extensive simulation results showing that a significant performance increase over traditional hard-decision decoding is achievable with a comparable computational complexity (as implemented with the BerlekampMassey Algorithm).
In this study we consider the challenge of reliable communication over a wireless Rayleigh flat-fading channel using multiple transmit and receive antennas. Since modern digital communication systems employ signal sets of finite cardinality, we examine the use of the Quadrature Amplitude Modulation (QAM) constellation to approach the capacity of this channel. By restricting the channel input to the M-QAM subset of the complex-plane, the maximum achievable information rate (C M-QAM ) is strictly bounded away from the channel capacity (C). We utilize a modified version of the Arimoto-Blahut algorithm to determine C M-QAM and the probability distribution over the channel input symbols that achieves it. The results of this optimization procedure numerically indicate that the optimal input symbol distribution factors into the product of identical distributions over each real dimension of the transmitted signal. This is shown to vastly reduce the computational complexity of the optimization algorithm. Furthermore, we utilize the computed optimal channel input probability mass function (pmf) to construct capacity approaching trellis codes. These codes are implemented independent across all antennas and symbol dimensions and, if used as inner codes to outer low-density parity check (LDPC) codes, can achieve arbitrarily small error rates at signal-to-noise ratios very close to the channel capacity C M-QAM . Examples are given for a 2-transmit/2-receive antenna (2 × 2) system. academic year.His research interests include the design of capacity approaching codes for the wireless MIMO channel, signal and code design for time-hopping and direct-sequence Ultra-Wideband (UWB) communication systems, modelling of the 3.1-10.6 GHz UWB channel, and decoding algorithms for Reed-Solomon Codes.
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