A soft-decision Reed-Solomon decoding algorithm has been proposed by Koetter and Vardy, which provides a significant coding gain by utilizing channel output reliability information. In this paper we present a Chase-type soft-decision algorithm which provides additional gains at the expense of a small increase in complexity. We evaluate the performance of this decoding algorithm on additive white Gaussian noise channel and Rayleigh fading channels. Simulation results show that coding gains on the order of several dB can be achieved on uncorrelated Rayleigh fading channels over traditional hard-decision Reed-Solomon decoding algorithms.
"The complexity of Chase decoding, however, may be significantly reduced over this traditional approach (we note here that a similar approach as that presented was considered in  and ), which acts to decrease the average decoding complexity of Chase RS and BCH decoding. Here, we consider the maximum complexity required to decode, a widely utilized figure-of-merit for computational complexity. "
[Show abstract][Hide abstract] ABSTRACT: In this paper, we present an algebraic methodology for implementing low-complexity, Chase-type, decoding of Reed-Solomon (RS) codes of length n . In such, a set of 2 <sup>Â¿</sup> test-vectors that are equivalent on all except Â¿ Â¿ n coordinate positions is first produced. The similarity of the test-vectors is utilized to reduce the complexity of interpolation, the process of constructing a set of polynomials that obey constraints imposed by each test-vector. By first considering the equivalent indices, a polynomial common to all test-vectors is constructed. The required set of polynomials is then produced by interpolating the final Â¿ dissimilar indices utilizing a binary-tree structure. In the second decoding step ( factorization ) a candidate message is extracted from each interpolation polynomial such that one may be chosen as the decoded message. Although an expression for the direct evaluation of each candidate message is provided, carrying out this computation for each polynomial is extremely complex. Thus, a novel, reduced-complexity, methodology is also given. Although suboptimal, simulation results affirm that the loss in performance incurred by this procedure is decreasing with increasing code length n , and negligible for long (n > 100) codes. Significant coding gains are shown to be achievable over traditional hard-in hard-out decoding procedures (e.g., Berlekamp-Massey) at an equivalent (and, in some cases, lower) computational complexity. Furthermore, these gains are shown to be similar to the recently proposed soft-in-hard-out algebraic techniques (e.g., Sudan, KoÂ¿tter-Vardy) that bear significantly more complex implementations than the proposed algorithm.
IEEE Transactions on Information Theory 04/2010; 56(3-56):945 - 959. DOI:10.1109/TIT.2009.2039073 · 2.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Type-II hybrid ARQ protocols are widely used in current packet-oriented systems, such as wireless ATM, in combination with powerful error-correction codes for robust transmission and high channel throughput. In this paper, we investigate Reed-Solomon codes and soft-decision decoding algorithms for type-II hybrid ARQ systems, which lead to improved performance and higher channel throughput.
Global Telecommunications Conference, 2004. GLOBECOM '04. IEEE; 01/2004
[Show abstract][Hide abstract] ABSTRACT: We propose efficient forward recursive algorithms for algebraic soft-decision list decoding of Reed-Solomon codes, which utilize channel reliability information, and outperform the Koetter-Vardy (KV) algorithm with lower decoding latency. We evaluate the performance of the proposed decoding algorithms on additive white Gaussian noise and partial response channels. Simulation results show that we can achieve better performance on a modified extended-extended partial response class 4 channel than on the best possible performance of the KV algorithm, as given by the asymptotic bound for high-rate codes.
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