正交調變/RS編碼系統的軟式解碼法之研究

Abstract

本論文旨在研究正交調變/RS編碼通訊系統相同的系統設計議題。其中尤以軟式解碼方法為我們的研究重點。我們的解碼演算法是根據連續擦拭之最小距離解碼方法(Successive Erasure Minimum Distance Decoding, SEMDD)的原理而來。對於此演算法, 我們同時探討了同調檢測(coherent detection)與非同調檢測(noncoherent detection)分別在白色高斯雜訊(AWGN)通道及瑞雷衰褪(flat Rayleigh fading)通道下的效能。此外，我們也推導出在各種通訊環境下最佳與次佳的貝氏可靠度函數(Bayesian reliability function)。 在傳統的SEMDD中，我們需要做[(d+1)/2]次的代數解碼。為了減低解碼過程中的延遲以及其硬體複雜度，我們利用廣義的解碼徵狀演算法(generalized syndrome algorithm)，因為這個演算法只需要做一次代數解碼即可。在本論文中，我們以不同的RS碼為例，模擬各種解碼法的效能然後與部分的理論值作比較，最後我們並提出一種實際可行的解碼器設計建議。

Issues concerning the design of an orthogonal-modulated RS-coded communication system are studied in this thesis. The major focus is on soft-decision decoding of RS-coded orthogonal signals. Our decoding algorithm is based on the principle of successive erasure minimum distance decoding (SEMDD). We consider both additive white Gaussian noise(AWGN) and flat Rayleigh fading channels and investigate the effectiveness of both coherent and noncoherent detectors. Optimum and suboptimal Bayesian reliability functions for various operating scenarios are derived. In order to reduce the decoding delay and complexity, a fast generalized syndrome algorithm is used to implement SEMDD. This fast algorithm calls for a single-run algebraic decoding instead of $(\frac{d+1}{2})$ runs that are needed in conventional SEMDD. We examine the performance of different RS codes predicted by computer simulations and suggest practical and efficient soft decision decoder design. Analytic performance bounds for some decoders are also computed and compared with the simulation results.