里德所羅門碼之改良式信念傳遞解碼演算法

Abstract

由於具有良好更正叢集錯誤的能力和有效率的代數硬式決策解碼演算法，里德所羅門碼 (Reed Solomon Codes) 在最近已成為許多通訊系統所選擇使用的錯誤更正碼。眾所皆知，里德所羅門碼的軟式決策解碼相較於傳統的硬式決策解碼能夠提供明顯的效能改善，但由於其軟式決策解碼的高複雜度，目前大部分的系統仍然使用傳統的硬式決策解碼器。Jiang 和Narayanan於2006 年提出了一種利用適應性校驗矩陣，對里德所羅門碼進行軟式輸出輸入解碼的演算法(JN 演算法) 。JN 演算法能夠避免校驗節點飽和化以及低信任度位置之錯誤傳遞等問題，然而其潛在的問題在於過度信任高信任度位置的訊息。在本篇論文中，我們首先分析JN 演算法失敗的理由。基於我們的討論，我們提出一個新的演算法來避免發生在高信任度的錯誤所對JN演算法帶來的影響並改進其效能。我們的演算法之構想來自於1995 年由Fossorier 和Lin 所提出的OSD 演算法。在做JN 演算法之前，我們先對收到的向量做一些調整。如此一來，一些發生在高信任度位置的錯誤可以被減少。因此，發生在高信任度的錯誤所造成的影響也可以被減少。和原本的JN 演算法比較，在可加性白色高斯雜訊通道並使用雙相位鍵移調變之下，我們的演算法有大約0.5-1.2dB 的效能增進。

Recently, Reed-Solomon (RS) codes have been the error-correction codes (ECCs) of choice in many communication systems because of their ability to correct burst errors and the availability of efficient algebraic hard decision decoding algorithms. It is known that soft-decision decoding (SDD) of RS codes provides significant performance gain over hard decision decoding (HDD), but most systems still are based on HDD because of the high complexity of SDD. In 2006, Jiang and Narayanan (JN) proposed an iterative soft-in soft-out decoding algorithm of RS codes by adapting the parity check matrix. The JN algorithm can avoid the problem of check node saturation and the error propagation from the least reliable positions, but the drawback of the JN algorithm is to over believe the messages from the most reliable positions. In this thesis, we first analyse the reason of decoding failure in the JN algorithm. Based on our discussions, we propose a new algorithm to avoid the influence of errors in most reliable positions in the JN algorithm and improve the decoding performance. The basic idea of our algorithm comes from the OSD algorithm, which was proposed in 1995 by Fossorier and Lin. We modify the received vector before the JN algorithm. Some errors in the most reliable positions may be reduced. Therefore, the influence of errors in high reliable positions can also be reduced. Compared with the original JN algorithm, the proposed algorithm has about a 0.5-1.2dB coding gain while decoding RS codes in the additive white Gaussian noise (AWGN) channel under binary phase shift keying (BPSK) modulation.