適用於里德所羅門碼之適應性信念傳遞解碼法則其效能改進之研究

Abstract

由於里德所羅門碼的良好錯誤更正能力常被應用在如數位通訊與數位儲存媒體中，為目前被廣泛使用的錯誤控制碼之一。解碼方面，目前已知軟式決策解碼相較於傳統的硬式決策解碼器有明顯的改善。但軟式決策解碼可能會面臨高解碼複雜度的困難，因此有學者針對複雜度與錯誤率的權衡提出了相關的研究，包括基於信任度解碼與疊代解碼等等，其中本論文對疊代解碼進行討論。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)。而於本篇論文中，我們將討論造成JN演算法解碼失敗的原因，包括JN演算法中高信任度位置錯誤以及JN演算法在疊代過程中收斂至錯誤的合法碼字所造成的影響，並基於討論提出適當的演算法來避免此問題，並以1995 年由Fossorier和Lin所提出的OSD演算法輔助JN在疊代過程中的訊息傳遞機制，並增進其解碼效能。最後綜合論文中提出的演算法和JN-OSD(1)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，大約有0.5 - 2.0 dB的效能改善。

Reed-Solomon (RS) codes have been the error-correction codes of choice in many communication systems because of their good correction capability. For the decoding of RS codes, it is known that soft-decision decoding (SDD) of RS codes provides significant performance gain over algebraic hard decision decoding (HDD). There are many researches including reliability-based decoding and iterative decoding which are devoted to better trade-off between the decoding complexity and performance 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. In this thesis, we discuss the reasons of decoding failure in the JN algorithm. Based on our discussion, we propose different algorithms to avoid the influence of the errors in the most reliable positions and the output of JN convergence to an erroneous valid codeword during iterations. We propose the algorithms using the Ordered Statistic Decoding algorithm which was proposed in 1995 by Fossorier and Lin to modify the message passing rule during the iterations in JN algorithm and helps to improve the decoding performance. Finally, compared with the original JN-OSD(1) algorithm, our design has about a 0.5-2.0dB coding gain while decoding RS codes in the additive white Gaussian noise channel under binary phase shift keying Modulation.