還迴旋碼在錯誤更正系統下之研究與應用

Abstract

本篇論文主要探討環迴旋碼應用在兩類的錯誤更正系統下的種種設計問題。這兩個不同的系統分別為禮德-所羅門碼 (RS Code)串接上環迴旋碼(Ring Convolutional Code)的連續相位調變(CPM) 信號所組合的系統以及使用環迴旋碼為組成碼(component codes)的渦輪碼 (Turbo Code)加上QPSK調變的系統。 在設計這兩種不同的錯誤更正系統時所面臨的一個關鍵性的問題就是如何適當的將可靠度的資訊傳遞到下一輪的解碼器。而目前為止，比較常用的做法有兩種，一個是軟式輸出腓特比解碼法(SOVA)而另一種則是最大後驗機率法 (MAP)。 Hagenaurer所提出的軟式輸出的腓特比解碼法乃是針對二位元的改錯碼推導出來的。在非二元的環境下不但不適用於渦輪碼且對於可靠度的估計較為不精確。因此我們提出非二元式軟輸出腓特比解碼法(nonbinary SOVA) 來解決這個問題。 最大後驗機率的解碼法最有名的要算是雙向的BCJR演算法。這種演算法需要等到整個字串(code word)傳完才能開始動作解碼的延遲相當可觀(尤其是渦輪碼)。我們於是提出一種新的單向最大後驗機率法 (one-way MAP)。而此解碼法較之於舊的單向最大後驗機率法較為簡單且保留了原有特性。

Because of the existence of a simple maximum-likelihood (ML) soft-decision algorithm and their powerful error-correcting capability, convolutional codes have been used in many wireless and satellite communication systems. However, most of convolutional codes used, except for the class of dual-k codes, are binary codes. The discussion of extending the code symbol size to arbitrary non-binary size has not been reported until recently, e.g., ring and group convolutional codes. This thesis presents an investigation on the application of ring convolutional codes (RCC) to and the performance of various forward error-correcting systems in multipath fading environments. More specifically, we investigate (i) a RCC-coded continuous phase modulation (CPM) system, (ii) a concatenated RS-RCC-coded CPM system and (iii) a RCC-based turbo code system. The associated design issues of concern to us are mainly due to the non-binary nature of the codes used, the statistics of the communication channel and the detection method of the receiver. Besides the algebraic structure of the code system, the issues are centered around the decoding algorithm, the decoding metric and the associated performance analysis. Among other topics studied, we derive an iterated maximum a posterior probability (MAP) decoding algorithm for noncoherently decoding the above non-binary codes over fading channels. We also present a modification of the soft-output Viterbi algorithm (SOVA) to serve the same need. Numerical results are provided to estimate the optimal or suboptimal system parameters and to predict the system behavior and performance trends so that better design choice can be found.