使用奈奎斯頻寬的可實現錯誤更正區塊編碼系統技術

Abstract

在本篇論文中，我們提出一個可實現奈奎斯頻寬（Nyquist-bandwidth）的錯誤更正區塊編碼系統技術，目的是希望能在有限頻帶的通訊系統中，可使用最小奈奎斯頻寬傳送資料因而達到增加頻寬效益的目的，同時結合錯誤更正的功能。在本論文先提出實現奈奎斯頻寬的系統中使用的錯誤更正碼要符合的限制，就是更正碼的碼字在奇數位置的漢明權重（Hamming weight）要等於偶數位置的漢明權重。之後介紹我們提出兩種可符合限制的修正更正碼：修正里得-米勒碼(Reed-Muller codes)和交錯式的定權碼（constant weight codes）。我們分別為這兩種碼設計專用的系統架構，其中各自的軟決策解碼器(soft decision decoder)包含最大概似解碼器（maximum likelihood decoder）和複雜度較低的近似最大概似解碼器。由於複雜度越高的近似最大概似解碼器會越接近理想的最大概似解碼器，故解碼時會得到越好的錯誤率性能，我們分析使用不同複雜度下的近似最大概似解碼器所得到的錯誤率和訊雜比的模擬圖，藉此在可接受的錯誤率效能下選擇較低的複雜度的解碼器。最後在本論文將比較正交多速率調變、平方根升餘弦（square-root raised cosine）系統及我們提出的系統在使用多種更正碼下其頻寬效益對雜訊比的模擬圖，分析各個系統頻寬效益和錯誤率的比較。結果發現在所有系統使用相同的定權碼下，我們的系統可以得到最好的頻寬效益，並且在某些定權碼可以得到較好的錯誤率表現。

In this thesis, we propose the realizable Nyquist-bandwidth block-coded systems. We design a bandlimited error-correction system occupying the Nyquist-bandwidth and hence improve bandwidth efficiency. The constraint of the error correcting codes for the realizable Nyquist-bandwidth block-coded systems is developed. The constraint of code is that the Hamming weight of the odd positions must equal the Hamming weight of the even positions. We propose the modified Reed-Muller codes and the interleaved constant weight code, in which the two modified codes can satisfy the developed constraint. We design the system structures for the modified error correcting codes which we propose. The soft decision decoders including maximum likelihood decoder (ML) and approximate maximum likelihood decoder (AML) are also derived. When the complexity of AML decoder is higher, the error performance is better. We analyze the error performance between the different complexity of the AML decoders. Eventually, we compare the error performance and spectral efficiency between orthogonal multirate modulation, square-root raised cosine pulsed modulation, and the Nyquist-bandwidth block-coded systems when using different error correcting codes. When the three systems use the same constant weight code, it’s shown that the proposed system has better spectral efficiency. We can also find some constant weight codes which have better error performance than orthogonal multirate modulation and square-root raised cosine pulsed modulation.