對於數位無線麥克風來說，穩定且可靠的通道傳輸非常重要，所以會使用錯誤更正碼(Error Control Coding，ECC)來保護資料以避免被糟糕的通道品質所影響。但是數位無線麥克風通常為嵌入式系統，應使用複雜度較低的錯誤更正碼來確保整體系統的低延遲性以及較少的系統資源使用。Bose-Chaudhuri-Hocquenghem code(BCH碼)的低複雜度和高可靠度的特性，適合用於數位無線麥克風。在這論文中，我們將會實作BCH碼，該BCH碼使用線性反饋移位暫存器(Linear Feedback Shift Register，LFSR)當作編碼器；並使用Peterson演算法搭配秦式搜尋(Chein Search)當作解碼器。另外，我們透過使用查表法減少計算徵狀值(Syndrome)的延遲時間；以及使用變數變換來省略秦式搜尋。除此之外，我們實作交錯放置器(Interleaver)以抵抗叢發錯誤(Burst Error)，並更換重要資料位元的位置好讓其有更好的ECC保護。為了進行實驗，我們實作C語言版本的錯誤更正碼，並針對ARM的微處理器進行程式優化。我們使用了數位無線麥克風雛型系統來做當作實驗平台，並將錯誤更正碼程式燒錄至該平台的ARM微處理器以評估效能。實驗結果中，使用錯誤更正碼將平均增加0.35 ms的系統延遲時間，並將提升麥克風的有效傳輸距離約47%。

For digital wireless microphone, reliable channel communication is essential, so it uses error control coding (ECC) to protect data from bad channel quality. But digital wireless microphone is usually a embedded system, the complexity of ECC should be low to make sure low latency and low resource consumed. Bose-Chaudhuri-Hocquenghem code (BCH code) has low complexity and high reliability; it is suitable for digital wireless microphone. In this thesis, we will implement BCH code, and use Linear Feedback Shift Register (LFSR) as encoder; Peterson's algorithm and Chein search as decoder. Besides, we reduce the latency in syndrome computation by using look-up table, and omit Chein search by using variable transformation. In addition, we implement the interleaver to alleviate burst error, and change the location of important bits of data for stronger ECC protection. For experiment, we implement the ECC in C language and program is optimized for ARM microcontroller. In experiment, we use a prototype of digital wireless microphone system as platform; then load our ECC program to the ARM microcontroller in the system to evaluate the performance. In result, the latency of ECC is 0.35 ms in average and the transmission distence of microphone increases 47%.

1 簡介. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 回顧. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 BCH碼及有限域. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
2.2 BCH碼編碼. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
2.3 BCH碼解碼. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8
3 在嵌入式系統上實做BCH碼. . . . . . . . . . . . . . . . . . . . . . . . . 12
3.1 概要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
3.2 BCH 編解碼實作. . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
3.3 嵌入式C 語言寫法調整. . . . . . . . . . . . . . . . . . . . . . . . . .20
4 數位無線麥克風系統. . . . . . . . . . . . . . . . . . . . . . . . . . . .23
4.1 系統架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
4.2 無線傳輸行為. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25
4.3 整合錯誤更正碼. . . . . . . . . . . . . . . . . . . . . . . . . . . . .29
5 系統效能及可靠度優化. . . . . . . . . . . . . . . . . . . . . . . . . . .33
5.1 錯誤更正碼優化. . . . . . . . . . . . . . . . . . . . . . . . . . . . .33
5.2 系統可靠度優化. . . . . . . . . . . . . . . . . . . . . . . . . . . . .37
6 實驗結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45
6.1 實驗環境. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45
6.2 距離測試. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51
6.3 延遲時間. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60
7 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63
Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .64

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