可以達到接近薛農極限(Shannon limit)的渦輪編解碼，近年來在編解碼的研究領域引起了廣範的注意與熱烈的研討。渦輪碼的編碼器是由兩個以上的平行鏈結的迴旋編碼器(convolutional code)及連結於這些迴旋編碼器間的交錯器(interleaver)所構成。除了所採用的迴旋編碼器、交錯器的長度與其交錯排列的方式直接影響到渦輪碼於位元錯誤率(bit error rate)上的表現。
研究顯示[1][2]，在訊號雜訊比(signal to noise ratio)為0.5 dB的情況下，傳輸率為1/2之渦輪碼可以將位元錯誤率降低到10-5以下。因為如此高的編碼增益與可容許的解碼複雜度，許多制訂中的無線通訊協定、如3GPP，已考慮採用渦輪碼做為錯誤更正碼。在本篇論文，我們首先著重在對3GPP中名為PIL之交錯器的分析，尤其是對它交錯排列方式的瞭解。進一步的我們發現了它設計上的缺陷並加以改進，使得交錯排列的結果更加的紊亂而沒有秩序可循。依據這樣的修正，我們在最後由模擬證實修改後的PIL運用於渦輪碼上表現得更好。

另者，在研究過程中除了列舉數種交錯器及各自對應的參數值異同的比較，最重要的是我們提出一種省時快速的方法，在不須要採取軟體模擬的前提下，我們可以從提供的交錯器中評比出應用於渦輪碼時熟優熟劣。在最後的模擬結果，除了得以證明我們提出的快速評比演算法的正確性，我們也藉以觀察到所列舉的各種交錯器運用於渦輪碼時的好壞，同時分析交錯器長度對渦輪碼表現的相對影響，並在最終做簡明的總結。

Turbo codes, proposed by Berrou, Glavieux, and Thitimajshima in
1993, have been perhaps the most exciting development in coding

theory in recent years. Due to the powerful coding gain and

acceptable decoding complexity, wireless communication systems,

like the $3^{rd}$ Generation Partnership Project (3GPP), seriously consider utilizing the turbo code as the forward error correcting code. In this thesis, in addition to analysis of the prime interleaver (PIL) which is employed as the internal interleaver of the turbo code in 3GPP, a modified PIL is proposed to yield better bit error rate (BER) performance than PIL. Furthermore, several interleaver parameters are utilized to examine several previously proposed interleavers. Most important of all, we propose a fast comparison algorithm to evaluate the BER performance of turbo codes with different interleavers. The comparison algorithm offers a time-efficient method to judge performances between distinct interleavers without complicated software simulations. Finally, computer simulations of turbo codes with several interleavers under distinct interleaver sizes are conducted, and the estimation

results are validated.

[1] C. Berrou, A. Glavieux, and P. Thitimajshima, "Near Shannon limit error-correcting coding and decoding: Turbo-codes," in Proc. IEEE Int. Conf. Commun., Geneva, Switzerland, May 1993, pp. 1064-1070.
[2] C. Berrou and A. Glavieux, "Near optimum error correcting coding and decoding: Turbo-codes," IEEE Trans. Commun., vol. 44, pp. 1261-1271 Oct. 1996.
[3] P. Robertson, "Illuminating the structure of code and decoder of parallel concatenated recursive systematic (TURBO) codes," in Proc. IEEE Global Telecommun. Conf., San
Francisco, CA, Dec. 1994, pp. 1298-1303.
[4] D. Divsalar and F. Pollara, "Turbo codes for deep-space communications," TDA Progr. Rep. 42-120, JetPropulsion Lab., Pasadena, CA, Feb., 1995.
[5] D. Divsalar and F. Pollara, "On the design of turbo codes," TDA Progr. Rep. 42-123, Jet Propulsion Lab., Pasadena, CA, pp. 99{121, Nov., 1995.
[6] S. Dolinar and D. Divsalar, "Weight distributions for turbo codes using random and non-random permutations," TDA Progr. Rep. 42-122, Jet Propulsion Lab., Pasadena, CA, pp. 56-65, Aug., 1995.
[7] D. Divsalar and F. Pollara, "Multiple turbo codes for deep-space communications," TDA Progr. Rep. 42-121, JetPropulsion Lab., Pasadena, CA, May, 1995.