二元籬柵之反覆曲折平方建構

Iterative Twisted Squaring Construction of Binary Trellis

詹益坤(Ji-Kuen Jan)

指導教授 ： 馬尚智

中原大學/工學院/電機工程研究所/碩士(2006年)

https://doi.org/10.6840/cycu200600326

摘要

本篇論文是討論利用平方建構(Squaring Construction)來建立線性區段碼(Linear Block Codes)的籬柵(Trellis)，並試著將其應用在區段碼調變(Block Code Modulation)做為組成碼(Component codes)。與一般迴旋碼(Convolutional Codes)及渦輪碼(Turbo Codes)不同的是，線性區段碼的籬柵生成複雜度以及解碼複雜度將隨著碼長的增加而增加，應用了平方建構的觀念，我們可以由較短的線性區段碼分割(Partition)生成較長的線性區段碼，比傳統方式較為容易的建立線性區段碼的籬柵，並且降低威特比演算法(Viterbi Algorithm)的複雜度，也就是較少的加法(Addition)與比較(Comparison)，當我們結合區段碼調變的觀念後，可以建立符合我們想要的碼長及碼率之線性區段碼，帶入其分層(Level)當中，獲取較好的表現(Performa- nce)，並且減少實作上的解碼運算量。

關鍵字

線性區段碼 ； 籬柵 ； 平方建構 ； 區段碼調變

並列摘要

This paper attempts to apply trellis of linear block codes that constructed by SC (squaring sonstruction) into BCM (block coded modulation). Different from convolutional codes and turbo codes, the difficulty and complexity of trellis of linear block codes will increase along with code lengths. Easier than the traditional methods, the application of squaring construc- tion can span the longer codes from the shorter codes; furth- ermore, it lowers the complexity of Viterbi algorithm, which means fewer addition and comparison. Following the concept of block coded modulation, it constructs the codes with code lengths and code rates that correspond with our expectations, and then we can bring it in one level of block code modulation to obtain better performance without too many decoding compu- tations.

並列關鍵字

trellis ； block code modula- tion ； squaring construction ； linear block code

參考文獻

[1] L. Bahl, J. Cocke, F. Jelinek, and J. Raviv. "Optimal decoding of linear codes for minimizing symbol error rate," IEEE Trans. Inform. Theory, vol. IT-20, pp. 284- 287, Mar. 1974.

[2] J.K. Wolf, "Efficient maximum likelihood decoding of linear block codes using a trellis," IEEE Trans. Inform. Theory, vol. IT-24, pp. 76-81, January 1978.

[3] A. J. Viterbj, “Error bounds for convolutional codes and an asymto- tically optimum decoding algorithm,” IEEE Trans. Inform. Theory, vol. IT-13, pp. 260-269, Apr. 1967.

[4] G. D. Forney. Jr., "Cosets codes - part 11: Binary lattices and related codes," IEEE Trans. Inform. Iheory, vol. 34, pp. 1152-1187, 1988.

[5] H. Imai and S. Hirakawa, “A new multilevel coding method using error correcting codes,’’ IEEE Trans. Inform. Theory, vol. IT-23, pp. 371-377, 1977.