基於非二位元時變累加碼之渦輪碼於二位元輸入高斯通道設計與分析

根據其它文獻上證明的結果，我們得知隨機旁集(random-coset)非二位元的低密度同位檢查碼(low-density parity-check code, LDPC codes)及非規則重覆累加碼(irregular repeat-accumulate code, IRA code)在搭配q-ary的非均勻訊號星雲時，可達到無限制的通道極限。而在[19]中可得知隨機旁集IRA碼，因為使用的是簡單的時變累加碼(time-varying accumulate code)編碼，所以複雜度會比LDPC碼還低。且模擬的結果顯示，當我們將變數節點的度數固定為2時，就能得到不錯的效能，這也意味著對於非二位元重覆累加碼而言，只要將訊息重覆二次即可得到相當好的效能。因為訊息重覆二次，該編碼器就會擁有類似渦輪碼的架構。因此我們預測若將原本渦輪碼(turbo code)中的迴旋碼(convolutional code)改用時變累加碼來代替，應該可以得到不錯的效能。另外，我們也提出了一個新的編碼調變方案(modulation and coding scheme, MCS)，透過特定的轉換器，將累加碼的輸入與輸出限制在一個較小的符號系統(alphabet)，因此相較於一般的累加碼，其輸入輸出都是在整個有限場，我們的調變方案使之能更適用於現代通訊系統不同通道條件下的速率適應調整(rate adaptation)。

關鍵字

渦輪碼；重覆累加碼；低密度同位檢查碼；有限場GF(q)

並列摘要

According to the results of other research, random-coset low-density parity-check (LDPC) codes and irregular repeat-accumulate (IRA) codes with q-ary nonuniform signal constellations, under belief-propagation (BP) decoding, will approach the unrestricted Shannon limit. It has been shown that, random-coset LDPC codes has much higher encoding complexity than the IRA code, because IRA code can be encoded using the concept of time-varying accumulate code as proposed in [19]. And the simulation results show that, the best SNR thresholds of random-coset LDPC or IRA codes are obtained when the average variable node degree as close as possible to 2. This also means that we can get good performance, as long as repeat the information twice, which implies the turbo codes with two branches encoded by two independent time-varying accumulate (RA) codes may have good potential to construct good codes. In addition, compared with conventional repeat accumulate codes with input and output from the entire Galois field , we also proposed a time-varying accumulate codes with input and output restricted to a small-sized alphabet (smaller than ).This construction allows better flexibility of modulation and coding scheme (MCS) for rate matching in modern communication systems.

並列關鍵字

Turbo code ； IRA code ； LDPC code ； Galois field(q)

參考文獻

[2] R. M. Tanner, “A recursive approach to low complexity codes,” IEEE Trans. Inform. Theory, vol. 27, pp. 533–547, Sept. 1981.

[3] J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. San Mateo, CA: Kaufmann, 1988.

[5] D. MacKay, “Good error correcting codes based on very sparse matrices,” IEEE Trans. Inform. Theory, vol. 45, pp. 399–431, March 1999.

[7] H. D. Pfister and P. H. Siegel, “The serial concatenation of rate-1 codes through uniform random interleavers,” IEEE Trans. Inform. Theory, vol. 49, pp. 1425–1438, Jun. 2003.

[9] C. Berrou and A. Glavieux, “Near optimum error correcting coding and decoding: turbo-codes,” IEEE Trans. Commun., vol. 44, pp. 1261–1271, Oct. 1996.

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基於非二位元時變累加碼之渦輪碼於二位元輸入高斯通道設計與分析

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