基於非二位元的時變累加碼之渦輪碼設計與分析

The Design and Analysis of Turbo Codes Based on Nonbinary Time-Varying Accumulate Codes

林子程(Tzu-Cheng Lin)

指導教授 ： 邱茂清

國立中正大學/工學院/通訊工程學系/碩士(2013年)

摘要

文獻上已經證明基於belief-propagation(BP)解碼演算法下的隨機旁集(random-coset)非二位元GF(q)的低密度檢查碼(low-density -parity-check code, LDPC codes)及非規則重複累加碼(irregular repeat-accumulate code, IRAcode)搭配q-元非均勻訊號星雲可以達到無限制的通道極限。隨機旁集GF(q)LDPC碼的編碼複雜度比IRA碼還高，原因是IRA碼可以使用簡單的時變累加碼(time-varying accumulate code)進行編碼。初步模擬顯示隨機旁集GF(q)的LDPC及IRA碼，當變數節點階數固定為2時就可達到相當好的性能。這樣的結果意味著對於非二位元GF(q)重複壘加碼(repeat-accumulate code, RA code)，只要將訊息重複兩次就可得到相當好的性能。因為訊息重複兩次，該編碼器就會類似於渦輪碼(turbo code)。因此我們預測如果將時變累加碼取代原有渦輪碼中的迴旋碼(convolutional code)應該可以得到相當不錯的性能。這就是這篇論文的研究動機。隨後我們會專注於基於非二位元的時變累加碼之渦輪碼，並利用外在訊息轉換圖(extrinsic information transfer(EXIT) charts)的技術來分析及設計好的碼，並與GF(q)下的不規則重複累加碼和規則重複累加碼做比較。

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

It has been shown that, under belief-propagation (BP) decoding, random-coset GF(q)low-density parity-check (LDPC) codes and irregular repeat-accumulate (IRA) codes with q-ary nonuniform signal constellations approach the unrestricted Shannon limit. Random-coset GF(q)LDPC code has much higher encoding complexity than that of the IRA code, since the IRA code can be encoded using the structure of time-varying accumulate code [5]. However, we observed that best SNR thresholds of random-coset GF(q)LDPC or IRA codes are obtained for average variable node degree as 2. This means that for repeat-accumulate (RA) codes twice repetitions may be sufficient to provide good performance which implies that turbo codes with two branches encoded by two independent time-varying accumulate codes may be a good alternative to construct good codes. This is the research motivation of this paper. Then we will concentrate our attention on the Turbo code based on GF(q) time-accumulated code, and use the extrinsic information transfer(EXIT) charts to design and make good codes. Then we use our simulation result to compare with the GF(q) irregular repeat-accumulate (IRA) codes.

並列關鍵字

turbo codes ； repeat-accumulate codes ； LDPC codes ； GF(q)

參考文獻

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