新穎的高效能渦輪低密度同位元檢查碼

Abstract

低密度同位元檢查碼(Low-Density Parity-Check Code)是在1962由R.G. Gallager所發表，它的獨特編碼方式使其具有稀疏(sparse)的同位元檢查矩陣(parity check matrix)，這使得解碼時所需的複雜度降低，而它的效能比其他碼更逼近向農極限(Shannon limit)。本論文將低密度奇偶校驗碼應用在乘積碼(product code)的架構裡，使其反覆式的解碼也具有渦輪式解碼(turbo decoding)的概念。然而就單一的列解碼或行解碼(row or column decoding)而言，次數過多的軟式解碼(soft decoding)將使得額外資訊(extrinsic information)在訊息交錯(message interleaving)後而有可能失真(distortion)，而使效能降低。對於這個失真，本論文提出的絕對平均值對映常態法(absolute-mean mapping normalization)僅需少量的額外計算複雜度即可獲得相當程度的改善。舉例來說，考慮渦輪(63,37,8,8)^2 EG-LDPC code且其渦輪解碼次數固定在兩次，其效能將因為此常態法而獲得最多1.2dB的效能提升(performance improvement)，而針對渦輪解碼次數固定在四次，其效能更有最多2dB的效能提升。搭配了絕對平均值對映常態法，渦輪(63,37,8,8)^2 EG-LDPC code的效能極限(performance limit)將比原始的(63,37,8,8) EG-LDPC code多了大約3.4dB的效能提升。

Low-density parity-check (LDPC) code was introduced by R.G. Gallager in 1962, which has sparse parity check matrix due to its unique code construction. With sparse parity check matrix, the complexity required for decoding is low. LDPC code has the performance which is closer to Shannon limit than other codes. In this thesis, we apply LDPC codes to product code form so that the iterative decoding of LDPC code includes the concept of turbo decoding. However, for single row (column) decoding in turbo decoding, the extrinsic information generated by soft decoding in sufficiently high iteration number may come with distortion after message interleaving, and hence the performance is degraded. For this distortion, we propose the absolute-mean mapping normalization which achieves a considerable performance improvement with only little additional computational complexity. For example, for turbo (63,37,8,8)^2 EG-LDPC code with LDPC iteration number fixed to 2, its performance is improved at most 1.2dB by this normalization. For LDPC iteraion number fixed to 4, its performance improvement even achieve 2dB. With the absolute-mean mapping normalization, the turbo (63,37,8,8)^2 EG-LDPC code has about 3.4dB performance limit improvement from the original (63,37,8,8) EG-LDPC code.