適用於最小和重組LDPC解碼演算法之補償技術

Abstract

Shuffled BP(belief propagation) algorithm是一種低密度同位檢查碼(low density parity check，LDPC)的解碼演算法，它的解碼錯誤更正效能高而且解碼遞迴次數收斂快。由於shuffled BP algorithm使用了非線性的計算，使得硬體的設計變得十分複雜。針對這個問題，設計者常使用最小項來近似此種複雜的非線性運算，以簡化硬體，此演算法稱為min-sum shuffled BP algorithm。然而，min-sum shuffled BP algorithm雖然達到硬體簡化的目的，卻造成解碼錯誤更正效能的下降。為了解決這個問題，本論文探討對min-sum shuffled BP algorithm的補償技術，包括了一維，二維 normalization、或offset之靜態補償方法，以及動態補償技術等，希望藉由補償技術將min-sum shuffled BP algorithm的編碼增益修正，使其達到與傳統的shuffled BP algorithm一樣好的效能。我們以IEEE 802.11n系統做模擬實驗，模擬結果顯示，經過補償後的compensated min-sum shuffled BP algorithm，不但保有硬體簡化的特性，其解碼錯誤更正效能也十分接近傳統的shuffled BP algorithm。

Shuffled belief propagation (BP) algorithm for the decoding of low-density parity-check (LDPC) codes achieves a remarkable error performance and fast convergence. Nevertheless, it seems to be too complex for hardware implementation. The shuffled BP algorithm can be simplified by using the min-sum approximation, namely the min-sum shuffled BP algorithm; however, the min-sum shuffled BP algorithm suffers from remarkable performance degradation. In this thesis, to solve this problem, we explore some compensation techniques for the min-sum shuffled BP algorithm, including 1D-, 2D-normalization/-offset static schemes and the dynamic scaling approach. Simulations show that the compensated min-sum shuffled BP algorithm achieves the performance very close to that of the original shuffled BP algorithm in IEEE 802.11n system.