穿刺位元的設計針對碼率相容的低密度檢測碼

Abstract

為了使通道的使用更加有效率，我們會針對同一個錯誤更正碼依據不同的通道狀況使用不同的碼率來傳送資料。為了使穿刺碼的錯誤更正能力的損失降低，我們針對有限長度的低密度檢測碼提供一個建立穿刺位元的方法。我們考慮了穿刺位元的恢復能力以及對其他位元造成的影響來設計我們的演算法並以數學推導得知有哪些參數將對這些產生作用。最後我們以模擬結果以及數據觀測與分析得知我們設計的方向與方法能夠使得有效降低改錯能力的損失。

In this thesis, we study puncturing schemes for finite-length rate-compatible lowdensity parity-check codes. A new bit-by-bit puncturing pattern searching scheme is proposed. The ultimate goal of the proposed method is to improve the recovery error probability of the punctured bits. We also take into account the detrimental effects on previous punctured and unpunctured bits brought about by the new selected punctured. Given the bit locations which have been punctured, a new one is chosen from the set of candidate bits by i) examining its recovery capability (which depends on the number and reliabilities of its connected check node message) and ii) assessing the impact a candidate bit may make. Numerical experimental results show that the proposed scheme outperforms existing puncturing methods. The superiority and robustness of our scheme are further verified by some observed statistics and are consistent with a Gaussian approximation based analytic prediction.