以串接碼建構短線性區塊碼的編解碼的進一步研究

Abstract

二元短線性區塊碼的軟式解碼(soft decoding)一直是個很有挑戰性的研究課題。一般而言，ordered statistic decoding (OSD) 以及 A* 解碼演算法(A* decoding)為對短線性區塊碼進行軟式解碼的兩大主流。這兩個主流解碼方法都有利用到最可靠基底(most reliable basis, MRB)或是又稱為最可靠及獨立位置(most reliable and independent positions, MRIP)的觀念，並且假設在MRIP內發生的錯誤不超過λ個位元。傳統的作法是利用接收信號的絕對值大小來決定MRIP。我們實驗室先前以串接碼的架構設計了一些二元短線性區塊碼，使用里德-所羅門碼(Reed-Solomon code)作為外碼，並以二進位碼作為內碼，此內碼必須具備soft-in soft out (SISO) decoding的能力。對短串接碼做解碼時需要先對內碼的SISO解碼器進行解碼，取得解碼的軟輸出對數似然比（log likelihood ratio,LLR）值，然後以這些LLR的絕對值大小來決定MRIP。以此方式獲得的MRIP會比傳統方式所獲得的MRIP更可靠。這樣所建構的短串接碼在利用使用改良後的MRIP時與使用傳統MRIP的binary extended BCH code相比可以用較小的λ值取得類似或更低的解碼錯誤率。在此論文中我們設計更多的串接碼來進一步驗證使用短串接碼的優越性。特別是我們指出在比較使用各種內碼LLR所得的MRIP的可靠性時不能單單以LLR的variance的大小來決定。我們將LLR乘以正確的data然後取其平均值，以此計量可以更正確的評估各種內碼的優劣，對不同類型之串接碼進行效能比較與分析。

Soft decoding of binary short linear block codes has long been a challenging research topic. At present, the two mainstream approaches—ordered-statistic decoding (OSD) and A* decoding—both exploit the concept of the most reliable basis, also known as the most reliable and independent positions (MRIP), under the assumption that at most λ bit errors occur within the MRIP. Traditionally, the MRIP is determined by the magnitudes of the received signal.Our laboratory previously designed several binary short concatenated codes that employ a Reed–Solomon outer code and a binary inner code capable of soft-input soft-output (SISO) decoding. During decoding, the SISO decoder for the inner code is executed first, producing log-likelihood ratios (LLRs); the absolute values of these LLRs are then used to select the MRIP. The MRIP obtained in this way is more reliable than that derived by the conventional method. Consequently, the proposed short concatenated codes can achieve similar or lower decoding error rates with a smaller λ compared with binary extended BCH codes that use the traditional MRIP.In this thesis we construct additional concatenated codes to further verify the superiority of the short-code approach. We point out in particular that the reliability of MRIPs derived from different inner-code LLRs cannot be judged solely by the variance of the LLRs. By multiplying each LLR by the correct data bit and then averaging, we obtain a metric that more accurately evaluates inner-code quality and facilitates meaningful performance comparisons across concatenated code types.