乘積低密度奇偶檢查校驗碼之位元翻轉解碼演算法

Abstract

本篇論文針對乘積低密度奇偶檢查校驗碼提出了數種位元翻轉解碼演算法。我們 修改了傳統乘積碼的解碼排程並結合Gallager 位元翻轉解碼器用以解碼乘積低密度奇 偶檢查校驗碼。在我們的演算法中包含了兩階段解碼-一維和二維解碼。在二維解碼 階段，每一列/行向量會被更新當其相應組成碼位元翻轉解碼器輸出為一合法的組成 碼字串。基於二維解碼的結果，一維解碼階段應用位元翻轉解碼器解碼整體乘積碼以 求取進一步的錯誤更正效能。我們也另提出一種維度間延遲處理程序以避免被列解碼 器更正的位元於行解碼器中立即再被翻轉一次。模擬結果顯示相較於單純使用位元翻 轉解碼器或是採用位元翻轉解碼器於傳統乘積碼解碼排程的效能，我們的演算法獲得 明顯的錯誤率效能精進。 因為位元翻轉解碼器的錯誤更正能力取決於位元決策後的可靠度，我們同時也提 出了一種估測位元可靠度的新型度量。模擬結果顯示此種新型度量位元翻轉解碼器優 於傳統型位元翻轉解碼器。在新型度量位元翻轉解碼器的輔助下我們針對提出的乘積 低密度奇偶檢查校驗碼解碼演算法的解碼效能再進一步獲得提升。

In this thesis, we present several bit-flipping (BF) decoding algorithms for product low-density parity-check (PLDPC) codes. We modify the conventional decoding schedule of product codes and combine the modified schedules with Gallager’s BF decoder to decoding PLDPC codes. Two decoding phases–the 1-dimensional (1-D) and 2-dimensional (2-D) decoding–are involved in our algorithms. In the 2-D decoding phase, each row/ column vector is decoded by the corresponding component code’s BF decoder and can be updated by the decoded result only if the decoder outputs a valid codeword (of the component code). Based on the result given by the 2-D decoding, the 1-D decoder performs the BF decoding on the whole PLDPC code for further error correction. We also present a delay-handling procedure to prevent the bits corrected by the row (column) decoder from being immediately re-flipped by column (row) BF decoder. The numerical results show that our algorithms yield significant error-rate performance improvements in comparison with using a simple BF decoder or applying the BF decoding to the conventional product code decoding schedule to decode PLDPC codes. Since a BF decoder’s error correction capability depends on the reliability metric of bit decisions, we also introduce a new metric for estimating the bit reliability. Numerical results indicate that the BF decoder based on the new reliability metric can outperform that of using the original metric in decoding LDPC codes. With the aid of the new reliability estimate, the performance of the proposed decoding algorithms for PLDPC codes can also be further improved.