本論文主要研究為多階層渦輪乘積編碼系統。多階層渦輪乘積編碼是指乘積碼(Product Code)利用渦輪碼(Turbo Code)的遞迴式解碼(Iterative Decoding),並使用區段編碼調變(Block Coded Modulation)的系統。區段編碼調變是結合編碼與調變兩部份,因此能獲得較好的增益且又不會增加頻寬的需求。利用多層解碼演算法可以使每一層都能獲得較佳之性能與低複雜度。 渦輪碼具有良好的錯誤更正能力,但渦輪碼在高訊雜比時並沒有獲得更好的錯誤率,這稱為錯誤地板現象(Error Floor)。渦輪碼是利用MAP演算法(Maximum A Posteriori algorithm)來達到良好的更正能力,但MAP算法的計算卻非常複雜,故Pyndiah將渦輪碼中反覆解碼的觀念用於乘積碼中,稱之為渦輪乘積碼(Turbo Product Code)。渦輪乘積碼改進了傳統渦輪碼的缺點,因此將渦輪乘積碼的架構運用在區段編碼調變中,將設計出一套更正能力良好的編碼系統。
The main idea of this thesis was doing research of the product code which used iterative decoding method of the turbo code and block coded modulation (BCM) system. BCM was combined with coding and modulation technique that achieves significant coding gain without bandwidth expansion. The most powerful method for constructing BCM codes were the multilevel decoding technique. Turbo code has good performance, but it can’t achieve better in high signal to noise rate (Eb/No) called ‘Error floor’. The maximum a posteriori (MAP) algorithm was used by turbo code, but it has very large computation complexity. So Pyndiah used a new iterative decoding algorithm for product code, which was called turbo product code (TPC). It was expected that TPC for multilevel coding system would be a powerful coding scheme.