當使用遞迴式的可靠度傳遞 (Belief Propagation, BP) 演算法進行低密度機偶檢查 (low-density parity-check, LDPC) 碼的解碼時，
收斂速度和錯誤平面(error floor)都是很重要的性能指標。在本篇論文中，將以解碼排程的技巧改善這兩方面的性能。

若使用動態排程的解碼演算法，可以挑出較重要的訊息，並且給予較多的更新機會，進而加快收斂速度。然而動態排程可能觸發 greedy group 和 silent variable nodes，而得到較差的收斂結果。在本篇論文中，提出了兩種動態排程解碼演算法，分別是 Q-RBP 和 SVNF-RBP。借由限制各個解碼訊息所能更新的次數，Q-RBP 可以強迫那些可能型成 greedy group 的解碼訊息讓出更新的機會。而 SVNF-RBP 則是一開始就保證所有接收的信號都有相等的機會提供其所攜帶的訊息，進而完全避免 silent variable nodes 的發生。相較於之前其他文獻中所發表的動態排程解碼演算法，Q-RBP 和 SVNF-RBP 能提供更好的解碼性能表現。

動態排程解碼演算法需要與多額外的運算決定解碼的順序，而且需要針對每個接收的碼字分別找出不同的排程，複雜度非常高。相較之下，固定的解碼排程可以用在所有接收的碼字，而且不需要額外的運算，較為實用。在本篇論文中，推出了$M^2I^2$-based 的演算法。
針對碼的結構，M2I2-based 演算法可以找出能提供最大的互訊息(mutual information)的更新順序。使用這個順序進行解碼，也能有加速收斂的效果。

在低密度機偶檢查碼中，造成錯誤平面的原因主要是因為陷阱集(trapping set)。陷阱集的型成和碼字在通道中所加上的雜訊，以及解碼順須相關。在本篇論文中，可以發現若使用多個不同的解碼順序對單一個接收碼字進行解碼，可以得到許多不同的解碼結果。只要有一個解碼結果沒有觸發陷阱集，最後的錯誤平面就可以明顯降低。這種使用多個解碼順序以得到多個解碼結果，並成功降低錯誤平面的方法，被稱為 schedule diversity。

因為本篇論文中所提出的 Q-RBP，SVNF-RBP，以及使用 M2I2-based 演算法找出的排程都能顯著加快收斂速度。將這些解碼排程使用在 HARQ 的應用環境中，可以縮短每次重傳後解碼所需的遞迴次數。其中 M2I2-based 演算法可以在針對遞增式解碼(incremental decoding)修正排程的出使條件，進而在遞迴次數受限的情況下，明顯增加系統的吞吐量。

When the iterative Belief Propagation (BP) decoding algorithm is applied to low-density parity-check (LDPC) codes, the convergence speed in the waterfall region
and the error floor in the high SNR region are two of the most important metrics of performance measurement. Both can be significantly improved using the scheduling techniques proposed in this thesis.

Fast convergence can be achieved using informed dynamic scheduling (IDS) since the important decoding messages have more opportunities of being updated. However, greedy groups and silent variable nodes can be observed in many IDS decoders, and these obstruct the decoders from providing a satisfactory convergence error-rate performance. In this thesis, Q-RBP (Quota-based residual BP) and SVNF-BP (Silent-Variable-Node-Free BP) are proposed in order to suppress greedy groups and silent variable nodes, respectively. Since the number of updates for each message is limited by the proposed Q-RBP schedule, the message updates that would potentially form a greedy group are forced to release the occupied computation resources. On the other hand, following the SVNF-RBP schedule, the messages associated with all variable nodes are arranged to have an equal chance of contributing their intrinsic messages, and hence the silent variable nodes are totally avoided. Both the Q-RBP and SVNF-RBP schedules can provide a significant improvement in decoding performance when compared to other IDS decoders presented in the previous literature.

Additional pre-computations are required in most of IDS decoders, including Q-RBP and the SVNF-RBP schedules,
so as to order customized decoding sequences for individually received codewords. However, rather than arranging the decoding schedule based on each received codeword, the proposed maximum mutual information increase (M^2I^2)-based algorithm determines the schedule based on maximizing the increase in mutual information. A pre-determined and fixed decoding schedule can be applied to all codewords, and the decoding convergence can be accelerated without increasing the decoding complexity. Moreover, when multiple distinct schedules are applied to a single codeword to create schedule diversity, the error floor can be significantly lowered without requiring any knowledge of trapping sets.

When the proposed decoding schedules are applied to punctured LDPC codes, the benefit in increasing convergence speed can be more significant compared to dedicated codes. If rate-compatible (RC)-LDPC codes constructed based on puncturing are considered, the $\mathrm{M^2I^2}$-based algorithm can be used to arrange fixed schedules for incremental decoding, and further reduce the required number of iterations. With the assistance of the proposed decoding schedules, the puncture-based RC-LDPC codes can be a potential solution for delay-sensitive HARQ (Hybrid-Automatic Repeat reQuest) applications.

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