能夠達到薛農極限 (Shannon Limit) 的編碼技術首次在2008年，由土耳其畢爾肯大學的Arikan教授提出。其建構的核心為通道極化現象，因此稱為極化碼。目前極化碼的解碼演算法，大致分為兩類，一類是逐次消去演算法，另一類是置信度傳播演算法。
往後對於解碼演算法的研究，都是基於這兩類作為延伸，而有SCAN、SCL、CA-SCL演算法等等。
極化碼近期已經被第三代合作夥伴計畫 (3GPP) 採用為第五代行動通訊 (5G) 增強移動寬帶情境下，上行以及下行傳輸的控制信道編碼。3GPP的技術文獻中指出，為了減少解碼時間的延遲及功率消耗，提早終止解碼 (Early Termination) 應該被支援在極化碼的解碼程序中。目前，提早終止解碼的演算法主要分為兩大類別 : 路徑計量值演算法、輔助位元演算法。本論文提出一新式分散奇偶檢查極化碼。我們利用華為 (Huawei) 所提出的獨立通道極化權重，去決定額外檢核點的數量。此外，為了讓解碼器能夠盡早遇到奇偶檢查碼，我們將奇偶檢查碼的位置盡量往前移動。在這個情境下，我們預期可以節省更高的比例複雜度。此技術減少了80\%檢查點數量以及提升40%到50%提早終止解碼比率。

Polar Code has been recently adopted as channel
coding scheme for uplink and downlink channel in 5G (5th
generation) eMBB (enhanced mobile broadband) scenario. In
order to reduce decoding latency and power consumption, ET
(early termination) should be used in the decoding of the Polar
Codes.
Two general categories of the ET algorithms are path-
metric-based and assistant-bit-based. In this work, a novel early termination scheme for list-based polar decoder belongs to assistant-bit-based is proposed. Firstly, we use channel independent polarization weight proposed by Huawei to decide the total number of additional check points which is needed to check. After deciding these positions of the check points, we put parity check bits forwardly so that the decoder can meet these bits as early as possible.
In that case, a higher complexity reduction can be expected. A
number of 80\% check points are reduced and a 40\%-50\% ET
gain are achieved.

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . .. .1
2 Polar Codes . . . . . . . . . . . . . . . . . . . . . . . .. . 3
2.1 Polar encoder . . . . . . . . . . . . . . . . . . . . . . . .3
2.1.1 Channel polarization . . . . . . . . . . . . . . . . . . . 4
2.1.2 Code construction for polar codes . . . . . . . . . . . . 4
2.2 SC-based decoding algorithms . . . . . . . . . . . . . . . . 5
2.2.1 LLR-based successive cancellation list decoder . . . . . . 5
2.2.2 CRC-aided successive cancellation list decoder . . . . . . 8
2.3 Puncturing pattern . . . . . . . . . . . . . . . . . . . . .10
2.4 Reliability of subchannels . . . . . . . . . . . . . . . . .12
2.4.1 Bhattacharyya parameter . . . . . . . . . . . . . . . . . 13
2.4.2 Polarization weight . . . . . . . . . . . . . . . . . . . 14
2.5 Reviews of early termination method . . . . . . . . . . . . 14
3 Early Termination Schemes For SCL-based Polar Decoding Using Parity Check Matrix . . . . . . . . . . . .. . . . . . . . . . .18
3.1 Polar codes using parity check bit and crc . . . . . . . . .19
3.2 Decoding algorithm for early termination . . . . . . . . . .20
3.3 Proposed early termination scheme . . . . . . . . . . . . . 22
3.3.1 Early Termination using additional check points . . . . . 22
3.3.2 Selection of additional check points . . . . . . . . . . .25
3.3.3 Optimization of location of parity check bits . . . . . . 39
3.4 Performance evaluation . . . . . . . . . . . . . . . . . . .44
3.4.1 Definition of performance metric . . . . . . . . . . . . . 44
3.4.2 Simulation results . . . . . . . . . . . . . . . . . . . .46
4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 51

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