近年來，出現了一種新的編碼方式，稱為極化碼。極化碼是由土耳其畢爾肯大學Erdal Arikan在2008年提出，是一種能夠被嚴格證明可以到達通道容量的編碼方法，其主要概念是透過通道極化，找出各個子通道的錯誤概率。在碼長無限長時，一部分的通道會呈現通道容量為1的完美通道，另一部份的通道容量為0的純躁聲通道。

本論文方向會在極化碼(Polar codes)與低密度同位檢測碼(LDPC codes)上的結合去探討。由於極化碼碼長不是無限長的情況下，會有一部份子通道極化不完全，這些子通道容易造成解碼錯誤。目前已提出的Enhanced belief propagation decoder中，利用短碼長的低密度同位檢測碼作為外碼，與極化不完全的子通道作連接，來輔助極化碼的標準置信度傳播解碼(standard Belief Propagation decode)。我們會針對論文提出的方法上做出改良，利用不同的不規則低密度同位檢測碼與不同可靠度的極化碼子通道做連接，來改善其錯誤率。

另一方面，本論文也提出一種系統性 LDPC-Polar code的編解碼方式。此方式會先利用加入循環冗餘校驗(Cyclic Redundancy Check)的低密度同位檢測碼的解碼結果來輔助極化碼的解碼。最後再與極化碼的標準置信度傳播解碼做比較。

In recent years, a new coding method called polar code has emerged. The polar code was proposed by Erdal Arikan of the University of Birken in Turkey in 2008. It is a coding method that can be strictly proved to have reached the channel capacity if code length approaches infinity. The main concept is to find the error probability of each sub-channel through channel polarization. When the code length is infinitely long, part of the channel will present a perfect channel with a channel capacity of 1, and another part purely useless channel with a channel capacity of 0.

This work addresses the combination of polar codes and low-density parity check codes. Since the code length of polar code is not infinite, some sub-channels are not fully polarized. For this reason, decoding errors may happen easily on these sub-channels. In the enhanced belief propagation decoder, the short code length low-density parity check code is used as an outer code connected with sub-channels of polar code which are not fully polarized to assist the standard belief propagation decoding of polar codes. We try to improve the method proposed in paper by using different irregular low-density parity check codes to connect with different reliability sub-channels of a polar code .

Moreover, this paper also proposes a codec method for systematic LDPC-Polar code. In this way, the decoding result of the low-density parity check code added with the Cyclic Redundancy Check is used to assist the decoding of the polar code. In the end, we compare our method with standard Belief Propagation decoding .

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