極碼的可信度傳遞解碼排程

Abstract

通道編碼藉由將訊息增加冗餘，讓訊息傳輸更可靠。一直以來有許多專家學者致力於研究通道編碼系統，期望可以建構出一套在傳輸速率不大於通道容量的條件下，可以可靠的傳送訊息的編碼系統。極碼（Polar codes）在使用接續消除解碼（Successive cancellation decoding）的方式下，理論上可以讓傳輸速率達到通道容量。 除了接續消除解碼之外，當我們把碼長增加時，尚有其他解碼方式可以讓錯誤率衰減的更快速。可靠度傳遞解碼（Belief propagation decoding）為其中一種方法。可靠度傳遞解碼已被用來當作極碼的解碼方式，解出的訊息錯誤率相對於接續消除解碼解出的錯誤率，前者較低。 為了方便解碼，接續消除解碼器忽略了某些可利用的訊息，而這些訊息則被可靠度傳遞解碼器善加利用。論文[1]說明了相對於接續消除解碼，將可靠度傳遞解碼作為極碼解碼方式的優越性。 在本篇論文中，我們使用類似接續消除解碼的解碼方式，作為可靠度傳遞解碼的排程。藉由模擬二位元輸入高斯通道，我們可以看出在某些情況下，將可靠度傳遞解碼加入此排程會比單純使用可靠度傳遞解碼有較好的效能。

Channel coding is a scheme that adds redundancy to messages for reliable transmission. Many works have been devoting to constructing a coding scheme that can transmit messages reliably at rates set below the channel capacity. Polar code is one such scheme that can achieves channel capacity theoretically under successive cancellation (SC) decoding. Besides SC decoding, there are other decoding algorithms such that as code length increases, error rates of polar codes decrease more rapidly. For instance, belief propagation (BP) decoding has been used to decode polar codes with error rates better than the SC decoding. BP decoder uses the information ignored by SC decoder, and its superiority over SC decoder has been established in [1]. In this thesis, we propose a scheduling for the BP decoding of polar codes that resembles the SC decoding. By simulation over binary-input AWGN channel, we see that in some cases, error performance in this schedule is better than that of BP decoding alone.