高斯-馬可夫通道之疊代最大事後機率演算法

Abstract

我們在此篇論文中，嘗試並實驗一個新的想法：亦即在兩個連續的傳送區塊間，穿插傳送一串長度不短於通道記憶長度 (channel memory) 或記憶延展(channel spread)的隨機位元 (random bits)，則通道原本的長程記憶特性可被削弱為近似區塊獨立特性 (blockwise independent)。我們同時推想，或許可以使用經由交錯器 (interleaver) 打亂序列順序的訊息序列 (information bit sequence) 的同位檢查位元 (parity check bits)， 來作為上述的“隨機位元”，以使接收端可經由解交錯器 (de-interleaver) 得到額外的同位檢查訊息，來進一步提升系統效能。而一個最直接符合以上想法的範例架構，就是平行串接旋積碼 (parallel concatenated convolutional code)。為了驗證我們的想法，我們採用隨時間改變衰減的一階高斯-馬可夫通道為實驗平台。 首先，我們推導出疊代最大事後機率演算法 (iterative MAP algorithm) 在直接假設接收向量「因為以兩位元為單位，穿插一位元的交錯訊息序列的同位檢查碼」而具有2 位元區塊為單位的區塊統計獨立的對應量度公式。接著我們進行此直接假設下所導出的量度，在原本一階高斯-馬可夫通道的效能模擬。模擬的結果顯示，在區塊獨立假設下所推導出來的疊代最大事後機率解碼器 (iterative MAP decoder) 量度的效能，不僅非常接近有完美通道狀態資訊(channel state information) 的解碼機制效能，且在某些情況下，與單農傳輸極限 (Shannon limits)最多只有0.9 dB 的差距。

In this paper, we experiment on the idea that the channel-with-memory nature can be nearly weakened to blockwise independence by the insertive transmission of informationless "random bits" (of length no less than the channel memory or channel spread) between two consecutive blocks. We found that these "random bits" can indeed be another parity check bits generated due to interleaved information bits such that additional coding information can be provided to improve the system performance. An exam- pli‾ed structure that follows this idea is the parallel concatenated convolutional code (PCCC). We thus derived its respective iterative MAP algorithm for time-varying channel with first-order Gauss-Markov fading, and tested whether or not the receiver can treat the received vector as blockwise independence with 2-bit blocks periodically separated by single parity-check bit from the second component recursive systematic convolutional (RSC) code encoder. Simulation results show that the iterative MAP decoder that is de- rived based on blockwise independence assumption not only performs close to the CSI(channel state information)-aided decoding scheme but is at most 0.9 dB away from the Shannon limit.