高斯干擾信道容量區域的研究

馬嘯

摘 要：多用戶信道是一種有著多個發送者和多個接收者的通信系統，它可以通過發送者和接收者的字母表以及信道轉移概率來刻畫。半個多世紀以來，人們對包括多接入信道，廣播信道，中繼信道以及干擾信道等多用戶信道的容量區域問題進行了廣泛的研究。只有少數的信道，例如多接入信道已經得到了較為滿意的答案，其他信道只在特殊的情形下得到了解答。可以說對任何一種多用戶信道的容量區域認知的推進都凝結了無數研究者們的心血。該文主要針對高斯干擾信道的容量區域問題進行了研究，其中衍生出來的計算容量界的方法也可以用做計算離散無記憶的組合信道、只有公共信息的廣播信道的容量區域。主要的工作如下：（1）從主次用戶的角度重新考慮高斯干擾信道，提出了可接入容量的概念，并給出了該容量的上下界。（2）利用信息譜的方法刻畫了一般兩用戶干擾信道的容量區域的通用公式。證明了干擾信道的容量區域是由一簇矩形區域取并集得到的，每個矩形區域都是由一對獨立的輸入過程定義的。數值結果顯示知道干擾結構可以給譯碼帶來增益，且譯碼時知道的干擾的結構越多，獲得的增益就越大。

關鍵詞：多用戶信道 高斯干擾信道 容量區域 信息譜

Abstract：A system with many senders and receivers forms a multi-users channel. Multi-users channel can be defined by the alphabets of the senders and receivers and the probability transition matrix. Over half a century， people spent many time on research the multi-users channel， including multiple access channel （MAC）， broadcast channel （BC）， relay channel （RC） and interference channel （IC）. Up to now， we only know the capacity region of general MAC. For the other channels， only in some special cases， the capacity regions can be known. It is very difficult to characterize the capacity region for multiple-users channel. This paper focus on the capacity region of Gaussian interference channel （GIFC）. In the process of seeking the bounds of the capacity of GIFC， we also find an algorithm to compute the capacity of compound channel or the maximum rate of broadcasting common messages to multiple receivers. The main contributions of our work are summarized as follows： （1）A new problem formulation is presented for the Gaussian interference channels （GIFC） with primary and secondary users. We also proposed a new concept， accessible capacity of secondary user. Meanwhile， the upper and lower bounds of the accessible capacity were given. （2）We present a general formula for the capacity region of the interference channel with two pairs of users. The formula shows that the capacity region is the union of a family of rectangles， where each rectangle is determined by a pair of spectral inf-mutual information rates. The results show that the decoding gain can be achieved by taking into account the structure of the interference.

Key Words：Multi-user Channel； Gaussian Interference Channel； Capacity Region； Information Spectrum

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