具和餘計算和聯合解碼多重擷取中繼通道系統之晶格碼

Abstract

我們考慮兩個使用者的多重擷取中繼通道系統。在此系統中，兩個使用者用一個半工的中繼器來幫助傳送訊息到一個共同的目的端。在我們之前的研究中顯示，解碼後傳送之晶格碼在多重擷取中繼通道系統中是有效的[1]。然而,當使用者到中繼器這段連線比較差時，解碼後傳送的協定在中繼端可能無法解出所有使用者的訊號。為了解決這個問題，我們提出了一個新的晶格編碼方式，在中繼端只要解出整數加權的使用者編碼，再用餘數對應器對應，再傳送相對的編碼。 雖然在中繼端的解碼方式類似於正交計算後傳送協定，我們放寬了之前研究中使用者不能傳送資料當中繼器正在傳送以避免干擾的限制。主要的內容是在目的端的聯合多個使用者之晶格解碼。此種聯合解碼不僅複雜了相對應的碼的設計，也使的錯誤分析更為複雜。為了在中繼端找到適合的整數加權的使用者編碼，我們藉由轉換和放寬限制解決了一個非凸的整數問題。我們也發展了控制使用者和中繼站能量的策略。模擬結果顯示我們提出的非正交晶格碼可以在多種通道下好過一些現行的架構。

We consider the two-user multiple access relay channel(MARC), in which two users transmit messages to a common destination with the assistance of a half-duplex relay. The decode-and-forward (DF) based lattice coding was shown to be effective for the MARC in our previous work [1]. However when the links from the users to the relay are weak, DF protocol may fail to decode all users at the relay. Aiming to solve this problem, we propose a new lattice coding where the relay only needs to decode an integer-weighted-sum of users' lattice codewords, re-maps it with a modulo-based mapper and then forwards the corresponding codeword. Although the decoding at the relay is akin to the orthogonal compute-and-forward protocol, we relax the restriction imposed by previous works that the users have to be silent when the relay is transmitting to avoid interference. The key ingredient is the joint multi-user lattice decoding performed at the destination. This jointly decoding strategy not only complicates the corresponding code design but also the error analysis. To find the proper integer-weighted-sum at the relay for the destination's joint decoder, we also solve a non-convex integer programming by carefully transforming and relaxing it to a convex one. Also, we develop the power allocation policy to control users' and relay's power. Simulation results show that the proposed non-orthogonal lattice coding can outperform existing schemes in a variety of channel settings.