在高斯多重存取通道下的聯合星座點和編碼設計

Abstract

隨著時代的演進，多重存取技術已漸漸成為無線通訊技術發展的核心。從1G 的分 頻多工存取，2G 的分時多工存取，3G 的分碼多工存取到4G 的正交分頻多工存取，而 上述皆為建立在使用者彼此正交的系統。然而無線通訊近年來快速的發展，現今的系 統速度已經慢慢不足以負荷多樣的需求。為了解決此問題，非正交多重存取技術被提 出來討論，並將之應用在5G 系統上面。 在此篇論文中，考慮對於在高斯通道中，兩個二進制輸入且同步的使用者、聯合 星座點和LDPC 編碼的設計。本文在不考慮使用分時作業系統和速率分裂的情況下， 此問題在聯合兩個LDPC 解碼下可達到的最大對稱通道容量。我們延伸置信傳播演算 法到兩個使用者，使其能同步解碼。並且，利用對於訊息分布的高斯逼近法和外信息 轉移特性法來分析此解碼的收斂性，和透過最佳化演算法和線性規畫來設計相對應的 LDPC 碼。在不同的訊雜比下，必須使用不同的星座點分布來達到最大通到容量。值得 一提的是，在某個訊雜比區間，一個非對稱性的星座點設計會帶來較好的表現。

Multiple access techniques are at the core of the evolution in wireless communications technologies. Frequency-division multiple access (FDMA) was first employed used for 1G, time-division multiple access (TDMA) for 2G, 3G relies on code-division multiple access (CDMA), and orthogonal frequency-division multiple access (OFDMA) is employed in 4G. The above techniques all rely on the orthogonalization of the users’ transmissions toward the base station. However, due to the rapid development of wireless communication, orthogonalization of the transmissions is no longer sufficient to support the demand of the various wireless devices. To satisfy these requirements, non-orthogonal multiple access (NOMA) has been proposed in 5G. NOMA allows multiple users to share time and frequency simultaneously in a certain location: the information theoretical channel model which addresses the simultaneous transmission of information of two encoders toward a central unit is the multiple access (MAC) channel. Unfortunately, although this model is very well understood from an information theoretic perspective, practical coding and modulation schemes which are practically relevant are yet to be developed. In this thesis, we consider the joint design of both transmit constellation and LDPC codes for the two users, symbol-synchronous, binary-input Gaussian multiple access channel. We consider the problem of attaining the symmetric capacity without the use of time-sharing or rate-splitting by joint decoding of the noisy sum of two LDPC codewords. To this end, a decoding algorithm is considered which extends the classic belief propagation algorithm to allow for the simultaneous decoding of two codewords. We then exploit a Gaussian approximation of the message distribution and EXIT charts to investigate the convergence of the decoding process and also introduce a linear programming technique for joint code design. For this decoding algorithm and proposed code optimization procedure, different constellation choices are obtained which perform well in different SNR regimes. In particular, it is shown that, quite surprisingly, in the moderate SNR regime the best performance is obtained by an asymmetric constellation.