高斯多重存取通道中可達區域之近似分析

Abstract

在第五代行動通訊技術(5G)下，許多多重存取網絡的應用都有著嚴格的延遲限制，除此之外，許多系統也需要可以同時支援對延遲以及信賴度有著嚴格需求的無線傳輸技術。我們研究了在有限編碼長度架構中的高斯多重存取通道。在無線編碼長度中的漸近分析所得到的通常是傳統消息理論的結果，然而在有限編碼長度中無法直接依賴這些結果，需要能得出接近真實結果的合適的非漸近分析。我們針對利用了隨機編碼以及修改過之特徵解碼技巧的可達二階近似進行研究。當系統中人數很多時，可達區域的計算量會非常驚人，所以我們嘗試設計了一些演算法去近似可達區域，其中在使用者人數增加時也能有可接受的複雜度。我們也將這些理論結果與實際編碼的表現進行比較，基於理論分析結果提出一種方法來預估編碼的表現。根據此預估的結果，我們也設計了一種傳輸的流程。另外此論文也探討了高斯多重存取通道套用不同設定下的其餘延伸議題。

In the next generation of wireless cellular systems (5G), more and more applications of multi-access networks have strict delay constraints. Besides, many systems also require wireless connectivity that is able to support some strict requirements on both latency and reliability. We investigate the Gaussian multiple access channel(MAC) in the finite blocklength regime. The asymptotic analysis for the infinite blocklength usually implies conventional information theoretic results. However, in the finite blocklength regime, we cannot directly rely on those results, so we require proper non-asymptotic results that are tight for finite blocklength. We focus on the achievable second-order approximation using the random coding and modified typicality decoding method. Since the evaluation of the achievable region may be cumbersome if there are large numbers of users in the systems, we try to design some algorithms to approximate the achievable region with acceptable complexity even though the number of users is growing. We also compare those result with practical codes, and provide an approach to make a prediction base on analysis result. We design a transmission protocol according to our prediction. Lastly, some extension of the Gaussian MAC with some different settings of constraints are also discussed in this thesis.