Research On Network Coding Oriented Constellation Shaping Technology

In Point-to-Point communication system with AWGN channel, Shannon has derived the theoretical upper bound of channel capacity, which is called Shannon limit.In addition, Shannon showed the computational formula of channel capacity and concluded that the upper bound is achievable when the channel input follows Gaussian distribution. According to the practical communication system such as LTE, input signals which are based on constellation usually follow uniform distribution. Such phenomenon will cause the loss of capacity which is de?ned as shaping loss. Through theoretical research, when the order of modulation becomes in?nite, the ultimate shaping loss is about 1.53 dB. However, in multiple point communication network, there are no corresponding researches and solutions on such shaping loss problem. In this paper, we focus on the problem of shaping loss in two-way relay system and propose Physical-Layer Shaped Network Coding(PLSNC) scheme. Through the combination of Physical-Layer Network Coding(PLNC) technology and constellation shaping technology, shaping loss in two-way relay system has been effectively solved and the achievable rate has been signi?cantly promoted.This paper ?rstly presents the system model of PLSNC system. Through the introduction of shaping encoder in transmitter, the distribution of transmitted signals is changed. In the module of transmitter, we explicitly illustrate the design rule and formulation process of network-coding-based non-linear shaping code. In the module of receiver, we express the PLNC demapper algorithm and shaping decoding algorithm.In addition, we derive the computational formula of Log-Likelihood Ratio(LLR) in PLNC demapper and shaping decoder respectively.This paper gives the performance analysis of PLSNC system from two aspects, which are error probability and achievable rate. According to the analysis of error probability, we start from the basic concept and derive the error exponent of PLSNC system. When analyzing the achievable rate, we start from the formula of mutual information and derive the computational formula of the constellation-based achievable rate in PLSNC system according to its particular characteristics.This paper builds the software simulation platform, corresponding to the system model and performance analysis mentioned above. The numerical results verify the signi?cant effectiveness of PLSNC system in improving the shaping loss. Compared with traditional two-way relay system, PLSNC system could obtain approximately 0.6dB in BER performance and 2.6dB in achievable rate performance. In addition, PLSNC system has larger error exponent which means its average error probability is lower.