Construction Of The Uniquely Decodable Codes And Its Application On Cooperation Communications

With the development of wireless communication technology, there is a growing demand for the data rate, especially in a multi-access scenario. The method to make the normalization rate greater than 1 becomes a subject, which is worth studying. In this paper, the method of constructing the uniquely decodable code(UDC) is introduced. The uniquely decodable code could be used in the relaying system by the amplify-and-forward(AF) mode and the decode-and-forward(DF) mode. It’s assumed that the perfect synchronization is utilized in every user’s node. With the help of the uniquely decodable code, the data of all the users are transmitted in the same time slot at the same frequency. The combined data sequence may be reverted to the users’ data without ambiguity. The paper focused on how to construct the UDC. The bit error rate(BER) or the symbol error rate(SER) and the system throughput are analyzed in the UDC-PNC system.Firstly, the mathematical foundation of the UDC is introduced before the definition and the properties. By the definition, a simple criterion is given to construct the UDC. The necessary and sufficient condition of UDC provides a convergence condition. The upper bound of the sum rate is given measure the effectiveness of UDC, which is derived by the information theory.Moreover, after reviewing the coset construction of the UDC, it’s investigated the traversal algorithm based on the sum set. The traversal algorithm makes the UDC with higher sum rate than the coset construction UDCs. The examples of short codes and long codes are also given. Then the multi-user UDCs are mainly discussed. The difference matrix is used to construct the multi-user UDC. It’s deduced that the sum rate would approach the upper bound of the sum rate when the users’ number is infinity. If there exists simple feedback among the users, a kind of UDC would be designed, which could reach the upper bound of the sum rate with the user number of 2.Finally, the paper applies the UDC in the physical-layer network coding system. The 2 users situation and the multi-user situation are discussed respectively. In the 2 users part, it’s introduced the amplify-and forward mode and the decode-and-forward mode. The block diagram of the system is described in each time slot. The SER and throughput are deduced in the Rayleigh channel case and the AWGN channel case. Then the pre-coding scheme are discussed in order to improve the SER performance for the Rayleigh case. After narrating the 2 users’ scenario, the multi-user scenario is given. The BER and throughput are derived in the AWGN channel. Besides, the application of UDC with higher-order modulation is introduced.