Research On Performance Analysis And Design Of Multi-user Digital Fountain Codes

In order to ensure the real-time,efficient and reliable transmission of large amounts of data in the network,the feedback-based transmission protocol is no longer applicable due to "feedback" storms and large latency problems.Digital fountain codes can generate any number of codewords adaptively according to channel states and user requirements,which can solve the above problems well.In addition,the coding and decoding method of digital fountain codes are simple to achieve and have low complexity,which makes fountain codes have good prospects in large data real-time communication.Multiple access technology allows multiple users to share common wireless resources while meeting their transmission needs.High-order modulation technology can effectively improve the spectrum utilization.Both of them have broad application prospects in their respective fields,but the research on combining digital fountain codes with them is relatively rare.In this paper,the degree distributions of single-user and multi-user access high-order modulation digital fountain codes are optimized,and the performance of random access multi-user fountain coding system is analyzed.The main work and contributions of this paper are as follows:1.Aiming at the asymptotic performance of high-order modulated digital fountain codes for single-user and multi-user access,the Gaussian approximation(GA)asymptotic analysis method of binary phase shift keying(BPSK)modulated digital fountain codes is extended to high-order modulation system over additive white Gaussian noise(AWGN)channel,and the asymptotic bit-error-rate(BER)expression and the approximate lower bound closed-form expression of high-order modulated digital fountain codes are derived.The log-likelihood ratio(LLR)messages of each user are calculated by signal to interference plus noise ratio(SINR)in the case of independent coding and decoding for each user.The single user high-order modulation asymptotic analysis method is extended to the multi-user system.The numerical simulation results show that the performance curve approximates the derived higher-order modulation asymptotic BER expression and lower bound expression.2.Aiming at the degree distribution optimization design of single-user and multi-user access high-order modulated digital fountain codes,combined with the asymptotic analysis of high-order modulated digital fountain codes,the degree distribution optimization model of BPSK modulated fountain codes is extended to high-order modulation system,and the single-user degree distribution optimization model and the multi-user joint degree distribution optimization model are proposed respectively.The simulation results show that for single-user access system,the BER performance of the degree distributions designed by the new optimization model under higher-order modulation is significantly improved;for multi-user access system,the degree distributions designed by the proposed multi-user joint degree distribution optimization model achieve better BER performance under the conditions of equal transmission power and unequal transmission power.3.For multi-user fountain coding system,a "two-dimensional" fountain coding scheme with user-dimension random access and time-dimension fountain coding is proposed.Fountain coding can effectively improve the reliability of multi-user information transmission,and belief propagation(BP)decoding algorithm can be used to decode all users,which can fully reduce the decoding complexity.The simulation results show that the proposed random access multi-user fountain coding system has better throughput performance.