| To ensure reliable transmission of data over binary erasure channel(BEC),in recent years,scholars have proposed a class of rateless code,namely digital fountain code.Based on a source block with fixed length,infinite encoded symbols are generated and then transmitted to the receiver until enough symbols are received.More importantly,due to the adaptability to the code rate,the receiver does not necessarily need to know the channel state information using digital fountain codes.Either in the BEC or in the noise channel,the digital fountain codes have performed well.Multiple access technology has been widely studied in recent decades.Allow multi-user to share a common channel resource to meet the data transmission requirements of each user.Intuitively multiple access channels is a channel via which more than one transmitter transmits data to a common receiver,with each transmitter remaining relatively independent.Multiple access technology can greatly improve the channel utilization,and digital fountain code can improve the adaptability to complex communication environment.Combination of Multiple access technology and digital fountain code has great theoretical and practical significance.However,the current academic research on digital fountain codes mainly focuses on single-user channels.Research on the performance of digital fountain codes in multi-user channels,such as multiple access channels,is still limited.This article focuses on the performance analysis and optimization of digital fountain codes over multiple access channels.The main work and contribution of this paper are as follows:1.For single-user additive Gaussian white noise(AWGN)channel model,when using the belief propagation algorithm to recover the code of a digital fountain code,many variable nodes may have accumulated enough likelihood ratio(LLR)information before the iteration times reaches the preset value,and the iterative process afterwards does not lead to a qualitative change to the judgments but greatly wastes the computational power of system.Therefore,in order to improve the efficiency of the belief propagation algorithm,we introduce the idea of "early decision" and propose an incremental decoding algorithm based on translatability,which improves the computational efficiency of the belief propagation algorithm.At the same time,we propose a single-user fountain transmission protocol based on data frame structure,which regards the data frame as the basic transmission unit to realize the non-stop data transmission and reduces the impact of latency on system throughput performance.2.For the multiple access channel model,firstly,due to the repeated computations of the belief propagation in multiple access channels,we propose a simplified method for calculating the likelihood ratio of multi-user based on look-up table.By looking up the look-up table to avoid repetitive calculations to improve decoding efficiency of the digital fountain multiple access system.Then we extend the asymptotic performance analysis from the single-user AWGN channels to the multiple access channels,and the formula of the lower bound curve of the asymptotic bite error rate of any user in the multiple access channels is obtained.Although there are still some gaps between the analysis results and the actual simulation results,it is sufficient to meet the requirements of designing the degree distributions with excellent performance.3.The performance of the systematic Luby Transform(SLT)codes mainly relies on the output degree distribution.Based on the existing research results of degree distribution optimization over single-user channels and the asymptotic performance analysis of SLT codes over multiple access channels,we propose a degree distribution optimization model suitable for multiple access channels.Simulation results show that compared with the classical degree distributions,the degree distributions optimized in this paper have better BER performance over both equal power and unequal power multiple access channels. |
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