Optimal Design For Encoding And Decoding Of Fountain Codes

In wireless communication systems,since electromagnetic waves are often affected by noise and interference during transmission,the information obtained after demodulation would be inconsistent with the transmitted information.The error control system can recover the original messages from the affected received signals to achieve the reliability requirements of the communication system.As a forward error correction coding scheme of the error control system,the fountain codes is rateless,which makes the codes have excellent channel adaptive coding performance,and can play an important role in timevarying channels and various application scenarios.The fountain codes mainly include LT codes and Raptor codes.This paper has carried out in-depth research on the coding of fountain codes,the strategy of non-decodeable codewords elimination and the design of joint decoding.The main work is as follows:(1)Aiming at the fountain codes – R10 codes – in 3GPP MBMS scenario,a fast coding algorithm based on neighbor set matching is proposed.Considering the coding of the first stage of the R10 codes,the intermediate symbol with a relatively small degree is used to reduce the number of XOR operations of solving the intermediate symbol with a relatively large degree.The method is to construct a set of operation instructions,according to which the intermediate symbols are generated along the index order and a calculation formula.For the construction of the set of operation instructions,two algorithms are proposed,which are based on the subset matching and the overlap matching of the neighbor set respectively.The former matches the subset of the current intermediate symbol's neighbor set;and the latter searches the current intermediate symbol's neighbor set which meets a certain depth of overlap extent.The simulation results show that the proposed algorithm can significantly reduce the encoding complexity and encoding time.Furthermore,the algorithm based on the overlap matching optimizes the encoding efficiency and construction complexity of the instruction set.(2)A Greedy spreading serial belief propagation(GSSBP)algorithm for LT codes on binary additive white Gaussian noise channel is proposed.Considering the characteristics of the non-fixed code rate of the LT codes,the newly arriving LLR messages are spread and propagated to the entire decoding graph.The proposed algorithm takes the newly received code symbols as a group,and delivers the message first at each iteration,and then the message is spread to all nodes by the neighbor nodes continuously transmitting the message to the opposite neighbor nodes.By proposing the concept of merged nodes,the diffusion rate of messages in GSSBP algorithm is analyzed by probability theory and recursive formula.The convergence speed of the algorithm is analyzed by Gaussian approximation theory,which indicates that it is better than traditional algorithms.The simulation results show that GSSBP has better error rate performance.(3)The phenomenon that the fountain codes can not be decoded is revealed,and the reason for the phenomenon is analyzed.The experimental verification of several possible strategies shows that the accumulation and transmission of error messages are the main factors of the non-decodeable codewords.The paper propose the policy of absorption and release of the decoding messages to eliminate the non-decodeable codewords,which retains the messages delivered by the decoding attempt several times and reset it a second time.After solving the problem of non-decodeable codewords,the method of optimizing the decoding overhead at high SNR is explored.The idea is achieved by adding Gaussian elimination aid in decoding.The Gaussian elimination-assisted decoding strategy of LT codes and the LLR Gaussian elimination-assisted decoding strategy of Raptor codes are proposed.The simulation shows that the proposed decoding strategy can significantly reduce the decoding overhead at high SNRs.(4)The Polar codes is used as the pre-code of LT codes to form the Polar-LT concatenated codes.The local-iteration decoding design of the Polar-LT cascade system based on CA-SCL algorithm is proposed,and global-iteration decoding design of the Polar-LT cascade system based on SCAN algorithm is proposed.Combining the proposed GSSBP algorithm of LT codes,the BER performance of concatenated codes is explored;the proposed absorption and release strategy is applied to local iteration and global iteration,and the performance of local iteration and global iteration is compared;by applying LLR Gaussian elimination to the local-iteration decoding design of the Polar-LT concatenated codes,the decoding overhead can still be significantly optimized at high SNRs.