Research On Key Technologies Of LT Codes And Their Applications

Digital Fountain codes(DFC)are a kind of error-correction codes.Due to the advantages of good encoding/decoding performance,code rate adaption to the channel state and less feedback,DFC have been widely applied in wireless communication to ensure the reliability and efficiency of information transmission.As the first realization of DFC,Luby Transform(LT)codes are the basis for other types of DFC.However,there are many problems in the traditional encoding and decoding methods for LT codes,such as,high decoding overhead,high probability of decoding failure,and so on.Therefore,both theory and application of LT codes have been research hotspots in the field of DFC.This dissertation focuses on two key technologies:the degree distribution and encoding/decoding method of LT codes.The propoesd degree distribution and encoding/decoding methods are applied to link maintenance in cognitive radio systems,in order to improve the reliability and efficiency of secondary communication.The main contents and results are as follows:1.A novel design method of degree distribution for LT code is proposed.The good degree distribution is obtained by combine the degree distribution which achievies high decoding success rate with low overhead and the Robust Soliton Distribution(RSD)which achievies high decoding success rate with high overhead.Firstly,the Improved Poisson Distribution(IPD)is proposed by refining the Poisson Distribution(PD).The appropriate value of parameter λ is obtained according to the mathematical properties of PD and the average degree of the encoding symbols.The successful decoding rate for IPD with appropriate λ reaches more than 90%when the decoder receives less encoding symbols,while RSD performs better as received encoding symbols grow.The following three methods can be used to combine IPD and RSD to construct a new degree distribution,so as to improve the successful decoding rate and encoding/decoding efficiency of LT codes.(1)Combine IPD and RSD by a weighting coefficient ω to derive the function of Combined Poisson Robust Soliton Distribution(CPRSD).Based on the properties of the expected ripple size,the golden section algorithm is introduced to obtain the optimal ω.(2)Add the IPD to RSD and normalize to obtain Poisson Robust Soliton Distribution(PRSD).There are two important parameters δ and c in PRSD,which directly affect the encoding/decoding performance of LT codes.Based on the properties of expected ripple size,the Bird Swarm Algorithm(BSA)is employed to search the appropriate values of δ and c for different-length input symbols correspondingly.(3)Because the two combination modes above are fixed,we consider adopting a flexible combination method.We present the Improved Binary Exponential Distribution(IBED).The decoding performance of IBED is similar to that of IPD.Based on the properties of expected ripple size,the Artificial Fish Swarm Algorithm(AFSA)is used to search the optimal degree distribution between IBED and RSD.Based on Matlab,simulation results show that all three methods of degree optimization for LT codes can improve both the successful decoding rate and the encoding/decoding efficiency,and perform better than the traditional RSD and other optimized degree distributions.After comparing these three methods,it is obvious to find that each has its advantages.2.The Memory-based(MB)encoding and decoding scheme of LT codes is proposed over Binary Erasure Channel(BEC).The encoder generates several memory symbols by storing the original information in the generator matrix as additional columns.Then,an infinite amount of common encoding symbols and memory symbols are sent over BEC.The decoder employs different methods to decode the input symbols,according to no memory symbols dropout,multiple memory symbols dropout or all memory symbols dropout.In addition,the PRSD is used with MB method to improve both the successful decoding rate and encoding/decoding efficiency.3.As a channel coding scheme,LT codes have been applied in cognitive radio system.The primary user interference is compensated by redundant codes,so as to realize link maintenance of the secondary communication.Based on the research results above and specific applications,the degree distribution and the encoding/decoding method are improved and supplied appropriately to improve the reliability and efficiency of secondary communication.Two aspects are researched as followed:(1)The correlations between two important features(expected ripple size of LT codes and goodput of secondary user link)and the degree distribution of LT codes are analyzed to concrete optimization objects.Then,the Two-layer Hierarchical Optimization Algorithm(THOA)is presented to search the optimal degree distribution between IPD and RSD,in order to improve the BER performance of LT codes and goodput of secondary user link.(2)Unlike the MB method,part of original information is stored in the columns of degree-1 and degree-2,rather than additional columns.And a new method is used to produce the generator matrix to ensure that the encoding symbols of degree-1 and degree-2 contain original information as much as possible.Based on the encoding symbols received and the reconstructed matrix,the decoder employs the BP decoding algorithm to recover the input symbols.Then some bit information unrecovered can be filled by the memory information in the memory columns,so as to further reduce the BER of LT codes in a certain extent.