Research On Systematic-form Construction Mechanism Of Finite-length Fountain Codes

In recent years, the fountain codes which can approach erasure channelcapacity with low coding complexity were highly concerned by researchers.Fountain codes cause the traditional channel error correction coding extended tothe data packets, provides an efficient erasure correction mechanism withoutfeedback link. Especially the short code length fountain codes at103level,applicable for the limited computing power nodes information packet erasurecorrection in the DTN scenes(the internet of things, Deep space exploration). Butin application always need systematic coding structure, LT codes and Raptor codeswith random coding mode can not achieve systematic structure. In order to reducethe high complexity in systematic fountain coding and raise up erasure probabilitytolerance, in this paper we focus on the intermediate nodes during the systematicfountain coding process, designed a new degree distribution based onsuperposition degree distribution and optimized the pre-coding matrix, proposed anew systematic coding scheme for finite-length fountain codes. The mainresearches are as following three fie lds:Firstly, after the investigation on systematic fountain coding, it can be foundthat in the existing coding scheme there is an inverse transformation on thegeneration matrix with complexity O(k3) to generate intermediate nodes. To reducedecoding overhead the receiver need to use GE decoding algorithm with O(k2)complexity. So we proposed a scheme without pre-coding structure by interleavingthrough intermediate nodes LT codes designed system programs, and design thesuperimposed degree distribution for intermediate nodes, to achieve linear codingcomplexity.Secondly, the existing degree distribution is always based on non-systemstructure RSD LT codes asymptotically optima l design, for a finite length of themessage packets is difficult to obtain complexity and decoding performancetradeoffs. And RSD LT code decoder receives the majority required packets toenter the BP decoding code-words waterfall area, the usage of the received packetsas soon as possible to restore the origina l information has become a hot researchissue in recent years. This paper further optimized SPDD distribution and thedoping component superimposed ratio, making stacking degree distribution systemBP decoding LT codes obtained asymptotic performance.Lastly, for practical application, we proposed and optimized the pre-codematrix of SPDD systematic fountain codes according to the code-length, erasureprobabilities and decoding overheads, respectively. The practical parameters of the systematic codes were obtained. As the simulation results shown, the proposedscheme of finite-length LT codes had outperformed better performances under thebroadcasting and worse erasure channels environments.