Research On Fountain Codes Degree Distribution Optimization And Decoding Algorithms Of LT Code

Fountain codes have obvious advantages in the multimedia multicast and broadcastapplications. Fountain code has been selected for the third generation mobilecommunication MBMS component parts by3GPP. To Fountain code as the researchobject, this paper has studied the degree distribution and decoding algorithm ofFountain code.This article has discusses the advantages characteristic, development, research status andthe application of Fountain code, then analyzes the existing problems; and expounds the basicprinciple, encoding and decoding algorithm of the random linear fountain code, Tornado code,LT code and Raptor code, then has points out their advantages and disadvantages.Because of the degree distribution of Fountain code is the key factors to influence theperformance of encoding and decoding. To LT code as the research object, this paper hasstudy the influence of the degree distribution to the decoding costs and the bit error rate, anddesigns a new degree distribution-CRS degree distribution. CRS degree distribution is achopped degree distribution. We have compared the CRS degree distribution with otherdegree distributions in the decoding costs and bit error rate, and find the advantages anddisadvantages of CRS degree distribution by the simulation, and analyze the reasons. In viewof the characteristics of the CRS degree distribution, we have structure Raptor code bycascade LDPC code, and analyze the performance of bit error rate.Another important factor is the decoding algorithm to influence the performance ofFountain code. The decoding algorithms of LT code are divided into two classes: BPalgorithm and Gaussian elimination algorithm. Based on the BP algorithm and Gaussianelimination method, this paper was put forward a new kind of decoding algorithm: BP-GEjoint decoding algorithm, and analysis the three algorithms in decoding cost, bit error rate andthe decoding complexity. BP-GE joint decoding algorithm has certain advantages relative toBP algorithm in the decoding costs.