Fountain Codes And Its Applications To Data Compression

Fountain codes are a kind of Forward Error Correcting codes which based on theTanner graph,it uses the idea of random encoding and flexible rate-controlled, and haveadvantages of robustness, high-efficiency and strong contingency ofchannel.Recently,Fountain codes are universally applied and promoted incommunications field with its strong technical advantages.Focusing on the designingand application of Fountain codes, and using principles of encoding and decoding ofFountain codes as the base for the study, which is mainly concerned with reducedcomplexity decoding algorithm of LT codes, Unequal error protection(UEP) of Fountaincodes and the application of Fountain codes in data compression.First of all, reduced complexity decoding algorithm with LT codes is given, BPiterative decoding algorithm is a classic decoding algorithm of Fountain codes when itis in case of wireless channel, its performance approaches Shannon limit. But update ofinformation of check nodes of BP algorithm iterative process has high complexitybecause of the use of the complex hyperbolic tangent function and the inversehyperbolic tangent function,which affect its application in communicate system. Inorder to reduce the complexity of decoding algorithm, a method based on piecewiselinear approximation for complex curve is used to deal with function of check nodes.simulation results show that, the proposed algorithm can be close to BP algorithm,greatly reduces the computational complexity and save memory resources, decreaseshardware costs.Secondly, Unequal error protection(UEP) scheme of Fountain codes is discussedand analysed, Expanding Window is introduced and a concatenated UEP-LT codes isproposed. Simulation results show that, the protection for More Important Bits (MIB) isimproved and loss of performance of Less Important Bits (LIB) is decreased based onconcatenated UEP-LT codes with Expand Window, and it has favorable UEPperformance.Finally, Fountain codes are applied to data compression, the data compression model based on LT codes is given,and lossless compression algorithm with LT codes isproposed, and iterative doping algorithm and incremental degree puncturingcompression algorithm are proposed. Simulation results show that the incrementaldegree puncturing compression algorithm has lower computational complexity andbetter compression performance than the iterative doping algorithm, and has betternoise-robustness for the BI-AWGN channel, compressive performance of algorithmsbased on LT codes is close to arithmetic coding algorithm, and has strong anti-jammingcapability.