Encoding And Decoding Algorithm Of Fountain Codes And Its Implementation

The LT (Luby Transform, LT) codes are the first realization of Fountain codes,which was invented by Luby in2003. As the first kind of rateless codes based on thetechnology of erasure code, LT codes have the characteristics of unfixed coding rate,high robustness, high reliability and low complexity of encoding and decoding. So theyare regard as one of hot topics of the channel coding.In this paper, the encoding and decoding algorithm of Fountain codes is introducedat first. Then the encoding and decoding algorithm of LT codes is optimized andimproved. Finally, the encoder and decoder of LT codes is designed and realized basedon the technology of DSP. Main contents are as follows.First of all, the encoding and decoding algorithm of LT codes based on chaoticcombination is applied. The chaotic combination pseudo-random number generator isused to take the place of the traditional LCG (linear congruential algorithm, LCG)pseudo-random number generator. In this way, we can receive the random numbersequences which have features such as high independence and long period. So therandomness of degrees and sets of neighbors of the code signals are improved. What ismore, the complexity of encoding and decoding algorithms of LT codes is reduced. Inthe binary erasure channel, simulation results show that the algorithm have theadvantage of higher decoding efficiency and easier realization. In addition, it canpreserve the advantage of smaller header packets costs of LCG.Secondly, the encoding and decoding algorithm of LT codes based on chaoticcombination and exploiting redundancies method is brought in. The decoding algorithmuses the redundancies of code signals to generate new code signals of degree one andbreak the deadlock which is generated when code signals of degree one are exhausted.In that case, the decoding process goes smoothly. Simulation results show while thenumber of source samples is small, applying the exploiting redundancies method canbreak the deadlock and further reduce the decoding overhead. Finally, the TMS320VC5416of TI (Texus Instruments, TI) is used to design andrealize the encoder and decoder of LT codes. As the computational burden and memoryusage of the encoder and decoder increase rapidly with the length of code signals,feedback control signal, redundancy process and positional coefficient storagemechanism are introduced. The feedback control signal could control the length of codesignals. The redundancy process can remove the redundancies of code signals, whichcan result in the efficiency growth of decoding process. Positional coefficient storagemechanism of neighbors’ list of the code signals can make the memory resources ofDSP chip rationally utilized.