Optimal Design And Performance Analysis Of Fountain Codes

Fountain codes are a new kind of forward error correction coding technology, with its outstanding performance and powerful technology advantages, obtained a rapid development. At present, fountain codes have been extensively used in reliable broadcasting communication, multi-source download, wireless collaborative relay network etc., and are spread to more and more other application fields. In this thesis, we focus on the Raptor codes, and study in design methods of Raptor codes over erasure channels and AWGN channels according to their characteristic. The main contents of our research are as follows:Firstly, this paper introduces the concepts, development, advantages and application of fountains codes. And then we specially introduce the basic concepts, encoding and decoding algorithms of Raptor codes, and point out that the overall performance of the Raptor codes is jointly decided by precoding and LT codes. After that, we introduce the inside codes (LT codes) and outside codes (LDPC codes) of Raptor codes, and describe their performance analysis methods in details.Secondly, we analyze the optimal design of Raptor codes in binary erasure channel. Using the unequal error protection (UEP) property of irregular low density parity check (LDPC) codes' variable nodes, we optimize the encoding scheme of Raptor codes. According to degrees of LDPC codes' variable nodes, the input symbols of LT codes are divided into different sets, and then the degree distribution of LDPC codes and input symbols selected probability of LT codes jointly optimized through the differential evolution. Meanwhile, the corresponding theoretical error rate of Raptor codes obtained. Simulation results show that, Raptor codes with the proposed encoding scheme can improve the decoding performance. Finally, aiming at the Raptor codes in AWGN channels, we study the optimization design of its output nodes degree distribution. Firstly, according to the characteristics of Raptor codes in AWGN channels, we discuss two kinds of decoding algorithm of the fixed rate Raptor codes: local iteration decoder and global iteration decoder. Then we propose the Gaussian Approximation of Raptor codes according to its global iteration decoder, and propose a design method of output nodes degree distribution of Raptor codes in AWGN channels. Simulation results show that, the proposed Raptor codes in AWGN channels have an obvious performance gain.