Research On Encoding And Decoding Schemes To Enhance The Security Of LT Codes

As a kind of error control technology, digital fountain codes can achieve the efficient and reliable transmission of information. However, the most common belief propagation decoding algorithm for fountain codes requires a large number of encoded packets with degree 1, which are the copies of source information and can easily lead to the leakage of information. In addition, the generator matrix, which plays an important role in decoding, is transferred to the decoder usually placed in the encoded packets' header. In this way, eavesdroppers can immediately gain the encoding information as long as they steal the encoded packets. Then the corresponding information will be easily recovered so that the basic security cannot be guaranteed. This paper focuses on the encoding and decoding scheme of LT codes under the circumstance with special security requirements. To enhance communication system security, the way of encoding and decoding of LT codes have been modified, while the generated method of the generator matrix also has been changed. The main work is as follows:1. To solve the problem of information leakage caused by a large number of LT encoded packets with degree 1 which are the copies of source information packets, in this thesis, the way of encoding of LT codes has been modified. Each packet with degree 1 is replaced with a pair of packets with degree 2 and 3. As the conventional BP algorithm can not decode this kind of codes, a BP-based decoding algorithm in which an extra processing for degree 2 packets(D2BP) is included is presented, while a complexity reduced Gaussian elimination decoding algorithm(SGE) is also given. The simulation results show that D2 BP and SGE algorithms can successfully decode LT codes where degree 1 packets are deleted. The former has lower decoding complexity and the latter has lower decoding overhead. Compared with traditional Gauss elimination algorithm, the complexity of SGE algorithm is obviously decreased.2. To make the generator matrix transmit safely, a pseudo-random and synchronous generation scheme of the generator matrix at encoder and decoder is given. First, the pseudo-random generators are used to generate the uniform and pseudo-random numbers from(0, 1). Then the generated numbers are converted to pseudo-random degrees which are in accordance with the specified degree distribution, and pseudo-random numbers for the source packets' selection. Finally, the thesis verifies if the generated pseudo-random degrees are in accordance with the specified degree distribution, and if the pseudo-random selection of the source packets meets the requirement. By this way, the encoder and decoder only need to exchange seeds and the same pseudo-random sequence can be generated. Pseudo-random and synchronous generation of the generator matrix at encoder and decoder avoids direct transmission of the generator matrix in channels, which can not only effectively improve information security, but also reduce transmission cost.