Research On Key Technologies For Fountain Applications In Wireless Communications

With the rapid development of communication technology and continuous reliability requirements of a variety of transmission method, channel coding technology as an important means of anti-interference technology, is shown more and more important effect in digital communications technology and digital transmission systems. The purpose of channel coding is to improve the transmission quality of digital communication systems. As the existence of noise and interference in the actual channel, the received information after channel transmission is different from the original. Channel coding technology is based on specific laws, by adding additional redundant information into the information to be transmitted, to ensure the reliability of transmission.Fountain codes are a new type of low-density rateless channel code word. It is characterized by adaptive link rate matching, which the transmitter can automately adjust its transmission rate to the most appropriate without knowing the channel state information. This code was originally designed for erasure channel conditions, with simple encoding and decoding algorithms, and excellent decoding performance, especially its adaptive link rate matching character gains widespread concern of scholars home and abroad. This thesis, on the basis of the channel coding theory and related disciplines, to the background of wireless communication environment, mainly studied on the optimization of codec and application extensions of fountain codes. That is to study channel coding strategies so as to increase the effectiveness of codec and decrease the decoding complexity while keep the decoding performance. In addition, we also study the performance of fountain codes in cooperation scenario to explore new applications. The main innovations of this thesis are as follows:First, from the perspective of encoder, this thesis presents an encoding matrix preprocessing algorithms to solve the problem that the randomly generate matrix for encoding may be not full rank. In practice, the fountain encoding matrix is generated randomly only according to the given check degree distribution, so the variable degree of the matrix may exit the probability of zero. When this situation happens, the rank of matrix will not be full, so the information can not be updated and result in decoding failure. What's more, the situation will become worse as the code length increase. Therefore, we propose a preprocess algrithom for encoding matrix. By calculating and judging the variable degree of the encoding matrix, we decide whether to do a local rearrangement and optimization. So that all the information can participate in the encoding process, which reduce the probability of failure and improve the system performance.Second, from the decoder point of view, we take the mathematical tools—External Information Transfer chart (EXIT chart) into fountain iterative decoding analyst for AWGN channel to extend the relevant theory. Fountain codes can be decomposed by bipartite graph theory into two parts:the symbol nodes and the parity check node. The corresponding component decoder in iteration is called symbol node decoder (SND) and parity check node decoder (PCND), both are soft in soft out (SISO) decoders. However, in the decoding process of the fountain, the information transfer between SND and PCND is not easy to describe and analysis. We derive the EXIT function of fountain codes in AWGN channel and draw the EXIT chart to describe the information transfer procesure. By analysis the information transfer procesure, we can effectively determine the maximum iteration numbers of fountain codes, so as to provide theoretical guidance for the following study.Third, from the angle of adaptive iteration control, we propose a mechanism for fountain decoding termination which effectively cutdown the iteration numbers. Fountian decoding in wireless channels use the belief propagation (BP) iteration decoding algrithom. Different from LDPC codes, foutntain codes lacks an effective mechanism for iteration termination. So, we usually use the fix-number iterantion to solve this problem. A larger number of iterations have to be set to improve the decoding reliability. At the same time, fountain codes use incremental redundancy decoding (IRD) mechanism, which increase the redundant parity bits and redecode in case of decoding failure. The combination of BP and the IRD will significantly increase in the number of decoding iterations. In this thesis, we study and explore the iterate control technology for decoding and proposed a termination algrithom based on extrinsic symbol difference (ESD). By full use of the relationship between a prior information and external information, we can fast determine convergence and stop iteration. Compare with fixed-number iteration, cyclic redundancy check (CRC), parity check (PC) and Cross Entropy and analysis by EXIT chart, we can find that the new scheme use few iterations and employ low complexity. It can significantly improve the efficiency of the iteration without performance sacrifice.Fourth, from the application point of view, we put forward scenarios of fountain codes used in cooperation systems. In the cooperative system, due to the restrictions of the traditional fixed coding rate FEC, the collaboration ratio is not flexible enough, so we propose a collaborative model of two relay fountain code, which combine the character of rateless and cooperative diversity. Based on the theory of pairwise error probability (PEP), we analyze the performance limits and diversity gain in Rayleigh slow fading and Rayleigh fast fading channels for theoretical guidance. Than we use the simulation to verify the diversity gain produced by the cooperative mode in these two channel conditions.