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1. T. Tirronen and J. Virtamo, Finding Fountain Codes for Real-Time Data by Fixed Point Method, in Proceedings of 2008 International Symposium of Information Theory and its Applications, ISITA2008, pp. 1244-1249, 2008, Auckland, New Zealand (bib)

   Abstract: We study fountain coding-like transfer method over an erasure channel for data with real-time requirements. A window of data blocks contains all the current data; new blocks enter at one end of the window and outdated blocks drop out from the other end. The proposed codes are systematic codes in the sense that each new block entering the window is once sent as such. In addition, every now and then correction packets are sent trying to fill the gaps left by the erasure channel. Each correction packet is formed in fountain code-like fashion as a stochastic combination (XOR) of the blocks in the window. In particular, we study a greedy strategy where the encoded packets are constructed so as to maximize the probability that they are immediately helpful, revealing one more block. Assuming that the channel loss probability is known, the receiver updates its belief on the state of the decoding and based on that constructs the optimal correction packet in the greedy sense. We find the stationary state of the system for long streams by a fixed point iteration. Correspondingly, we find the optimal construction of the correction packet, which remains always the same in the stationary state. As no feedback is assumed from the receiver, the codes have to be designed for a specific channel and therefore are not rateless. Two different cases are studied: i) a correction packet is sent every $s$th step with given numbers of blocks randomly selected out of each $s$ consecutive blocks (only the case where $s$ is half of the window size is studied), ii) at each step, after sending the new block intact, a correction packet is sent with probability $P$ with each block $i$ being included in the correction packet with probability $p_i$. The analyses of these cases are outlined. Preliminary results are promising. More extensive analyses and simulation tests of the proposed schemes will be reported in the final paper.