A Practical Implementation of Fountain Codes over WiMAX Networks with an Optimised Probabilistic Degree Distribution

摘要

Recently, rateless codes have attracted much attention in the communications research community. The most well known being Luby transform codes, were the first practical realisation of record-breaking sparse-graph codes for binary erasure channels. These codes have the advantage of not requiring a priori knowledge of specific channel conditions and lends itself to application in nondeterministic wireless networks. This paper revisits the Luby transform fountain code, predecessor of the well known Raptor codes, and proposes a novel parameterised probabilistic degree distribution, which is used in the encoding process, along with the belief propagation decoding algorithm. By combining piecewise-defined convex functions and running a non-symmetric Kullback-Leibler divergence measure between the expected and actual degree distributions, we optimise our degree distribution and substantiate a significant reduction in reception overhead and symbol operations. This will support such forward error correction codes in efficient multimedia communication systems. Our proposition was implemented over a WiMAX network and the practical results obtained indicate that a few conditions are sufficient to define an optimal encoding process.