Practical loss-resilient codes

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Abstract
We present randomized constructions of linear-time en- codable and decodable codes that can transmit over lossy channels at rates extremely close to capacity. The encod- ing and decoding algorithms for these codes have fast and simple software implementations. Partial implementations of our algorithms are faster by orders of magnitude than the best software implementations of any previous algorithm for this problem. We expect these codes will be extremely useful for applications such as real-time audio and video transmis - sion over the Internet, where lossy channels are common and fast decoding is a requirement. Despite the simplicity of the algorithms, their design and analysis are mathematically intricate. The design require s the careful choice of a random irregular bipartite graph, where the structure of the irregular graph is extremely important . We model the progress of the decoding algorithm by a set of differential equations. The solution to these equations can then be expressed as polynomials in one variable with coef-

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