Tornado Codes: Practical Erasure Codes Based on Random Irregular Graphs

Abstract

We introduce Tornado codes, a new class of erasure codes. These randomized codes have linear-time encoding and decoding algorithms. They can be used to transmit over lossy channels at rates extremely close to capacity. The encoding and decoding algorithms for Tornado codes are both simple and faster by orders of magnitude than the best software implementations of standard erasure codes. We expect Tornado codes will be extremely useful for applications such as reliable distribution of bulk data, including software distribution, video distribution, news and financials distribution, popular web site access, database replication, and military communications.

Despite the simplicity of Tornado codes, their design and analysis are mathematically interesting. The design requires 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 simple AND-OR tree analysis which immediately gives rise to a polynomial in one variable with coefficients determined by the graph structure. Based on these polynomials, we design a graph structure that guarantees successful decoding with high probability.

This talk is based on: “Practical Loss-Resilient Codes”, STOC ’97, Michael Luby, Michael Mitzenmacher, Amin Shokrollahi, Dan Spielman, Volker Stemann. and

“Analysis of Random Processes via And-Or Tree Evaluation”, SODA ’98, Michael Luby, Michael Mitzenmacher, Amin Shokrollahi and

“A Digital Fountain Approach to Reliable Distribution of Bulk Data”, SIGCOMM ’98, John Byers, Michael Luby, Michael Mitzenmacher, Ashu Rege