Posted by: atri | April 13, 2009

Lecture 34: Expander codes

In today’s lecture, we defined expander codes. In particular, we looked at the notion of lossless expanders. Next lecture, we will see  how binary linear codes whose factor graph is a lossless expander leads to asymptotically good codes. We will also see a natural decoding algorithm for such codes. Depending on the time, we will analyze the correctness (and maybe) the running time of the algorithm.

Expander codes were introduced in the paper by Mike Sipser and Dan Spielman, in their very appropriately titled paper Expander codes. The paper had to go through more calisthenics as then the explicit construction of lossless expanders were not know (the paper by Capalbo, Reingold, Vadhan and Wigderson that constructs explicit lossless expanders was 6 years in the future). The paper proved that expander codes are asymptotically good and presented a linear time decoding algorithm. A follow-up work by Spielman presented codes based on expanders codes that can both be encoded and decoded in linear time.

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