Distributed File Sharing: Network Coding Meets Compressed Sensing

Abstract

In a peer-to-peer file distribution network, a large file is split into blocks residing in multiple storage locations. A peer node tries to retrieve the original file by downloading blocks from randomly chosen peers. We compare the performance of four storage strategies: uncoded, erasure coding, random linear coding, and random linear coding over coded blocks. We show that, in principle, random linear coding makes a better tradeoff between the storage requirement and decoding complexity. However, the sparsity of the file blocks is not fully exploited by random linear combinations of all original blocks. Motivated by the recent results from compressed sensing, we study the design tradeoff in random linear coding over coded blocks and propose an efficient decoding algorithm based on basis pursuit. We show that the minimum number of storage locations that a peer note has to connect to reconstruct the entire file with high probability can be significantly smaller than the total number of blocks that the file is broken into