Probabilistic Models and Algorithms for Data Synchronization/Broadcast Via Network Coding

We investigate the problem of data synchronization in which a sender has a set of packets to be distributed to all the receivers via a broadcast channel. Initially, each receiver has some fraction of the packets. At each time slot, the sender might broadcast a packet to all the receivers. The goal is to find a broadcast scheme that minimizes the number of time slots until all the receivers successfully obtain all the packets. We propose two probabilistic models on how the initial fractions of packets at receivers are distributed. These models arise naturally in many large-scale systems, such as peer-to-peer networks, data centers, and distributed storage systems. Based on these models, we establish probabilistic bounds and asymptotic results on the minimum number of time slots to successfully transmit all the packets to all the receivers. Next, we propose and analyze a number of random network coding algorithms for finding the approximately optimal solution. Theoretical analysis and simulations are provided to verify the probabilistic bounds and the proposed algorithms.