Collecting Coded Coupons over Overlapping Generations

Coding over subsets (known as generations) rather than over all content blocks in P2P distribution networks and other applications is necessary for a number of practical reasons such as computational complexity. A penalty for coding only within generations is an overall throughput reduction. It has been previously shown that allowing contiguous generations to overlap in a head-to-toe manner improves the throughput. We here propose and study a scheme, referred to as the random annex code, that creates shared packets between any two generations at random rather than only the neighboring ones. By optimizing very few design parameters, we obtain a simple scheme that outperforms both the non-overlapping and the head-to-toe overlapping schemes of comparable computational complexity, both in the expected throughput and in the rate of convergence of the probability of decoding failure to zero. We provide a practical algorithm for accurate analysis of the expected throughput of the random annex code for finite-length information. This algorithm enables us to quantify the throughput vs.computational complexity tradeoff, which is necessary for optimal selection of the scheme parameters.