Performance analysis of finite-length spatial-temporal network coding

To achieve the capacity of erasure networks, the spatial-temporal network coding, i.e., coding across symbols received both from different edges as well as at different time slots, with infinite temporal length is generally required. However, in practice, only finite temporal coding length is feasible due to constraints such as tolerable delay, available buffer size, and acceptable coding/decoding complexity. A practical question to answer is, thus, what the minimum temporal coding length is needed to achieve a target percentage of the network capacity. To this end, we derive the expected throughput of erasure networks applied with spatial-temporal network coding as a function of coding length $M$. Numerical examples demonstrate a very good match between the theoretical and simulation results.