On BATS Codes With Variable Batch Sizes

BATS codes are a class of low complexity random linear network codes with high throughput. In a previous work, BATS codes were generalized to incorporate batches of different sizes, and a sufficient condition was obtained such that the belief propagation decoding can recover a given fraction of the input packets with high probability. In this paper, by investigating an optimization problem induced by the sufficient condition, we derive a condition such that it is optimal to use a constant batch size. This condition gives us a guideline for designing practical network protocol based on BATS codes. Moreover, we prove that this condition is always satisfied in line networks.