On the Memory Requirements of Block Interleaver for Batched Network Codes

Batched network coding is a practical branch of random linear network coding which encodes the input file into small batches of coded packets. Although burst erasures within the batches can reduce the advantage of network coding, it can be alleviated by applying a block interleaver which spreads the burst across multiple batches. On the other hand, the intermediate network nodes are required to perform recoding on the batches unlike the traditional forwarding strategy. The recoding of a batch can be started once all the packets in that batch which are not dropped by the channel are received. This means that the intermediate network nodes have to deinterleave the batches for recoding and reinterleave the batches again for transmission, which gives us a choice to use different interleaver depths at different network nodes. In this paper, we study the memory requirements of the schemes for transmitting batches which apply different interleaver depths. We investigate the periodic structure of buffer sizes and the connection between buffer sizes and the total delay induced by the interleaver. More importantly, we show that there exists a scheme which can achieve the lowest memory requirement and minimum total delay simultaneously.