Capacity Scalability of Line Networks with Batched Codes

The capacity of line networks with buffer size constraints is an open, but practically important problem. In this paper, we consider line networks formed by discrete memoryless channels, and study the achievable rate of batched codes, which include several existing coding schemes studied in literature for line networks as special cases. A batched code has an outer code and an inner code. The outer code encodes the information messages into batches, each of which is a group of coded symbols, while the inner code performs recoding on the symbols belonging to the same batch at all nodes that forwarding a batch. Batched codes enable us to impose various block-length and buffer size constraints by tuning coding parameters. Using a technique that captures the communication bottleneck of line networks, we derive upper bounds on the achievable rates of batched codes as functions of line network length for several coding parameter sets. We also discuss specific recoding schemes that can achieve rates of the same order of the line network length for these coding parameter sets. Our results shed light on how to design large multi-hop network communications in practical scenarios using a unified coding framework instead of the traditional layered approach.