On Achievable Rates of Line Networks with Generalized Batched Network Coding

TL;DR

This paper analyzes the achievable data transmission rates in multi-hop line networks using generalized batched network coding, providing new bounds and techniques that improve understanding of latency, buffer size, and coding schemes for diverse channel types.

Contribution

It introduces new upper bounds on achievable rates for GBNC, extends achievability results to non-identical channels, and refines bounds and coding schemes for packet erasure channels.

Findings

Bounds surpass min-cut for small batch sizes and inner blocklengths.

Channel reduction technique generalizes results to non-identical DMCs.

Numerical evaluations show proximity of bounds for packet erasure channels.

Abstract

To better understand the wireless network design with a large number of hops, we investigate a line network formed by general discrete memoryless channels (DMCs), which may not be identical. Our focus lies on Generalized Batched Network Coding (GBNC) that encompasses most existing schemes as special cases and achieves the min-cut upper bounds as the parameters batch size and inner block length tend to infinity. The inner blocklength of GBNC provides upper bounds on the required latency and buffer size at intermediate network nodes. By employing a bottleneck status technique, we derive new upper bounds on the achievable rates of GBNCs These bounds surpass the min-cut bound for large network lengths when the inner blocklength and batch size are small. For line networks of canonical channels, certain upper bounds hold even with relaxed inner blocklength constraints. Additionally, we employ a channel reduction technique to generalize the existing achievability results for line networks with identical DMCs to networks with non-identical DMCs. For line networks with packet erasure channels, we make refinement in both the upper bound and the coding scheme, and showcase their proximity through numerical evaluations.