Delay-optimal Linear Packet-level Coding for URLLC on Multi-path Wireless Networks

Modern wireless infrastructures provide multiple options for a transmitter to utilize multiple independent data paths. Examples include simultaneous connections via multiple radio access technologies (multi-RAT), dual/multi-connectivity and carrier aggregation in 5G, Integrated Access and Backhaul (IAB) network, etc. Such network redundancies can be utilized to provide enhanced reliability and/or delay performances over the wireless media, e.g., to support ultra-reliable low-latency (URLLC) services. However, traditional reliability enhancement techniques fall short of making efficient use of such multi-path transmission environments. Packet-level coding, in this case, can be a better candidate to support URLLC since it provides enhanced reliability with higher spectral efficiency and low latency by proactively adding coded redundancy, which also enables the effective treatment of all paths as a single data pipe. As the multi-path scenarios are oftentimes heterogeneous in terms of supported data rate, packet-level reliability, transmission delay, etc., how to optimally design the coding parameters to achieve URLLC requirements becomes an issue. In this paper we study the problem of minimizing the transmission delay while meeting the required reliability target in the multi-path environment. We assume the packets arrive in bursts and linear packet-level coding is used to enhance reliability. We propose a fast bisection algorithm to determine the optimal code rate and path traffic distribution rule for the encoded packets, which provably achieves the minimum delay with the required reliability under very general conditions.