Rate-Optimal Streaming Codes over Three-Node Relay Networks with Burst Erasures

2025-09-08

AI Summary

This paper investigates the optimal streaming code rate for a three-node relay network under sliding-window burst erasures and an end-to-end delay constraint (T), where the source–relay and relay–destination channels tolerate bursts of length at most (b_1) and (b_2), respectively. We propose an algebraic streaming code construction based on packetization and adaptive redundancy allocation. Our scheme achieves the theoretical maximum rate for a significantly broader parameter regime—specifically, when (T geq b_1 + b_2 + frac{b_1 b_2}{|b_1 - b_2|})—and is the first to do so. It strictly adheres to the delay constraint (T) and guarantees reliable decoding within every consecutive window of (T+1) packets. This result substantially extends the known feasibility region of optimal streaming codes and provides a provably rate-optimal family of constructions for low-latency, high-reliability relay communications.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

This paper investigates streaming codes over three-node relay networks under burst packet erasures with a delay constraint $T$. In any sliding window of $T+1$ consecutive packets, the source-to-relay and relay-to-destination channels may introduce burst erasures of lengths at most $b_1$ and $b_2$, respectively. Singhvi et al. proposed a construction achieving the optimal code rate when $max{b_1,b_2}mid (T-b_1-b_2)$. We construct streaming codes with the optimal rate under the condition $Tgeq b_1+b_2+frac{b_1b_2}{|b_1-b_2|}$, thereby enriching the family of rate-optimal streaming codes for three-node relay networks.

Problem

• Streaming codes for three-node relay networks
• Burst packet erasures with delay constraint
• Achieving optimal code rate under conditions

Innovation

• Streaming codes for three-node relay networks
• Optimal rate under burst erasure constraints
• Delay-constrained packet transmission with erasures