Rate-Optimal Streaming Codes Under an Extended Delay Profile for Three-Node Relay Networks With Burst Erasures

2025-11-10

AI Summary

This paper investigates streaming coding for a three-node relay network subject to burst erasures—where the source-relay and relay-destination links tolerate maximum burst erasure lengths $b_1$ and $b_2$, respectively—and an end-to-end decoding delay constraint $T$. To overcome the restrictive divisibility condition $u mid (T - u - v)$ (with $u = max{b_1,b_2}$, $v = min{b_1,b_2}$) imposed by prior schemes, we propose the **extended delay profile method**, relaxing the feasibility condition for achieving the information-theoretic optimal rate to $(T - u - v)/(2u - v) leq lfloor (T - u - v)/u floor$. This condition strictly subsumes the prior constraint and admits a broader range of practical parameter tuples. By jointly optimizing sliding-window modeling, algebraic code construction, and delay profile design, we prove that our scheme achieves the capacity upper bound. The result significantly expands the design space for optimal streaming codes under burst erasures and strict delay constraints.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

This paper investigates streaming codes for 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. Let $u = max{b_1, b_2}$ and $v = min{b_1, b_2}$. Singhvi et al. proposed a construction achieving the optimal rate when $umid (T-u-v)$. In this paper, we present an extended delay profile method that attains the optimal rate under a relaxed constraint $frac{T - u - v}{2u - v} leq leftlfloor frac{T - u - v}{u} ight floor$ and it strictly cover restriction $umid (T-u-v)$. %Furthermore, we demonstrate that the optimal rate for streaming codes is not achievable when $0

Problem

• Designing rate-optimal streaming codes for three-node relay networks
• Addressing burst packet erasures under extended delay constraints
• Relaxing prior restrictions to achieve optimal transmission rates

Innovation

• Extended delay profile method for relay networks
• Relaxed constraint for optimal rate achievement
• Improved coverage over previous burst erasure restrictions