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

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 b₁ and b₂, respectively. Singhvi et al. proposed a construction achieving the optimal code rate when max₁,b₂\ (T-b₁-b₂). We construct streaming codes with the optimal rate under the condition T≥ b₁+b₂+b₁b₂/|b₁-b₂|, thereby enriching the family of rate-optimal streaming codes for three-node relay networks.