Detailed Asymptotics of the Delay-Reliability Tradeoff of Random Linear Streaming Codes
Pin-Wen Su, Yu-Chih Huang, Shih‐Chun Lin, I-Hsiang Wang, Chih-Chun Wang · 2023
Streaming codes eliminate the queueing delay and are an appealing candidate for low latency communications. This work studies the tradeoff between error probability peand decoding deadline ∆ of infinite-memory random linear streaming codes (RLSCs) over i.i.d. symbol erasure channels (SECs). The contributions include (i) Proving pe(∆) ∼ ρ∆−1.5e−η∆. The asymptotic power term ∆−1.5of RLSCs is a strict improvement over the ∆−0.5term of random linear block codes; (ii) Deriving a pair of upper and lower bounds on the asymptotic constant ρ, which are tight (i.e., identical) for one specific class of SECs; (iii) For any c > 1 and any decoding deadline ∆, the c-optimal memory length $\alpha _c^{\ast}(\Delta )$ is defined as the minimal memory length α needed for the resulting peto be within a factor of c of the best possible $p_e^{\ast}$ under any α, an important piece of information for practical implementation. This work studies and derives new properties of $\alpha _c^{\ast}(\Delta )$ based on the newly developed asymptotics.