Random Linear Streaming Codes in the Finite Memory Length and Decoding Deadline Regime

Abstract

Streaming codes take a string of source symbols as input and output a string of coded symbols in real time, which effectively eliminate the queueing delay and are regarded as a promising scheme for low latency communications. Aiming at quantifying the fundamental latency performance of random linear streaming codes (RLSCs) over i.i.d. symbol erasure channels, this work derives the exact error probability under, simultaneously, the finite memory length and finite decoding deadline constraints. The result is then used to examine the tradeoff among memory length (complexity), decoding deadline (delay), and error probability (reliability) of RLSCs for the first time in the literature. Two critical observations are made: (i) Too much memory can adversely impact the performance under a finite decoding deadline constraint, a surprising finding not captured by the traditional wisdom that large memory length monotonically improves the performance in the asymptotic regime; (ii) The end-to-end delay of the RLSC is roughly 50% of that of the MDS block code when under identical code rate and error probability requirements. This implies that switching from block codes to RLSCs not only eliminates the queueing delay (thus 50%) but also has little negative impact on the error probability.