Random Linear Streaming Codes Analyses — Part II: Asymptotics
Journal
IEEE Transactions on Information Theory
Start Page
1-1
ISSN
0018-9448
1557-9654
Date Issued
2025
Author(s)
Abstract
Streaming codes take a string of source symbolsas input and output a string of coded symbols in real time,which eliminate the queueing delay of traditional block codesand are thus especially appealing for delay sensitive applications.This work studies the asymptotics of random linear streamingcodes (RLSCs) in the large finite-field-size regime under thei.i.d. symbol erasure channel models. Two important scenariosare analyzed: (i) tradeoff between decoding deadline ∆ andprobability of error pe assuming infinite memory α = ∞; and(ii) tradeoff between α and pe assuming infinite ∆ = ∞. Foreach scenario, this work derives the corresponding asymptoticconstant ρ, power β and decay rate η that satisfy pe(x) ∼ ρxβe−ηx.The results of (i) and (ii) are then used to study an importantcode design problem: Under a given target deadline ∆, what is thememory length α needed for the error probability pe to be withina factor of c > 1 of the best possible p∗e over α. Further analysisalso suggests that regardless the c value being considered, thenecessary memory length is approximately 3–7% of the targetdeadline ∆ when ∆ is large, the actual percentage dependingon the channel model and the coding rate. Such a prediction isconsistent with existing brute-force-based evaluations
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Type
journal article