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Random Linear Streaming Codes Analyses-Part II: Asymptotics
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DOI：10.1109/TIT.2025.3619497.png)
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Abstract
En 中文
Streaming codes take a string of source symbols as input and output a string of coded symbols in real time, which eliminate the queueing delay of traditional block codes and are thus especially appealing for delay sensitive applications. This work studies the asymptotics of random linear streaming codes (RLSCs) in the large finite-field-size regime under the i.i.d. symbol erasure channel models. Two important scenarios are analyzed: (i) tradeoff between decoding deadline Delta and probability of error p(e) assuming infinite memory alpha = infinity; and (ii) tradeoff between alpha and p(e) assuming infinite Delta = infinity. For each scenario, this work derives the corresponding asymptotic constant rho, power beta and decay rate eta that satisfy p(e)(x) similar to rho x(beta)e(-eta x). The results of (i) and (ii) are then used to study an important code design problem: Under a given target deadline A, what is the memory length alpha needed for the error probability p(e) to be within a factor of c > 1 of the best possible p(e)(& lowast;) over alpha. Further analysis also suggests that regardless the c value being considered, the necessary memory length is approximately 3-7% of the target deadline A when A is large, the actual percentage depending on the channel model and the coding rate. Such a prediction is consistent with existing brute-force-based evaluations.
Keywords:
Codes
Delays
Symbols
Encoding
Decoding
Vectors
Low latency communication
Error probability
Complexity theory
Channel models
Streaming codes
packet erasure channels
asymptotic analysis
error exponent
difference equations
constraint length
Journal
I
IF:
2.9
Papers:
317
Citations:
0
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