Detailed Asymptotics of the Delay-Reliability Tradeoff of Random Linear Streaming Codes
Detailed Asymptotics of the Delay-Reliability Tradeoff of Random Linear Streaming Codes
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DOI：
10.1109/isit54713.2023.10206973
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发表时间：
2023-06
期刊：
影响因子：
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通讯作者：
Pin-Wen Su;Yu-Chih Huang;Shih-Chun Lin;I-Hsiang Wang;Chih-Chun Wang
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文献类型：
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作者：
Pin-Wen Su;Yu-Chih Huang;Shih-Chun Lin;I-Hsiang Wang;Chih-Chun Wang
流式代码消除了排队延迟，这是对低潜伏期通信的吸引力。 RLSC的第5个严格改善了随机线性的Δ -0.5项块代码（ii）在不对称常数ρ上得出一对上限和下限，对于任何c> 1的特定类别（iii）是紧密的（即相同）；在任何α下，最好的$ p_e^{\ ast} $，这是实用的重要信息实施此工作研究，并基于新开发的渐近学，得出了$ \ alpha _C^{\ ast} $的新属性。
Streaming codes eliminate the queueing delay and are an appealing candidate for low latency communications. This work studies the tradeoff between error probability pe and 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 ∆−1.5 of RLSCs is a strict improvement over the ∆−0.5 term 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 pe to 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.