Error Rate Analysis for Random Linear Streaming Codes in the Finite Memory Length Regime
Error Rate Analysis for Random Linear Streaming Codes in the Finite Memory Length Regime
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DOI：
10.1109/isit44484.2020.9174038
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发表时间：
2020-06
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
流编码是对一串源数据包进行真实的实时编码并输出一串编码后的数据包，消除了分组编码的延迟，特别适合于对延迟敏感的应用。本文研究了随机线性流码（RLSC）和i.i.d.分组擦除信道。虽然现有的工作集中在渐近误差指数分析，这项工作的特点，在有限的内存长度制度的错误率和贡献包括：（一）一个新的信息债务为基础的描述的错误事件;（二）一个矩阵为基础的表征的错误率;（三）一个封闭形式的近似的错误率，这是可证明的紧大内存长度;和（iv）一个新的马尔可夫链为基础的分析框架，这可以是独立的研究兴趣。数值结果表明，近似，即（iii），密切匹配的准确的错误率，即使对于小的内存长度（1020）。结果可以被视为在RLSC的专门设置下的块编码的有限长度分析的顺序编码对应物[Polyanskiy等人10]。
Streaming codes encode a string of source packets and output a string of coded packets in real time, which eliminate the queueing delay of block coding and are thus especially suitable for delay-sensitive applications. This work studies random linear streaming codes (RLSCs) and i.i.d. packet erasure channels. While existing works focused on the asymptotic error-exponent analyses, this work characterizes the error rate in the finite memory length regime and the contributions include: (i) A new information-debt-based description of the error event; (ii) A matrix-based characterization of the error rate; (iii) A closed-form approximation of the error rate that is provably tight for large memory lengths; and (iv) A new Markov-chainbased analysis framework, which can be of independent research interest. Numerical results show that the approximation, i.e. (iii), closely matches the exact error rate even for small memory length (≈ 20). The results can be viewed as a sequential- coding counterpart of the finite length analysis of block coding [Polyanskiy et al. 10] under the specialized setting of RLSCs.