|Error Rate Analysis for Random Linear Streaming Codes in the Finite Memory Length Regime
|Pin-Wen Su, Purdue University, United States; Yu-Chih Huang, National Taipei University, Taiwan; Shih-Chun Lin, National Taiwan University of Science and Technology, Taiwan; I-Hsiang Wang, National Taiwan University, Taiwan; Chih-Chun Wang, Purdue University, United States
|C.9: Streaming Codes
|Coding for Communications
|Click here to download the manuscript
|Click here to watch in the Virtual Symposium
|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-chain-based 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.