Random Linear Streaming Codes in the Finite Memory Length and Decoding Deadline Regime—Part I: Exact Analysis
Random Linear Streaming Codes in the Finite Memory Length and Decoding Deadline Regime—Part I: Exact Analysis
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DOI：
10.1109/tit.2022.3178036
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发表时间：
2022-10
影响因子：
2.5
通讯作者：
Pin-Wen Su;Yu-Chih Huang;Shih-Chun Lin;I-Hsiang Wang;Chih-Chun Wang
中科院分区：
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
流编码以一串源符号为输入，实时输出一串编码符号，消除了传统分组码的排队延迟，特别适合对延迟敏感的应用。已有的流编码性能研究主要集中在渐近误差指数分析上，或者在确定性对抗信道模型下的最优码构造上。相反，这项工作分析了随机线性流编码(RLSC)在随机I.I.D.上的大场大小情况下的精确错误概率。符号擦除信道模型。在有限存储长度和译码截止期约束下，推导了大场RLSC误码概率的闭合表达式。然后，使用结果来检查存储器长度(复杂性)、解码截止日期(延迟)、码率(吞吐量)和错误概率(可靠性)之间的复杂权衡。数值计算表明，在相同的码率和误码率要求下，RLSC的端到端时延是最优分组码(即MDS码)的40%~48%。这意味着从分组码切换到流代码不仅完全消除了排队延迟(占延迟减少的最初50%)，而且提高了可靠性(占额外的2%-10%的延迟减少)。
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. Existing works on streaming code performance either focused on the asymptotic error-exponent analyses, or on the optimal code construction under deterministic adversarial channel models. In contrast, this work analyzes the exact error probability of random linear streaming codes (RLSCs) in the large field size regime over the stochastic i.i.d. symbol erasure channel model. A closed-form expression of the error probability of large-field-size RLSCs is derived under, simultaneously, the finite memory length and decoding deadline constraints. The result is then used to examine the intricate tradeoff between memory length (complexity), decoding deadline (delay), code rate (throughput), and error probability (reliability). Numerical evaluation shows that under the same code rate and error probability requirements, the end-to-end delay of RLSCs is 40–48% of that of the optimal block codes (i.e., MDS codes). This implies that switching from block codes to streaming codes not only eliminates the queueing delay completely (which accounts for the initial 50% of the delay reduction) but also improves the reliability (which accounts for the additional 2–10% delay reduction).