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).

中文翻译：

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有限内存长度和解码截止期限机制中的随机线性流码——第一部分：精确分析


流码以一串源符号作为输入，实时输出一串编码符号，消除了传统分组码的排队延迟，因此对于延迟敏感的应用特别有吸引力。现有的流代码性能工作要么侧重于渐近误差指数分析，要么侧重于确定性对抗信道模型下的最优代码构造。相比之下，这项工作分析了随机线性流码（RLSC）在随机独立同分布符号擦除信道模型上的大字段大小范围内的精确错误概率。同时在有限存储器长度和解码期限约束下导出了大字段大小 RLSC 错误概率的封闭式表达式。然后将结果用于检查内存长度（复杂性）、解码期限（延迟）、码率（吞吐量）和错误概率（可靠性）之间的复杂权衡。数值评估表明，在相同码率和错误概率要求下，RLSC的端到端延迟是最佳分组码（即MDS码）的40%~48%。这意味着从块码切换到流码不仅完全消除了排队延迟（这导致了最初的 50% 的延迟减少），而且还提高了可靠性（这导致了额外的 2-10% 的延迟减少）。