Streaming codestake a string of source symbols as input and output a string of coded symbols in real time, which eliminate the queueing delay of traditionalblock codesand are thus especially appealing for delay sensitive applications. This work studies the asymptotics of random linear streaming codes (RLSCs) in the large finite-field-size regime under the i.i.d. symbol erasure channel models. Two important scenarios are analyzed: (i) tradeoff between decoding deadline Δ and probability of errorpeassuming infinite memory α = ∞; and (ii) tradeoff between α andpeassuming infinite Δ = ∞. For each scenario, this work derives the corresponding asymptotic constant ρ, power β and decay rate η that satisfype(x) ∼ ρxβe−ηx. The results of (i) and (ii) are then used to study an important code design problem: Under a given target deadline Δ, what is the memory length α needed for the error probabilitypeto be within a factor ofc> 1 of the best possiblep∗eover α. Further analysis also suggests that regardless thecvalue being considered, the necessary memory length is approximately 3–7% of the target deadline Δ when Δ is large, the actual percentage depending on the channel model and the coding rate. Such a prediction is consistent with existing brute-force-based evaluations.

Streaming codes eliminate the queueing delay and are an appealing candidate for low latency communications. This work studies the tradeoff between error probability peand 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 ∆−1.5of RLSCs is a strict improvement over the ∆−0.5term 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 peto 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.

Channel dispersion quantifies the convergence speed of coding rate to channel capacity under different latency constraints. Under the setting of packet erasure channels (PECs) with Bernoulli packet arrivals, this work characterizes the channel dispersions of random linear streaming codes (RLSCs) and MDS block codes, respectively. New techniques are developed to quantify the channel dispersion of sequential (non-block-based) coding, the first in the literature. The channel dispersion expressions are then used to compare the levels of error protection between RLSCs and MDS block codes. The results show that if and only if the target error probability peis smaller than a threshold (≈0.1774), RLSCs offer strictly stronger error protection than MDS block codes, which is on top of the already significant 50% latency savings of RLSCs that eliminate the queueing delay completely.

Streaming codestake a string of source symbols as input and output a string of coded symbols in real time, which eliminate the queueing delay of traditionalblock codesand 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 underdeterministic adversarial channel models. In contrast, this work analyzes the exact error probability ofrandom 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).

Streaming codes take a string of source symbols as input and output a string of coded symbols in real time, which effectively eliminate the queueing delay and are regarded as a promising scheme for low latency communications. Aiming at quantifying the fundamental latency performance of random linear streaming codes (RLSCs) over i.i.d. symbol erasure channels, this work derives the exact error probability under, simultaneously, the finite memory length and finite decoding deadline constraints. The result is then used to examine the tradeoff among memory length (complexity), decoding deadline (delay), and error probability (reliability) of RLSCs for the first time in the literature. Two critical observations are made: (i) Too much memory can adversely impact the performance under a finite decoding deadline constraint, a surprising finding not captured by the traditional wisdom that large memory length monotonically improves the performance in the asymptotic regime; (ii) The end-to-end delay of the RLSC is roughly 50% of that of the MDS block code when under identical code rate and error probability requirements. This implies that switching from block codes to RLSCs not only eliminates the queueing delay (thus 50%) but also has little negative impact on the error probability.

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.