Purdue University Graduate School

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Sequential Codes for Low Latency Communications

posted on 2024-04-16, 15:23 authored by Pin-Wen SuPin-Wen Su

The general design goal of low latency communication systems is to minimize the end-to-end delay while attaining the predefined reliability and throughput requirements. The burgeoning demand for low latency communications motivates a renewed research interest of the tradeoff between delay, throughput, and reliability. In this dissertation research, we consider slotted-based systems and explore the potential advantages of the so-called sequential codes in low latency network communications.

The first part of this dissertation analyzes the exact error probability of random linear streaming codes (RLSCs) in the large field size regime over the stochastic independently and identically distributed (i.i.d.) symbol erasure channels (SECs). A closed-form expression of the error probability pe of large-field-size RLSCs is derived under, simultaneously, the finite memory length α and decoding deadline Δ 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).

The second part of this dissertation focuses on the asymptotics of the error probability of RLSCs in the same system model of the first part. Two important scenarios are analyzed: (i) tradeoff between Δ and pe under infinite α; and (ii) tradeoff between α and pe under infinite Δ. In the first scenario, the asymptote of pe(Δ) is shown to be ρΔ-1.5e-ηΔ. The asymptotic power term Δ-1.5 of RLSCs is a strict improvement over the Δ-0.5 term of random linear block codes. A pair of upper and lower bound on the asymptotic constant ρ is also derived, which are tight (i.e., identical) for one specific class of SECs. In the second scenario, a refine approximation is proposed by computing the parameters in a multiterm asymptotic form, which closely matches the exact error probability even for small memory length (≈ 20). The results of the asymptotics can be further exploited to find the c-optimal memory length αc*(Δ), which is defined as the minimal memory length α needed for the resulting pe to be within a factor of c>1 of the best possible pe* for any Δ, an important piece of information for practical implementation.

Finally, we characterize the channel dispersions of 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 pe is 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.


Degree Type

  • Doctor of Philosophy


  • Electrical and Computer Engineering

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Chih-Chun Wang

Additional Committee Member 2

Xiaojun Lin

Additional Committee Member 3

David J. Love

Additional Committee Member 4

Michael D. Zoltowski

Additional Committee Member 5

Borja Peleato-Inarrea