Sequentially Mixing Randomly Arriving Packets Improves Channel Dispersion Over Block-Based Designs

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 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.