  In this work, the problem of communicating decisions of a classifier over a
noisy channel is considered. With machine learning based models being used in
variety of time-sensitive applications, transmission of these decisions in a
reliable and timely manner is of significant importance. To this end, we study
the scenario where a probability vector (representing the decisions of a
classifier) at the transmitter, needs to be transmitted over a noisy channel.
Assuming that the distortion between the original probability vector and the
reconstructed one at the receiver is measured via f-divergence, we study the
trade-off between transmission latency and the distortion. We completely
analyze this trade-off using uniform, lattice, and sparse lattice-based
quantization techniques to encode the probability vector by first
characterizing bit budgets for each technique given a requirement on the
allowed source distortion. These bounds are then combined with results from
finite-blocklength literature to provide a framework for analyzing the effects
of both quantization distortion and distortion due to decoding error
probability (i.e., channel effects) on the incurred transmission latency. Our
results show that there is an interesting interplay between source distortion
(i.e., distortion for the probability vector measured via f-divergence) and the
subsequent channel encoding/decoding parameters; and indicate that a joint
design of these parameters is crucial to navigate the latency-distortion
tradeoff. We study the impact of changing different parameters (e.g. number of
classes, SNR, source distortion) on the latency-distortion tradeoff and perform
experiments on AWGN and fading channels. Our results indicate that sparse
lattice-based quantization is the most effective at minimizing latency across
various regimes and for sparse, high-dimensional probability vectors (i.e.,
high number of classes).
