Few-Shot Channel-Agnostic Analog Coding: A Near-Optimal Scheme

In this paper, we investigate the problem of transmitting an analog source to a destination over
$N$
uses of an additive-white-Gaussian-noise (AWGN) channel, where
$N$
is very small (in the order of 10 or even less). The proposed coding scheme is based on representing the source symbol using a novel progressive expansion technique, partitioning the digits of expansion into
$N$
ordered sets, and finally mapping the symbols in each set to a real number by applying the reverse progressive expansion. In the last step, we introduce some gaps between the signal levels to prevent the carry-over of the additive noise from propagation to other levels. This shields the most significant levels of the signal from an additive noise, hitting the signal at a less significant level. The parameters of the progressive expansion and the shielding procedure are opportunistically independent of the SNR so that the proposed scheme achieves a distortion
$D$
, where
$-\log(D)$
is within O(log log (SNR)) of the optimal performance for all values of SNR, leading to a channel-agnostic scheme.