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 $\text{SNR}$ so that the proposed scheme achieves a distortion $D$, where $-\log (D)$ is within $O(\log \log (\text{SNR}))$ of the optimal performance for all values of $\text{SNR}$, leading to a channel-agnostic scheme.