# A Method Beyond Channel Capacity in the Low SNR Regime: Theoretical Proof and Numerical Confirmation

## TL;DR

This paper introduces the cocktail BPSK method, layering two BPSK streams in a Gaussian channel, achieving data rates beyond channel capacity at low SNR, supported by theoretical proof and numerical validation.

## Contribution

It presents a novel layered BPSK scheme that surpasses traditional channel capacity limits in the low SNR regime, with rigorous theoretical and numerical validation.

## Key findings

- Achieves data rates exceeding channel capacity at zero SNR.
- Theoretical proof confirms the method's effectiveness.
- Numerical results validate the theoretical predictions.

## Abstract

A method is proposed, referred to as the cocktail BPSK, to use two independent BPSK streams layered in a parallel transmission through the additive white Gaussian channel. The critical point of the method is to translate the interference between the two layered symbols into a problem of one symbol with two possible amplitudes, whereby we find that the achievable data rate (ADR) of the first layer equals to the channel capacity at zero signal-to-noise-ratio limit. By adding the contribution of the second layer, we find that the total ADR of the two layers can be larger than the channel capacity. The theoretical proof is done based on the mutual information and the numerical results are added for the confirmation.