# Cocktail BPSK: Achievable Data Rate beyond Channel Capacity

## TL;DR

This paper introduces cocktail BPSK, a layered transmission method that surpasses channel capacity at low SNR by combining two BPSK streams, demonstrating higher achievable data rates through theoretical analysis and numerical validation.

## Contribution

It proposes a novel layered BPSK scheme that achieves data rates beyond channel capacity at low SNR, supported by theoretical derivations and numerical results.

## Key findings

- Sum ADR exceeds channel capacity at low SNR
- Layered BPSK can be adjusted for high spectral efficiency
- The method is validated through numerical simulations

## Abstract

In this paper, we propose a method layering two independent BPSK symbol streams in parallel transmission through a single additive white Gaussian noise (AWGN) channel and investigate its achievable data rate (ADR). The receiver processes the two layered signals individually, where the critical point is to translate the interference between the two layers into the problem of one BPSK symbol having two equiprobable amplitudes. After detecting one symbol stream, we subtract the detected result to demodulate the other symbol stream. Based on the concept of mutual information, we formulate the ADRs and unearth an interesting phenomenon -- the sum ADR of the two BPSK symbol streams is higher than the channel capacity at low signal to noise ratio (SNR). Our theoretical derivations together with illustrative numerical results substantiate this phenomenon. We refer to this approach as cocktail BPSK because the amplitudes of the two layered BPSK streams can be adjusted at the transmitter to achieve high spectral efficiency.