List-Decoding Capacity of the Gaussian Arbitrarily-Varying Channel

Area of Science:

• Information Theory
• Wireless Communications
• Cybersecurity

Background:

• The Gaussian arbitrarily-varying channel (GAVC) presents challenges in information transmission due to uncertainty in channel state.
• Understanding channel capacity under adversarial conditions is crucial for secure communication systems.
• Existing models often simplify adversarial capabilities or decoder types.

Purpose of the Study:

• To determine the capacity of the GAVC with a stochastic encoder and deterministic list-decoder under average error probability.
• To analyze the impact of an adversary with power constraints on channel capacity.
• To establish conditions for secure communication against an informed adversary.

Main Methods:

• Utilizing a deterministic list-decoder and considering both legitimate and adversarial signal power constraints.
• Developing a converse proof demonstrating decoder confutation by adversarial signal superposition.
• Employing a novel variant of the Csiszár-Narayan method for achievability.

Main Results:

• The capacity is equivalent to a point-to-point Gaussian channel with increased noise variance, provided the adversary's power is limited relative to the transmitter's power and list size (L).
• If the adversary's power exceeds L times the transmitter power, the channel capacity becomes zero.
• The adversary's knowledge of the legitimate user's code is a key factor.

Conclusions:

• Secure communication over the GAVC is feasible under specific power constraints, balancing legitimate transmission against adversarial interference.
• The list size (L) plays a critical role in determining the threshold for secure communication.
• The findings offer insights into designing robust communication systems against sophisticated adversaries.