The Arbitrarily Varying Channel With Colored Gaussian Noise

DOI10.1109/TIT.2021.3063905zbMATH Open1475.94071arXiv1901.00929OpenAlexW3135871542MaRDI QIDQ5001760

Uzi Pereg, Y. Steinberg

Publication date: 23 July 2021

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Abstract: We address the arbitrarily varying channel (AVC) with colored Gaussian noise. The work consists of three parts. First, we study the general discrete AVC with fixed parameters, where the channel depends on two state sequences, one arbitrary and the other fixed and known. This model can be viewed as a combination of the AVC and the time-varying channel. We determine both the deterministic code capacity and the random code capacity. Super-additivity is demonstrated, showing that the deterministic code capacity can be strictly larger than the weighted sum of the parametric capacities. In the second part, we consider the arbitrarily varying Gaussian product channel (AVGPC). Hughes and Narayan characterized the random code capacity through min-max optimization leading to a "double" water filling solution. Here, we establish the deterministic code capacity and also discuss the game-theoretic meaning and the connection between double water filling and Nash equilibrium. As in the case of the standard Gaussian AVC, the deterministic code capacity is discontinuous in the input constraint, and depends on which of the input or state constraint is higher. As opposed to Shannon's classic water filling solution, it is observed that deterministic coding using independent scalar codes is suboptimal for the AVGPC. Finally, we establish the capacity of the AVC with colored Gaussian noise, where double water filling is performed in the frequency domain. The analysis relies on our preceding results, on the AVC with fixed parameters and the AVGPC.

Full work available at URL: https://arxiv.org/abs/1901.00929

zbMATH Keywords

colored Gaussian noisearbitrarily varying channel (AVC)random code capacityarbitrarily varying Gaussian product channel (AVGPC)deterministic code capacitydouble water filling

Mathematics Subject Classification ID

Channel models (including quantum) in information and communication theory (94A40) Source coding (94A29)

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