State-Dependent Z Channel

TL;DR

This paper investigates the capacity and achievable rate regions of state-dependent Z channels with non-causal side information at encoders, employing advanced coding schemes like Marton, Gelfand-Pinsker, and lattice strategies.

Contribution

It introduces new achievable rate regions and bounds for the state-dependent Z channel, including Gaussian cases, using combined coding and decoding techniques.

Findings

Achievable rate region matches the capacity for certain rates.

Outer and inner bounds coincide in specific regimes.

Lattice strategies effectively eliminate interference in Gaussian channels.

Abstract

In this paper we study the Z channel with side information non-causally available at the encoders. We use Marton encoding along with Gelfand-Pinsker random binning scheme and Chong-Motani-Garg-El Gamal (CMGE) jointly decoding to find an achievable rate region. We will see that our achievable rate region gives the achievable rate of the multiple access channel with side information and also degraded broadcast channel with side information. We will also derive an inner bound and an outer bound on the capacity region of the state-dependent degraded discrete memoryless Z channel and also will observe that our outer bound meets the inner bound for the rates corresponding to the second transmitter. Also, by assuming the high signal to noise ratio and strong interference regime, and using the lattice strategies, we derive an achievable rate region for the Gaussian degraded Z channel with additive interference non-causally available at both of the encoders. Our method is based on lattice transmission scheme, jointly decoding at the first decoder and successive decoding at the second decoder. Using such coding scheme we remove the effect of the interference completely.