State-dependent Z channel

Abstract

In this paper we study the "Z" channel with side information non-causally available at the encoders. We use Marton encoding along with Gelf'and-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. I. INTRODUCTIONThe Z channel is a two-transmitter two-receiver model shown in Fig. 1 where the first sender only wishes to send information to the first receiver whereas the second transmitter sends information to both of the receivers. The Z channel was first studied by Viswanath et al [1] where they introduced the model and found the capacity region of a specialclass of Z channels and the achievable rate of a special case of the Gaussian Z channel (GZC). In [2], Liu and Ulukus obtained several capacity bounds for a class of GZC. Chong-Motani-Garg (CMGE) [3] studied three different types of degraded Z channel and characterized the capacity region in one type. They also characterized the capacity region of GZC with moderately strong crossover link.The capacity region of the general Z channel is still an open problem. The best achievable rate region for the discrete memoryless Z channel until today is due to Do et al [4].Channels with side information were first studied by Shannon [5] where he characterized the capacity of a point-to-point channel with side information causally available at the transmitters. Gelf 'and and Pinsker [6] found the capacity of a single-user channel with side information non-causally available at the encoders. State-dependent multiuser settings have been studied in [7], [8], [9], [10], and [11].In this paper we study the Z channel with channel state information non-causally available at the encoders that is depicted in Fig. 2. The reason to study this channel model is buttressed by the applications it has in some wireless communication scenarios such as the case where two communication-involved cells are interfering with each other and thus suffer from a common interference modeled by some S non-causally available to two distinct destination base stations as shown in Fig. As in Fig. 2

Z-interference channel with side information at the transmitters

“…The main contributions of Ref. [21] are (i) to derive an achievable rate based on a two-layer binning scheme for the discrete case of the single dirty ZC and (ii) to present a lattice-based achievable rate for a degraded version of the Gaussian single dirty ZC that as we will describe in the following the results presented in Ref. [21] is different from our work.…”

“…A similar scenario has been studied previously in Ref. [21], where authors have considered a state-dependent Z channel with a common state which is non-causally known to both transmitters and therefore, it can be called the single dirty ZC. The main contributions of Ref.…”

“…The bound (20) is proved by considering the point-to-point channel between the second transmitter-receiver pair. Hence, we only prove (21). Considering the receiver 1 and applying the Fano's inequality we can write:…”

State-dependent Gaussian Z-channel with mismatched side-information and interference

“…1), in which transmitters 1 and 2 communicate with receivers 1 and 2, and only receiver 2 is interfered by transmitter 1's signal and a random state sequence. In contrast to the state-dependent Z-interference channel model studied previously in [9], which assumes that state interference at both receivers are known to both (corresponding) transmitters, our model assumes that state interference (only to receiver 2) is known noncausally only to transmitter 1, not to the corresponding transmitter 2. Hence, transmitter-side state cognition and receiver-side state interference are mismatched.…”

State-Dependent Interference Channel With Correlated States

“…In [10], a type of the state-dependent Z-IC with two states was studied, where each transmitter knows only the state that corrupts its corresponding receiver. In [11], a state-dependent Z-interference broadcast channel was studied, in which one transmitter has only one message for its corresponding receiver, and the other transmitter has two messages respectively for two receivers. Both receivers are corrupted by the same state, which is known to both transmitters.…”