We study the State-Dependent Gaussian Z-Interference Channel (SDG-ZIC), with two senders transmitting two independent messages through a Gaussian Z-interference channel with the same state. Transmitter 1 interferes with receiver 2, while transmitter 2 does not interfere with receiver 1. In addition, both receivers suffer from the same but differently scaled random state sequence, which is non-causally known at both transmitters. As mentioned in [1], the challenge here is to fully cancel differently scaled states at both receivers. Proposing transmission schemes based on nested lattice codes, we show that under some new conditions, the state at both receivers can be fully canceled and the capacity region can be fully achieved.

We study, using information-theoretic security methods, the so-called symmetric two-hop channel with an untrusted relay. In this model, a source wants to send its message reliably and securely to the destination through an honest but curious relay. The relay acts as a passive eavesdropper. Our investigation, in line with the relevant literature, seeks to determine what rate, termed secrecy rate, is achievable. To do that, we consider a typical setting, with the destination cooperating with the source, sending a 'scrambling' signal to conceal the message from the relay. To derive the achievable secrecy rate, we propose a novel scheme based on nested lattice codes. We show that our scheme outperforms all existing schemes and it achieves the outer bound for this channel model within 0.33 bits.

Lattice codes are known to outperform random codes for certain networks, especially in the Gaussian two-way relay channels (GTWRCs) where lattice codes are able to exploit their linearity. As an extension of the GTWRC, in this paper, we consider the asymmetric Gaussian two-way line network where two nodes exchange their messages through multiple relays. We first investigate the capacity region of the full-duplex two-way two-relay line network. The results can be extended to an arbitrary number of relays and to half-duplex scenarios. This channel consists of four nodes: 1 ↔ 2 ↔ 3 ↔ 4, where nodes 1 and 4 with the help of two full-duplex relays, i.e., nodes 2 and 3, exchange their messages with each other. Using lattice codes, we design a novel scheme that allows the relay nodes to send the data in both directions simultaneously under an asymmetric rate region. In the proposed scheme, each relay decodes the sum of lattice points and then re-encodes it into another lattice codeword (which satisfies the transmit power constraint at the relay). It is shown that the proposed scheme achieves the capacity region of asymmetric two-way line network within 0.5 bit independent of the number of relays.

In this paper, we consider the Ice-Wine problem: Two transmitters send their messages over the Gaussian Multiple-Access Channel (MAC) and a receiver aims to recover a linear combination of codewords. The best known achievable rate-region for this problem is due to [1], [2] as Ri≤ ½ log (½ + SNR) (i = 1, 2). In this paper, we design a novel scheme using lattice codes and show that the rate region of this problem can be improved. The main difference between our proposed scheme with known schemes in [1], [2] is that instead of recovering the sum of codewords at the decoder, a non-integer linear combination of codewords is recovered. Comparing the achievable rate-region with the outer bound, Ri≤ ½ log (1 + SNR) (i = 1, 2), we observe that the achievable rate for each user is partially tight. Finally, by applying our proposed scheme to the Gaussian Two Way Relay Channel (GTWRC), we show that the best rate region for this problem can be improved.

Deterministic approach of models the interaction between the bits that are received at the same signal level by the modulo 2 sum of the bits where the carry-overs that would happen with real addition are ignored. By this model in a multi-user setting, the receiver can distinguish most significant bits (MSBs) of the stronger user without any noise. A faithful implementation of the deterministic model requires one to “neutralize interference” from previous carry over digits. This paper proposes a new implementation of “interference neutralization” [2] using structured lattice codes. We first present our implementation strategy and then, as an application, apply this strategy to a symmetric half-duplex Gaussian butterfly network. In this network, two transmitters communicate their information to two destinations via a half-duplex relay. For duplexing factor 0.5 and under certain conditions, we show that our proposed scheme based on superposition of nested lattice codes can achieve the capacity region in high SNR. Also, regardless of all channel parameters, the gap between its achievable rate region and the outer bound is at most 0.293 bits/sec/Hz.

In this work, we consider an additive state-dependent Gaussian interference channel (ASD-GIC) where there is a common additive interference, known to both transmitters but not to the receivers. First, we obtain an outer bound on the sum-capacity for the asymptotic case where the interference is assumed to be Gaussian variable with unbounded variance. This asymptotic case has been referred to as the “strong interference” in [1]. By applying a lattice-based coding scheme, an achievable rate-region is provided. Under some conditions, which depend on the noise variance and channel power constraints, this achievable sum-rate region meets the outer bound and therefore lattice codes can achieve the sum-capacity of an ASD-GIC in the asymptotic case.