This paper is mostly a follow up on the work of Etkin and Ordentlich that studied the capacity regions of binary input deterministic interference channels. The only binary input deterministic interference channel whose capacity region is unknown (up to isomorphism) is when one receiver receives the Boolean AND of the two transmitted symbols, and the other receiver obtains the Boolean OR of the two transmitted symbols. Etkin and Ordentlich stated in the paper that they believed that time-division would be the capacity region for this interference channel. In this paper we show that one can achieve rates outside the time-division region. That time-division yields the zero-error capacity region for this setting is known as Simonyi’s sand-glass conjecture, a statement that has received considerable attention in the combinatorics community. Various upper-bounds on the sum-rate of the zero error capacity region had been proposed in the combinatorics community. In this paper we evaluate an outer bound to the (traditional notion of) capacity region due to Etkin and Ordentlich and show that this yields, surprisingly, a tighter bound that the best known bound for the sand-glass problem. Finally, we establish the capacity region of the some special classes of binary input interference channels by improving on the outer-bound proposed by Etkin and Ordentlich.
In this paper, we study the achievable rate performance and the design of using purely discrete input signaling and treating interference as noise (TIN) for the two-user complex Gaussian interference channel (G-IC), where the channel introduces random phase rotation for all links. To analyze the achievable rate performance under this scenario, we first look into the corresponding deterministic interference channel model and design schemes to achieve the entire capacity region under TIN. Then, we translate the scheme into a multi-layer superposition coding scheme based on discrete inputs for G-IC and analyze the achievable rate under TIN. Our simulation results show that our scheme is capable of approaching the (outer bound of) capacity region of the complex G-IC and performs significantly better than Gaussian signalling with TIN.
In this work we consider common randomness-aided secure communications, where a limited common randomness is available at the transmitters. Specifically, we focus on a two-user interference channel with secrecy constraints and a wiretap channel with a helper, in the presence of a limited common randomness shared between the transmitters. For both two settings, we characterize the optimal secure sum degrees-of-freedom (DoF) or secure DoF as a function of the DoF of common randomness. The results reveal that the secure sum DoF or secure DoF increases as the DoF of common randomness increases, bridging the gap between the extreme DoF point with no common randomness and the other extreme DoF point with unlimited common randomness. The proposed scheme is a two-layer coding scheme, in which two sub-schemes are designed respectively in two layers, i.e., at two different power levels, utilizing common randomness in the first layer only. The role of the common randomness is to jam partial information signal at the eavesdroppers, without causing interference at the legitimate receivers. To prove the optimality of the proposed scheme, a new converse is also derived in this work.
Under the assumption of perfect channel state information at the transmitters (CSIT), it is known that structured codes offer significant advantages in an interference network, e.g., lattice alignment allows a receiver to directly decode the sum of aligned interfering codewords at higher power levels even though individual codewords are not resolvable, subtract the aggregate interference, and then proceed to decode desired codewords at lower power levels. To what extent are such benefits of structured codes fundamentally limited by uncertainty in CSIT? To answer this question, we explore what is perhaps the simplest setting where the question presents itself -- a Z interference channel with secure communication. Using sum-set inequalities based on Aligned Images bounds we prove that the GDoF benefits of structured codes are lost completely under finite precision CSIT. The secure GDoF region of the Z interference channel is obtained as a byproduct of the analysis.