On the Two-user Interference Channel with Lack of Knowledge of the Interference Codebook at one Receiver

TL;DR

This paper investigates the capacity of a two-user interference channel where one receiver lacks knowledge of the interfering codebook, deriving bounds and strategies that show near-optimal performance despite the lack of full codebook information.

Contribution

It introduces a novel outer bound for the IC-OR, demonstrates achievable schemes with finite gaps, and explores input distributions that approach the classical capacity despite obliviousness.

Findings

Outer bound is achievable within a gap for injective semi-deterministic IC-ORs.

Gap is zero for injective fully deterministic IC-ORs.

Achieves within 3.34 bits of the classical Gaussian IC capacity with mixed input distributions.

Abstract

In multi-user information theory it is often assumed that every node in the network possesses all codebooks used in the network. This assumption may be impractical in distributed ad-hoc, cognitive or heterogeneous networks. This work considers the two-user Interference Channel with one Oblivious Receiver (IC-OR), i.e., one receiver lacks knowledge of the interfering cookbook while the other receiver knows both codebooks. The paper asks whether, and if so how much, the channel capacity of the IC-OR is reduced compared to that of the classical IC where both receivers know all codebooks. A novel outer bound is derived and shown to be achievable to within a gap for the class of injective semi-deterministic IC-ORs; the gap is shown to be zero for injective fully deterministic IC-ORs. For the linear deterministic IC-OR that models the Gaussian noise channel at high SNR, non i.i.d. Bernoulli(1/2) input bits are shown to achieve points not achievable by i.i.d. Bernoulli(1/2) input bits used in the same achievability scheme. For the real-valued Gaussian IC-OR the gap is shown to be at most 1/2 bit per channel use, even though the set of optimal input distributions for the derived outer bound could not be determined. Towards understanding the Gaussian IC-OR, an achievability strategy is evaluated in which the input alphabets at the non-oblivious transmitter are a mixture of discrete and Gaussian random variables, where the cardinality of the discrete part is appropriately chosen as a function of the channel parameters. Surprisingly, as the oblivious receiver intuitively should not be able to 'jointly decode' the intended and interfering messages (whose codebook is unavailable), it is shown that with this choice of input, the capacity region of the symmetric Gaussian IC-OR is to within 3.34 bits (per channel use per user) of an outer bound for the classical Gaussian IC with full codebook knowledge.