On The Design of Signature Codes in Decentralized Wireless Networks

TL;DR

This paper proposes a randomized spreading and masking scheme for decentralized wireless networks, achieving near-centralized performance and demonstrating that combined spreading and masking outperform masking alone.

Contribution

It introduces a novel randomized signaling scheme with spreading and masking, providing achievable rates and optimality results for decentralized wireless communication.

Findings

Achievable sum multiplexing gain approaches centralized schemes as users increase.

Spreading codes are generally non-uniform over the alphabet.

Spreading and masking together outperform masking alone in achievable rates.

Abstract

This paper addresses a unified approach towards communication in decentralized wireless networks of separate transmitter-receiver pairs. In general, users are unaware of each other's codebooks and there is no central controller to assign the resources in the network to the users. A randomized signaling scheme is introduced in which each user locally spreads its Gaussian signal along a randomly generated spreading code comprised of a sequence of nonzero elements over a certain alphabet. Along with spreading, each transmitter also masks its output independently from transmission to transmission. Using a conditional version of entropy power inequality and a key lemma on the differential entropy of mixed Gaussian random vectors, achievable rates are developed for the users. It is seen that as the number of users increases, the achievable Sum Multiplexing Gain of the network approaches that of a centralized orthogonal scheme where multiuser interference is completely avoided. An interesting observation is that in general the elements of a spreading code are not equiprobable over the underlying alphabet. Finally, using the recently developed extremal inequality of Liu-Viswanath, we present an optimality result showing that transmission of Gaussian signals via spreading and masking yields higher achievable rates than the maximum achievable rate attained by applying masking only.