Transmission of non-linear binary input functions over a CDMA System

TL;DR

This paper investigates the limits of transmitting non-linear binary functions over CDMA networks, motivated by environmental monitoring via mobile devices, and establishes a lower bound on the system's computational capacity.

Contribution

It introduces a lower bound on the computational capacity for transmitting non-linear binary functions over CDMA systems with a novel signature matrix design.

Findings

Established a lower bound on computational capacity

Modeled CDMA signature matrix as a parity check matrix

Extended analysis from linear to non-linear functions

Abstract

We study the problem of transmission of binary input non-linear functions over a network of mobiles based on CDMA. Motivation for this study comes from the application of using cheap measurement devices installed on personal cell-phones to monitor environmental parameters such as air pollution, temperature and noise level. Our model resembles the MAC model of Nazer and Gastpar except that the encoders are restricted to be CDMA encoders. Unlike the work of Nazer and Gastpar whose main attention is transmission of linear functions, we deal with non-linear functions with binary inputs. A main contribution of this paper is a lower bound on the computational capacity for this problem. While in the traditional CDMA system the signature matrix of the CDMA system preferably has independent rows, in our setup the signature matrix of the CDMA system is viewed as the parity check matrix of a linear code, reflecting our treatment of the interference.