Tight Bounds on the Capacity of Binary Input random CDMA Systems

TL;DR

This paper establishes tight upper bounds on the capacity of binary input CDMA systems with random spreading, confirming predictions from statistical physics methods and demonstrating concentration of key information-theoretic quantities.

Contribution

It provides rigorous bounds on system capacity that match non-rigorous replica method results, and introduces general mathematical techniques for analyzing multiuser communication systems.

Findings

Upper bounds on capacity match replica predictions

Concentration results for mutual information and free energy

Framework applicable to various multiuser scenarios

Abstract

We consider multiple access communication on a binary input additive white Gaussian noise channel using randomly spread code division. For a general class of symmetric distributions for spreading coefficients, in the limit of a large number of users, we prove an upper bound on the capacity, which matches a formula that Tanaka obtained by using the replica method. We also show concentration of various relevant quantities including mutual information, capacity and free energy. The mathematical methods are quite general and allow us to discuss extensions to other multiuser scenarios.