Capacity of Complexity-Constrained Noise-Free CDMA

TL;DR

This paper analyzes the capacity of a noise-free CDMA channel with strict receiver complexity constraints, showing that even with simple detection, a non-trivial capacity exists in large systems.

Contribution

It introduces a complexity-constrained CDMA model and rigorously derives its Shannon capacity using statistical mechanics methods, supported by finite-size simulations.

Findings

Non-trivial capacity exists despite simplicity constraints

Capacity analysis using statistical mechanics

Validation through finite-size simulations

Abstract

An interference-limited noise-free CDMA downlink channel operating under a complexity constraint on the receiver is introduced. According to this paradigm, detected bits, obtained by performing hard decisions directly on the channel's matched filter output, must be the same as the transmitted binary inputs. This channel setting, allowing the use of the simplest receiver scheme, seems to be worthless, making reliable communication at any rate impossible. We prove, by adopting statistical mechanics notion, that in the large-system limit such a complexity-constrained CDMA channel gives rise to a non-trivial Shannon-theoretic capacity, rigorously analyzed and corroborated using finite-size channel simulations.