Optimal sparse CDMA detection at high load

TL;DR

This paper investigates the trade-offs in CDMA detection efficiency and complexity at high load, revealing a threshold where detection becomes computationally challenging, especially for sparse codes.

Contribution

It introduces an analysis of the load threshold in sparse CDMA detection, highlighting the limitations of optimal detection methods at high load levels.

Findings

Existence of a load threshold causing a jump in computational complexity

Unit clause propagation works at low load but fails at high load

Sparse codes have fundamental limitations in optimal detection at high load

Abstract

Balancing efficiency of bandwidth use and complexity of detection involves choosing a suitable load for a multi-access channel. In the case of synchronous CDMA, with random codes, it is possible to demonstrate the existence of a threshold in the load beyond which there is an apparent jump in computational complexity. At small load unit clause propagation can determine a jointly optimal detection of sources on a noiseless channel, but fails at high load. Analysis provides insight into the difference between the standard dense random codes and sparse codes, and the limitations of optimal detection in the sparse case.