Composite CDMA - A statistical mechanics analysis

TL;DR

This paper analyzes composite CDMA codes combining sparse and dense spreading using statistical mechanics, showing they outperform traditional codes in high interference regimes.

Contribution

It introduces a novel composite code ensemble and applies replica symmetric analysis and belief propagation to evaluate performance.

Findings

Composite codes outperform sparse and dense codes at high interference.

Replica symmetric calculations provide insights into large system performance.

Finite system analysis confirms advantages of composite codes.

Abstract

Code Division Multiple Access (CDMA) in which the spreading code assignment to users contains a random element has recently become a cornerstone of CDMA research. The random element in the construction is particular attractive as it provides robustness and flexibility in utilising multi-access channels, whilst not making significant sacrifices in terms of transmission power. Random codes are generated from some ensemble, here we consider the possibility of combining two standard paradigms, sparsely and densely spread codes, in a single composite code ensemble. The composite code analysis includes a replica symmetric calculation of performance in the large system limit, and investigation of finite systems through a composite belief propagation algorithm. A variety of codes are examined with a focus on the high multi-access interference regime. In both the large size limit and finite systems we demonstrate scenarios in which the composite code has typical performance exceeding sparse and dense codes at equivalent signal to noise ratio.