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.Comment: 23 pages, 11 figures, Sigma Phi 2008 conference submission -
submitted to J.Stat.Mec
