Generalisation of code division multiple access systems and derivation of new bounds for the sum capacity

In this study, the authors explore a generalised scheme for the synchronous code division multiple access (CDMA). In this scheme, unlike the standard CDMA systems, each user has different codewords for communicating different messages. Two main problems are investigated. The first problem concerns whether uniquely detectable overloaded matrices (an injective matrix, i.e. the inputs and outputs are in one‐to‐one correspondence depending on the input alphabets) exist in the absence of additive noise, and if so, whether there are any practical optimum detectors for such input codewords. The second problem is about finding tight bounds for the sum channel capacity. In response to the first problem, the authors have constructed uniquely detectable matrices for the generalised scheme and the authors have developed practical maximum likelihood detection algorithms for such codes. In response to the second problem, lower bounds and conjectured upper bounds are derived. The results of this study are superior to other standard overloaded CDMA codes since the generalisation can support more users than the previous schemes.