Fast Code Design for Overloaded Code-Division Multiplexing Systems

We consider the problem of designing binary antipodal code sequences (signatures) for overloaded code-division multiplexing (CDM) systems where the number of concurrent users/signals is greater than the code length. Our goal is to provide an overloaded code that can be constructed and decoded quickly and, more importantly, provide satisfactory recovery performance in conjunction with decoder design specifics. We first introduce a fast and practical method for constructing a code set by operating the Kronecker product with two smaller codes. Under such construction, a fast two-stage maximum-likelihood (ML) detection scheme can dramatically reduce the computational complexity of the ML decoder and make CDM systems practically implementable. To improve the performance in terms of bit error rate, we propose hierarchical criteria for code design, which aims at reducing the cross-correlation of code while maintaining a uniquely decodable (errorless) code property. Simulation studies illustrate that the proposed code design can provide satisfactory performance with low-complexity two-stage ML detection.