Low-Complexity Decoder for Overloaded Uniquely Decodable Synchronous CDMA

We consider the problem of designing a low-complexity decoder for antipodal uniquely decodable (UD) /errorless code sets for overloaded synchronous code-division multiple access (CDMA) systems, where the number of signals Kamax is the largest known for the given code length L. In our complexity analysis, we illustrate that compared to maximum-likelihood (ML) decoder, which has an exponential computational complexity for even moderate code lengths, the proposed decoder has a quasi-quadratic computational complexity. Simulation results in terms of bit-error-rate (BER) demonstrate that the performance of the proposed decoder has only a 1-2 dB degradation in signal-to-noise ratio (SNR) at a BER of 10^-3 when compared to ML. Moreover, we derive the proof of the minimum Manhattan distance of such UD codes and we provide the proofs for the propositions; these proofs constitute the foundation of the formal proof for the maximum number users Kamax for L=8 .