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
$K_{\mathrm{max}}^{a}$
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
$K_{\mathrm{max}}^{a}$
for
$L=8$
.