A new set of codes with swift decoding for overloaded synchronous CDMA

We consider the designing of a new set of uniquely decodable codes for uncoded synchronous overloaded CDMA system that exists for arbitrary values of spreading gain (code length). A fast and recursive method of construction is proposed where the orthogonal Hadamard matrix of least dimension (two), as the basis of construction regularizes a ternary pattern which is further leveraged to attain a rich simplicity in decoder design. The simplicity gained in designing of the proposed Comparison Aided Decoder (CAD) is prominent enough to neglect the marginal sacrifice in Bit Error Rate (BER) as compared to the optimum Maximum Likelihood Decoder (MLD) for noisy transmission. Despite its low complex nature, the detection retains it uniquely decodable (errorless) attribute in the absence of noise. Moreover, for large dimension of the proposed matrices, the loading capacity of the system as compared to the conventional CDMA gets a two fold enhancement.