Blind deconvolution of multi-input single-output systems with binary sources

We present two novel methods for the blind extraction of multiple binary signals from a single observation generated from linear convolution and superposition. Both methods are based on two features: (a) the constellation structure of the successor set for each output value; (b) the concept of system deflation, i.e. the recursive shortening of the channel until it is reduced to an instantaneous mixture. The two methods differ in complexity as the latter requires significantly smaller amounts of data. Both methods are fast for small problem sizes but their complexities increase exponentially as the number of inputs and/or channel length increases. We present the complete analytical solution to the noiseless case and we thoroughly treat the related mathematical tools and concepts. The noisy case is discussed briefly, as the complete treatment would exceed the scope of the paper.