MMSE and ML estimation of chaotic sequences with coded signs with applications in coding discrete-time analog signals

We consider estimation of a set of tent-map chaotic sequences. These sequences are obtained by iterating a one dimensional chaotic function in the (-1,1) domain. We demonstrate how to construct a set of n sequences, in which information in the form of n arbitrary samples in the (-1,1) domain is embedded. Additionally the signs of all sequences jointly form a valid digital codeword. Each sequence in the set consists of m elements, hence the set of sequences is equivalent to a rate \lm analog error correcting-code. We present performance in terms of coding gain when maximum likelihood (ML) and minimum-mean-square-error (MMSE) estimation approaches are employed.