A (3; 1) error-correcting code consists of the two code words x(1) = (1; 0; 0) and x(2) = (0; 0;

A (3; 1) error-correcting code consists of the two code words x(1) = (1; 0; 0) and x(2) = (0; 0; 1). A source bit s 2 f1; 2g having probability distribution fp1; p2g is used to select one of the two code words fortransmission over a binary symmetric channel with noise level f. The received vector is r. Show that the posterior probability of s given r cane written in the form

and give expressions for the coefficients  and the bias, w0.Describe, with a diagram, how this optimal decoder can be expressed inters of a `neuron”.