On symbol-by-symbol MAP decoding of linear UEP codes

We present a method to evaluate post-decoding bit error probabilities for individual bit positions in a linear unequal error protection (LUEP) code with symbol-by-symbol MAP decoding. A matrix description of the LUEP code trellis is used to formulate the MAP decoding problem analytically in original domain. This can be illustrated by a weighted trellis with joint probabilities being the weights of the trellis. By way of a similarity transformation, the decoding problem is mapped into a spectral domain having a much simpler computational structure. Because the considered LUEP codes are simple to implement, the method may be used in applications where the decoding delay needs to be kept at a minimum