A union bound based evaluation technique for convolutionally and turbo coded communication systems

This paper explores the design of union bound based evaluation techniques to evaluate the MAP decoding error probability when the coded data are corrupted by additive white Gaussian noise (AWGN). Since linearity of the codes and uniformity of the source distribution are not assumed for the binary codes that are studied in this paper, new matrix based evaluation techniques are designed to overcome the high computing complexity to calculate the union bounds for selected codes. The proposed techniques can be applied to many coding schemes with trellis structures, such as convolutional codes, parallel turbo codes and convolutionally coded multiple-access channel (MAC) systems. Applications of the designed techniques to those types of codes are presented and it can be observed that the non-uniformity of the source has a clear effect on the tightness of the bounds calculated.