Performance bounds for high rate linear codes over partial-response channels

We develop union bounds for high-rate linear codes used for partial-response equalized channels with additive white Gaussian noise. The bounds assume uniform interleaving and are based on an approximation which is valid for high-rate linear codes. Furthermore, the derivation of the bounds assumes that maximum-likelihood decoding is employed. One particular application of the present setting is the computation of bounds for magnetic recording systems using turbo codes. The results can be considered as a generalization of the results of M. Oberg and P.H. Siegel (see Proc. Allerton Conf. Communications, Control and Computing, Sept. 1998) which develops the union bound for the dicode channel; however, our approach is completely different. We present several examples of the bounds developed together with the simulation results.