Error Exponents of Typical Random Trellis Codes

Abstract

In continuation to an earlier work, where error exponents of typical random codes were studied in the context of general block coding, with no underlying structure, here we carry out a parallel study on typical random, time–varying trellis codes, focusing on a certain range of low rates. By analyzing an upper bound to the error probability of the typical random trellis code, using the method of types, we first derive a Csiszar–style error exponent formula (with respect to the constraint length), which allows to characterize properties of good codes and dominant error events. We also derive a Gallager–style form, which turns out to be related to the expurgated error exponent. The main result is further extended to channels with memory and mismatch.