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 for general discrete memoryless channels, 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 easily identify and characterize properties of good codes and dominant error events. We also derive a Gallager-style form of this error exponent, which turns out to be related to the expurgated error exponent. The main result is further extended to channels with memory and mismatch.