Some Extensions of Gallager's Method to General Sources and Channels

The Gallager bound is well known in the area of channel coding. However, most discussions about it mainly focus on its applications to memoryless channels. We show in this paper that the bounds obtained by Gallager's method are very tight even for general sources and channels that are defined in the information-spectrum theory. Our method is mainly based on the estimations of error exponents in those bounds, and by these estimations we proved the direct part of the Slepian-Wolf theorem and channel coding theorem for general sources and channels.