Trade-offs Between Error Exponents and Excess-Rate Exponents of Typical Slepian-Wolf Codes

TL;DR

This paper investigates the error and excess-rate exponents of typical semi-deterministic Slepian-Wolf codes, revealing their trade-offs, optimal decoding strategies, and exponential decay of error probabilities for correlated sources.

Contribution

It introduces a semi-deterministic code ensemble, derives error exponents, and characterizes the trade-offs and optimal rate functions for these codes.

Findings

Error exponents of the semi-deterministic codes match the random binning error exponents in key cases.

Universal decoders like the stochastic likelihood decoder achieve optimal performance.

Both error and excess-rate probabilities decay exponentially with blocklength for correlated sources.

Abstract

Typical random codes (TRC) in a communication scenario of source coding with side information at the decoder is the main subject of this work. We study the semi-deterministic code ensemble, which is a certain variant of the ordinary random binning code ensemble. In this code ensemble, the relatively small type classes of the source are deterministically partitioned into the available bins in a one-to-one manner. As a consequence, the error probability decreases dramatically. The random binning error exponent and the error exponent of the TRC are derived and proved to be equal to one another in a few important special cases. We show that the performance under optimal decoding can be attained also by certain universal decoders, e.g., the stochastic likelihood decoder with an empirical entropy metric. Moreover, we discuss the trade-offs between the error exponent and the excess-rate exponent for the typical random semi-deterministic code and characterize its optimal rate function. We show that for any pair of correlated information sources, both error and excess-rate probabilities are exponentially vanishing when the blocklength tends to infinity.