Bit-wise Unequal Error Protection for Variable Length Block Codes with Feedback

TL;DR

This paper develops bounds for bit-wise unequal error protection in variable length block codes with feedback, providing a complete characterization of achievable rate-exponent regions.

Contribution

It introduces a novel encoding scheme and bounding technique that precisely characterizes the performance limits for unequal error protection with feedback.

Findings

Inner and outer bounds match asymptotically

Complete characterization of rate-exponent regions

Solution to message-wise unequal error protection problem

Abstract

The bit-wise unequal error protection problem, for the case when the number of groups of bits $\ell$ is fixed, is considered for variable length block codes with feedback. An encoding scheme based on fixed length block codes with erasures is used to establish inner bounds to the achievable performance for finite expected decoding time. A new technique for bounding the performance of variable length block codes is used to establish outer bounds to the performance for a given expected decoding time. The inner and the outer bounds match one another asymptotically and characterize the achievable region of rate-exponent vectors, completely. The single message message-wise unequal error protection problem for variable length block codes with feedback is also solved as a necessary step on the way.