An Importance Aware Weighted Coding Theorem Using Message Importance Measure

TL;DR

This paper introduces an importance-aware coding theorem that incorporates message importance measures into source coding, extending traditional coding bounds by considering user-defined importance weights for symbols.

Contribution

It proposes a new importance-aware measure for source coding that generalizes traditional theorems by integrating importance weights into code length calculations.

Findings

Derived bounds for importance-aware coding measures

Extended traditional coding theorems to include importance weights

Demonstrated the applicability of the measure in scenarios with user priorities

Abstract

There are numerous scenarios in source coding where not only the code length but the importance of each value should also be taken into account. Different from the traditional coding theorems, by adding the importance weights for the length of the codes, we define the average cost of the weighted codeword length as an importance-aware measure of the codes. This novel information theoretical measure generalizes the average codeword length by assigning importance weights for each symbol according to users' concerns through focusing on user's selections. With such definitions, coding theorems of the bounds are derived and the outcomes are shown to be extensions of traditional coding theorems.