On the Timeliness of Arithmetic Coding

Timeliness of information transfer is critical in real-time applications. Prioritizing timeliness, however, often comes at the cost of rate inefficiency, especially in block coding. In this work, motivated by the sequential nature of encoding and decoding in arithmetic source coding, the timeliness of arithmetic coding is investigated. For a generate-at-will source model, an upper bound is provided on the average peak age of information (PAoI). This upper bound builds on the arithmetic coding scheme of Shayevitz et al. (2007) which has a finite look-ahead parameter
$d$
. It captures interesting trade-offs between PAoI, compression rate, and the look-ahead parameter
$d$
. For periodic sources, rate efficiency is argued to be less critical than the look-ahead parameter
$d$
in minimizing the peak age, especially when the traffic load is moderate and small. Through simulations, two observations are made: (i) the optimal look-ahead parameter
$d$
is an increasing function of the traffic load, and (ii) asymptotically, as the traffic load gets close to its limit 1, the classical arithmetic coding (without a finite bound on
$d$
) performs better than the state-of-the-art age-optimal block codes.