Identify the bounded third-order remainder gap for the GMS–BLEC pair

Identify the bounded additive remainder separating the achievability and converse information-balance conditions for joint source-channel coding of a Gaussian memoryless source over a block erasure channel, after the common frac12\log k third-order term has been matched.

Background

The paper proves that the achievability and converse conditions for the Gaussian memoryless source over a nonstationary block erasure channel agree through the first-, second-, and logarithmic third-order terms. Their remaining discrepancy is confined to bounded additive constants in the information-balance conditions. The exact value or behavior of this bounded remainder is not determined by the stated results, leaving open whether the achievability and converse constants can be sharpened or matched.