Determine the optimal third-order terms for BMS–BSC and GMS–AWGN joint source-channel coding

Determine the optimal third-order terms for joint source-channel coding of binary memoryless sources over binary symmetric channels and Gaussian memoryless sources over additive white Gaussian noise channels, beyond the bounds currently available for those source-channel pairs.

Background

The paper establishes third-order optimality of the \1/2\log k term for the Gaussian memoryless source over a block erasure channel. It contrasts this result with previously known BMS–BSC and GMS–AWGN bounds, whose achievability and converse corrections do not coincide sufficiently to determine the optimal third-order coefficient. Consequently, the optimal third-order behavior for those two source-channel pairs remains unresolved.

References

However, this does not show that the BLEC intrinsically has a smaller optimal third-order term than the BSC or the AWGN channel. While Theorems~\ref{asymp_thm_achievability} and~\ref{thm_semiasympconverse} establish the third-order optimality of the \frac12\log k term for the GMS--BLEC pair, the bounds established for the BMS--BSC and GMS--AWGN pairs in do not identify their optimal third-order terms.

— Joint Source-Channel Coding of Gaussian Sources over Block Erasure Channels: Nonasymptotic Bounds and Channel-Uniform Normal Approximations  (2609.38725 - Mahmood, 30 Sep 2026) in Discussion of Theorem \ref{thm_semiasympconverse}, Section 'Converse Results'