Finite Blocklength Regime

Below you can find a few MATLAB routines for establishing coding bounds in the finite blocklength regime. The methods build upon the O(n^-k) approximations from:

[1] T. Erseghe, “On the Evaluation of the Polyanskiy-Poor-Verdu Converse Bound for Finite Block-Length Coding in AWGN”, IEEE Transactions on Information Theory, Vol. 61, No. 12, pp. 6578-6590, December 2015, available from

[2] T. Erseghe, “Coding in the Finite-Blocklength Regime: Bounds based on Laplace Integrals and their Asymptotic Approximations”,

Please give credits to these papers if you use the code available below for your research.


Version 1.0

The code is available here for download: fbr_dgt_v1.

The code generates the figures of [2].

The code needs MATLAB R2011b. More recent MATLAB versions require some modifications, especially in the settings of the ‘fmincon’ optimizer.

The code is optimized for the specific aim of obtaining the figures of [2], and may not work under different settings. I am working towards an enhanced version of the software, and hope to be posting it soon.

Please find additional MATLAB software for identifying coding bounds in the finite blocklength regime in the SPECTRE: Short packet communication toolbox available at


Version 2.0 ???

Hopefully available soon! ;-)