Jekyll2022-12-01T16:51:03+01:00https://gdurisi.github.io/feed.xmlGiuseppe DurisiProfessional website of Giuseppe DurisiGiuseppe DurisiTwo papers at NeurIPS 20222022-12-01T00:00:00+01:002022-12-01T00:00:00+01:00https://gdurisi.github.io/news-post/2022/12/01/neurips<p>We have just presented the following two papers at this year NeurIPS conference</p>
<ul>
<li>
<p>F. Hellström and G. Durisi, “A new family of generalization bounds using sample-wise evaluated CMI,” in Conf. Neural Information Processing Systems (NeurIPS), New Orleans, LA, U.S.A., Nov. 2022. <a href="https://arxiv.org/abs/2210.06422">arXiv</a></p>
</li>
<li>
<p>F. Hellström and G. Durisi, “Evaluated CMI bounds for meta learning: Tightness and expressiveness,” in Conf. Neural Information Processing Systems (NeurIPS), New Orleans, LA, U.S.A., Nov. 2022. <a href="https://arxiv.org/abs/2210.06511">arXiv</a></p>
</li>
</ul>
<p>Here is a short summary of the two papers:</p>
<p>The first paper deals with <strong>generalization bounds</strong>, i.e., theoretical guarantees on the test-time performance of machine learning algorithms, which, hopefully, provide insights on algorithm design.
We focus in the paper on <strong>information-theoretic</strong> bounds, which—differently from classic minimax bounds in statistical learning theory—have recently shown to be nonvacuous when applied to modern machine-learning algorithms such as deep neural networks.
The reason is that these bounds are typically both data and algorithm dependent.
In the paper, we present novel information-theoretic bounds in terms of the so called <strong>samplewise evaluated conditional mutual information</strong> (eCMI).
Through both theoretical investigations and numerical evaluations, we show that the proposed bounds are <strong>tighter</strong> than previously proposed bounds for the case of low training loss, and accurately approximate the empirically evaluated test error for a variety of settings, including the case of randomized labels.</p>
<p>In the second paper, we extend the bounds proposed in the first paper to the <strong>metalearning</strong> setup, where the objective is to improve the learning performance on a new machine-learning task by using the knowledge acquired from separate but related tasks.
For the case of standard learning, it has been shown that information-theoretic bounds based on the eCMI are <strong>expressive</strong> enough to allow one to recover from them classic minimax bounds in statistical learning theory.
In this paper, we obtain <strong>novel information theoretic generalization bounds</strong> based on the eCMI that are tighter than previously proposed bounds, and exhibit the convergence rate of the available minimax generalization bounds for metalearning. This allows us to establish a connection between information-theoretic results and results from classical learning theory for metalearning—two areas that have evolved separately thus far.
We also apply the proposed bounds to a representation learning setting, and—also for this case—derive information-theoretic bounds on the excess risk that recover the convergence rate of recently proposed minimax bounds.</p>Giuseppe DurisiTwo papers from our team at NeurIPS 2022 on information-theoretic generalization boundsSSF project approved2022-09-16T00:00:00+02:002022-09-16T00:00:00+02:00https://gdurisi.github.io/news-post/2022/09/16/saicom<p>The <a href="http://vr.se">Swedish Foundation for strategic research</a> has approved our project entitled <a href="https://strategiska.se/forskning/pagaende-forskning/ssf-future-software-systems-fuss-2021/projekt/11632/">SAICOM: Software artificial intelligence for communication</a>.
This 35MSEK project is lead by Prof. <a href="https://people.kth.se/~carlofi/">Carlo Fischione</a> at KTH, and involves <a href="https://framtidensforskning.se/2022/06/17/bryter-ny-vetenskaplig-mark-for-framtidens-smarta-samhalle/">senior researchers</a> at KTH, Chalmers, and Gothenburg University.</p>
<p>The objective of this project is to develop machine learning algorithms for 6G networks,
with specific focus on access protocols at the low layers, and services at the application layers that are
particularly sensitive to low-layer performance.
The project will be concerned with the design of machine-learning algorithms</p>
<ol>
<li>that are able to run efficiently over open radio access networks (O-RAN), and/or</li>
<li>that can be use to operate and manage O-RAN.</li>
</ol>
<p>Within this project, a number of PhD and post-doctoral students will be recruited at the three universities.
We currently have <a href="/vacancies">two PhD-student vacancies</a> in our group.
The two students will be jointly supervised by Ass. Professor <a href="https://www.chalmers.se/en/staff/Pages/christian-hager.aspx">Christian Häger</a>, and by Prof. Giuseppe Durisi.</p>Giuseppe DurisiThe Swedish Foundation for Strategic Research has granted a new project to our groupInformation-theoretic generalization bounds for learning and metalearning2022-06-13T00:00:00+02:002022-06-13T00:00:00+02:00https://gdurisi.github.io/news-post/2022/06/13/wasp<p>Our funding application “evaluated mutual information bounds for learning and metalearning”, which was
submitted to the
Wallenberg AI Autonomous Systems and Software program
(<a href="https://wasp-sweden.org">WASP</a>) call for
<a href="https://wasp-sweden.org/calls/wasp-industrial-phd-student-positions-2022/">academic PhD student projects</a>, has
been approved.</p>
<p>This project will be performed in collaboration with Prof. <a href="http://www.math.chalmers.se/~jornsten/">Rebecka
Jörnsten</a>, Division of Applied Mathematics and Statistics, Department
of Mathematical Sciences, Chalmers.</p>
<p>Within this project, we have just announced a <a href="https://www.chalmers.se/en/about-chalmers/Working-at-Chalmers/Vacancies/Pages/default.aspx?rmpage=job&rmjob=10639&rmlang=UK">PhD student vacancy</a>.</p>
<figure style="width: 680px" class="align-center">
<a href="/files/2022/it_gen.png" title="Evaluated mutual information bounds in a nutshell">
<img src="/files/2022/it_gen.png" /></a>
<figcaption>
The selection vector $S^n$ identifies $n$ entries of the sample matrix $Z^{2n}$ (the entries marked in red)
that are then used for training and result in the DNN weights $W$, drawn from the posterior distribution
$P_{W | Z^n(S^n)}$. Some of the tightest bounds available for this setup depend on the mutual information
$I(W;S_i | Z^{2n})$, $i=1,\dots, n$. The bounds to be obtained within this research program will depend
instead on the mutual information $I(\ell(W,Z_i), \ell(W,Z_{n+i}); S_i | Z^{2n})$, $i=1,\dots, n$. Here,
$\ell(W,Z_i)$ and $\ell(W,Z_{n+i})$ denote the loss function computed for a DNN with weights $W$ when given as
input the data samples $Z_i$, and $Z_{n+i}$, respectively.
</figcaption>
</figure>
<h2 id="project-description">Project description</h2>
<p>Deep neural networks (DNNs) are a crucial component of the data-scientist toolbox. Indeed, over the last
decade, the number of research fields in which deep learning algorithms have become part of state-of-the-art
solutions has increased significantly, encompassing areas as diverse as computer vision, speech recognition,
and natural language processing.</p>
<p>The empirical success of DNNs is, however, a puzzle to theoreticians. Despite many recent efforts, a theory
that explains satisfactorily why DNNs perform so well and that guides their design is still missing. As the
use of DNNs moves from academic-driven research, conducted on simple prototypes, to large-scale
safety-critical industrial applications such as autonomous driving, this state of affairs is becoming
increasingly unsatisfactory. DNNs can no longer be used as black boxes, and their design cannot be simply
based on empirical studies. There is an urgent need to develop theoretical tools that provide guarantees on
the performance of DNNs and inform their design.</p>
<h3 id="the-challenge">The challenge</h3>
<p>Information-theoretic generalization bounds, i.e., bounds on the generalization error of DNNs that depend on
information-theoretic metrics, such as mutual information and relative entropy, have recently emerged as a
promising tool to shed lights on the DNN-performance mystery. Indeed, differently from generalization bounds
that are in terms of classical statistical learning complexity measures such as VC dimension and
Rademacher/Gaussian complexities, information-theoretic bounds, when suitably optimized, have been shown to
yield accurate performance predictions for some DNNs scenarios of practical interest.</p>
<h3 id="the-goals-of-this-project">The goals of this project</h3>
<p>The goal of this project is to significantly advance the state of the art in this field by
deriving novel information-theoretic generalization bounds that depend on the so-called evaluated conditional
mutual information (eCMI). Given two data samples, this quantity
describes our ability to guess which one of the two has been used to train the DNN, after we observe the value
of the loss function computed at these two data samples.
We believe that the eCMI is
uniquely suited to shed lights on the theoretical performance of DNNs, since it does not suffer from the
disadvantages of the information-theoretic metrics used so far in this context. The specific objectives of the
project are:</p>
<ol>
<li>
<p>To determine the <em>expressiveness</em> of information-theoretic bounds that are explicit in the eCMI.</p>
</li>
<li>
<p>To demonstrate via comprehensive numerical experiments that bounds based on eCMI describe accurately the generalization performance of DNNs.</p>
</li>
<li>
<p>To explore the use of eCMI bounds in the context of metalearning, where the objective is to facilitate
learning of a new task by exploiting training data pertaining to related tasks.</p>
</li>
</ol>
<h3 id="relevant-literature">Relevant literature</h3>
<ul>
<li>
<p>T. Steinke and L. Zakynthinou, “Reasoning about generalization via conditional mutual information,” in Conf.
Learning Theory (COLT), Jul. 2020. <a href="https://arxiv.org/abs/2001.09122">[.pdf]</a></p>
</li>
<li>
<p>H. Harutyunyan, M. Raginsky, G. V. Steeg, and A. Galstyan, “Information-theoretic generalization bounds for
black-box learning algorithms,” in Conf. Neural Information Processing Systems (NeurIPS), Dec. 2021.
<a href="http://arxiv.org/abs/2110.01584">[.pdf]</a></p>
</li>
<li>
<p>M. Haghifam, G. K. Dziugaite, S. Moran, and D. M. Roy, “Towards a unified information-theoretic framework
for generalization,” in Conf. Neural Information Processing Systems (NeurIPS), Dec. 2021.
<a href="https://arxiv.org/abs/2111.05275">[.pdf]</a></p>
</li>
<li>
<p>F. Hellström and G. Durisi, “Nonvacuous loss bounds with fast rates for neural networks via conditional
information measures,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Sidney, Australia, Jul. 2021.
<a href="https://arxiv.org/abs/2010.11552">[.pdf]</a></p>
</li>
<li>
<p>A. Rezazadeh, S. T. Jose, G. Durisi, and O. Simeone, “Conditional Mutual Information Bound for Meta
Generalization Gap,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Sidney, Australia, Jul. 2021.
<a href="http://arxiv.org/abs/2010.10886">[.pdf]</a></p>
</li>
</ul>Giuseppe DurisiOur funding proposal on information-theoretic generalization bounds for learning and metalearning has been approved4 papers at Asilomar 20212021-12-09T00:00:00+01:002021-12-09T00:00:00+01:00https://gdurisi.github.io/news-post/2021/12/09/asilomar<p>Members of our team have been involved in the following four papers, which have been presented at this year’s <a href="https://www.asilomarsscconf.org">Asilomar conference on Signals, Systems, and Computers</a>.</p>
<ol>
<li>
G. Marti, O. Castañeda, S. Jacobsson, G. Durisi, T. Goldstein, and C. Studer, “Hybrid jammer mitigation for all-digital
mmWave massive MU-MIMO,” in Proc. Asilomar Conf. Signals, Syst., Comput., Pacific Grove, CA, U.S.A., Nov. 2021.
<a href="http://arxiv.org/abs/2111.13055">[.pdf]</a>
</li>
<hr />
<li>
A. Munari, F. Lázaro, G. Durisi, and G. Liva, “An age of information characterization of frameless ALOHA,” in Proc.
Asilomar Conf. Signals, Syst., Comput., Pacific Grove, CA, U.S.A., Nov. 2021. <a href="http://arxiv.org/abs/2112.00491">[.pdf]</a>
</li>
<hr />
<li>
K.-H. Ngo, G. Durisi, and A. Graell i Amat, “Age of information in prioritized random access,” in Proc. Asilomar Conf.
Signals, Syst., Comput., Pacific Grove, CA, U.S.A., Nov. 2021. <a href="http://arxiv.org/abs/2112.01182">[.pdf]</a>
</li>
<hr />
<li>
I. Atzeni, A. Tölli, and G. Durisi, “Low-resolution massive MIMO under hardware power consumption constraints,” in Proc.
Asilomar Conf. Signals, Syst., Comput., Pacific Grove CA, U.S.A., Nov. 2021. <a href="http://arxiv.org/abs/2112.02021">[.pdf]</a>
</li>
</ol>Giuseppe Durisi4 papers at this year's Asilomar conference from our teampaper at Globecom 20212021-12-09T00:00:00+01:002021-12-09T00:00:00+01:00https://gdurisi.github.io/news-post/2021/12/09/globecom<p>This week, we will present the following paper at the 2021 <a href="https://globecom2021.ieee-globecom.org">IEEE Global
Communications Conference (GLOBECOM)</a>:</p>
<ul>
<li>
A. Lancho, J. Östman, and G. Durisi, “On joint detection and decoding in short-packet transmission,” in Proc. IEEE Global Telecommun. Conf. (GLOBECOM), Madrid, Spain, Dec. 2021. <a href="https://arxiv.org/abs/2109.13669">[.pdf]</a>
</li>
</ul>
<p>We have by now accurate and easy to compute bounds on the maximum coding rate, or, equivalently,
the minimum error probability achievable in the short-packet regime, where each codeword spans
a limited number of degrees of freedom. In this paper, we present general nonasymptotic bounds on
these performance metrics for the scenario in which the receiver must first detect the presence of
an information packet, and, if detected, decode the message carried within it. The bounds apply to
both the setup in which detection is performed jointly with decoding on the entire data packet,
or separately on a dedicated preamble.</p>
<p>Numerical results for the binary-input AWGN channel reveal that packet
detection, even when performed jointly with decoding, is the performance
bottleneck when the packets are very short and the SNR is low. Performing
detection solely on a dedicated preamble is highly suboptimal, even when the
length of the preamble is optimized.</p>
<p>As an example, in the figure below, we present the maximum coding rate
achievable on the binary-input AWGN channel, as a function of the number of
degrees of freedom (discrete channel uses) occupied by a codeword, for the case
in which the SNR is 3 dB, the misdetection and false alarm probabilities are
set to $10^{-4}$, and the inclusive error (i.e., the probability that the
receiver does not decode correctly a transmitted codeword) is $10^{-3}$. We
consider the three cases of genie-aided detection, joint detection and
decoding, and preamble-based detection followed by decoding. As shown in the
figure, packet detection is indeed the bottleneck when the number of channel
uses is small. Furthermore, joint detection and decoding outperforms
significantly preamble-based detection. How to approach the joint detection and
decoding bound by means of low-complexity coding schemes is an interesting
<strong>open problem</strong>. <img src="/files/2021/2021-globecom.png" alt="" /></p>Giuseppe DurisiJoint detection and decoding for short-packet transmissionVR project approved2021-11-08T00:00:00+01:002021-11-08T00:00:00+01:00https://gdurisi.github.io/news-post/2021/11/08/vr<p>The <a href="http://vr.se">Swedish Research Council</a> has approved our project entitled <em>energy-efficient massive random access
for real time distributed autonomous systems</em>.
This 4MSEK project, which will run from 2022 to 2025 has the following premise:
To support the Internet-of-Things (IoT) vision of enabling distributed autonomous systems able to
operate in real time, we need a new wireless infrastructure, providing connectivity to a massive
number of sporadically active and energy-limited devices, which access the wireless medium in an
uncoordinated fashion. Indeed, current wireless systems are provably unable to provide low-latency,
energy-efficient communications in the presence of massive uncoordinated interference.</p>
<p>The purposed of this project is to obtain an information-theoretic characterization of the maximum
energy efficiency at which quality-of-service targets that are relevant for real-time decision making
can be achieved. Guided by the insights provided by this characterization, we will then design novel, low-complexity,
massive random-access protocols, able to operate close to the predicted theoretical limits.
The project involves the following novel elements: we will</p>
<ol>
<li>explicitly account, via the use of nonasymptotic tools from information theory, for the small payload size of IoT packets;</li>
<li>address <a href="https://github.com/gdurisi/asilomar-challenge">practically relevant</a> IoT scenarios, in which the devices have heterogeneous requirements
in terms energy efficiency and quality of service;</li>
<li>consider new metrics beyond packet error probability, which take into account the value of the information carried by each packet;</li>
<li>use techniques from machine learning, to disentangle packet collisions by exploiting commonly-observed traffic patterns.</li>
</ol>
<p>This project will be conducted together with my colleague at Chalmers, Prof. <a href="https://sites.google.com/site/agraellamat/">Alexandre Graell i Amat</a>, and my long-term collaborator at the
German Aerospace Center, <a href="https://www.wirelesscoding.org">Dr. Gianluigi Liva</a>.</p>Giuseppe DurisiThe Swedish Research Council has approved a new research project in our groupPlenary talk at ITW 20212021-10-23T00:00:00+02:002021-10-23T00:00:00+02:00https://gdurisi.github.io/news-post/2021/10/23/itw-plenary<p>It was a great pleasure to give a plenary talk at this year <a href="https://www.itw2021.org">Information Theory Workshop (ITW)</a>.
My talk was entitled “Short packets over wireless fading networks”.
The slides can be downloaded <a href="https://chalmersuniversity.box.com/s/rfqz5w5w4g93icjfh67mcwwlb107t6oi">here</a>.
A video recording is available on the ITW website for registered users and has also been made available to everyone on the Information Theory Society <a href="https://www.itsoc.org/video/plenary-short-packets-over-wireless-fading-networks">website</a>.</p>
<p>The theme of the talk was to show how to use finite-blocklength information-theoretic tools to optimally design wireless fading networks supporting the transmission of short packets.</p>
<p>What do I mean by short packets? In a nutshell, I refer to “short packets” as wireless traffic where one wants to deliver around hundreds of bits within around hundreds of degrees of freedom per user.
This regime turns out to be relevant for both ultra-reliable low-latency communications (URLLC) and massive machine-type communications (mMTC).</p>
<p>More specifically, I asked in the talk the following question.
Assume that we want to design a resource allocation algorithm, or maybe a user scheduling algorithm, for a wireless system that needs to support short packets.
Which information-theoretic formula shall we use to model the physical layer? Or more specifically,
what should we replace the typically used asymptotic $\mathbb{E}[\log(1+\text{sinr})]$ ergodic-capacity lower bound with?</p>
<p>In the talk, I provide an answer to this question: it involves the use of an achievability bound in finite-blocklength information theory called the <em>random coding union bound with parameter $s$</em>, the use of <em>pilot-assisted transmission</em> and <em>nearest-neighbor mismatch decoding</em>, and of the <em>saddlepoint method</em> in statistics to evaluate the resulting bound in a computational effective way.</p>
<p>I also clarify why the so called <em>normal approximation</em> should probably not been used when designing URLLC systems, and in particular why taking ergodic SINR expression and inserting them into AWGN-based normal approximation formulas does not lead to information-theoretic rigorous expressions.</p>
<p>Finally, I provide study cases relevant for $5G$ and beyond, which illustrate that the proposed approach can be applied to real-world wireless communication networks involving base stations with large-antenna arrays, realistic propagation models, multiuser interference, and imperfect acquisition of channel state information.</p>Giuseppe DurisiPlenary talk at the 2021 Information Theory Workshop3 papers at ISIT 20212021-07-16T00:00:00+02:002021-07-16T00:00:00+02:00https://gdurisi.github.io/news-post/2021/07/16/isit<p>Our group will present the following three papers at this year’s IEEE International Symposium on Information Theory (<a href="https://2021.ieee-isit.org">ISIT</a>).</p>
<ol>
<li> K.-H. Ngo, A. Lancho, G. Durisi, and A. Graell i Amat, "Massive uncoordinated access with random user activity," in <em>Proc. IEEE Int. Symp. Inf. Theory (ISIT)</em>, Sidney, Australia, Jul. 2021. <a href="https://arxiv.org/abs/2103.09721">[.pdf]</a>
</li>
<hr />
<li>
A. Rezazadeh, S. T. Jose, G. Durisi, and O. Simeone, Conditional Mutual Information Bound for Meta Generalization Gap, in <em>Proc. IEEE Int. Symp. Inf. Theory (ISIT)</em>, Sidney, Australia, Jul. 2021. <a href="https://arxiv.org/abs/2010.10886">[.pdf]</a>
</li>
<hr />
<li>
F. Hellström and G. Durisi, “Nonvacuous loss bounds with fast rates for neural networks via conditional information measures,” in <em>Proc. IEEE Int. Symp. Inf. Theory (ISIT)</em>, Sidney, Australia, Jul. 2021. <a href="https://arxiv.org/abs/2010.11552">[.pdf]</a>
</li>
</ol>Giuseppe DurisiMembers of our group will present three papers at this year IEEE International Symposium on Information TheoryTwo Marie Skłodowska-Curie fellowships in our team2021-04-16T00:00:00+02:002021-04-16T00:00:00+02:00https://gdurisi.github.io/news-post/2021/04/16/mc<p><a href="https://www.chalmers.se/en/staff/Pages/Alejandro-Lancho-Serrano.aspx">Dr. Alejandro Lancho</a> and <a href="https://www.chalmers.se/en/Staff/Pages/ngok.aspx">Dr. Khac-Hoang Ngo</a>, both post-doctoral researchers in our team, have been recently awarded a <a href="https://ec.europa.eu/research/mariecurieactions/node_en">Marie Skłodowska-Curie individual fellowship</a> from the European Union.
Congratulations, Alex and Hoang!</p>
<p>Below, you can read two short interviews about their projects.
The interviews were conducted by our communication officer at the Department of Electrical Engineering (Chalmers), Sandra Tavakoli.</p>
<h2 id="dr-alejandro-lancho-serrano-project-mascot">Dr. Alejandro Lancho Serrano, project MASCOT</h2>
<p>Alejandro Lancho Serrano has been rewarded a global fellowship and will work two years at the Massachusetts Institute of Technology in the US followed by one yeat at his alma mater, the Universidad Carlos III of Madrid, Spain.</p>
<blockquote>
<p>It feels like a big reward and at the same time a big responsibility. It’s a great opportunity for me as a young researcher to boost my career and reach my future goals. Also, having the opportunity to lead my own project feels very exciting. During the grant, I will explore, from an information-theoretical perspective, the fundamental limits of one of the main types of wireless communications that will dominate in the near future: the asynchronous massive connection to the network of battery-limited devices.</p>
</blockquote>
<p>Right now, Alejandro’s research is focused on finite-blocklength information theory applied to a wide range of problems related to wireless communications, such as ultra-reliable low-latency communications, Massive MIMO, the massive connectivity problem, security, and privacy.</p>
<h2 id="dr-khac-hoang-ngo-project-lantern">Dr. Khac-Hoang Ngo, project LANTERN</h2>
<p>Thanks to being rewarded a European fellowship, Khac-Hoang Ngo can meet his career goal.</p>
<blockquote>
<p>It is a fantastic feeling. This provides me the opportunity to develop my profile in order to meet the requirements to obtain a faculty position. I finished my Ph.D. last year and am now taking further steps in pursuing an academic career. The fellowship comes at a crucial moment when I am eager to broaden my expertise, gain experience and develop my skills.</p>
</blockquote>
<p>Hoang will spend the funding on his two-year research project LANTERN: Low-latency and private edge computing in random-access networks, which will be performed at Chalmers.</p>
<blockquote>
<p>In this project, we will investigate how low-latency and private edge computing protocols can be developed in wireless random-access networks. The results of this project will help pave the way to the full realisation of the Internet of Things (IoT) in the near future. With this funding, we will conduct research activities in these directions as well as communicate the research results to different target audiences.</p>
</blockquote>Giuseppe DurisiTwo postdoctoral researchers in our team received prestigious individual fellowshipsNumerical routines for reproducible research2021-04-16T00:00:00+02:002021-04-16T00:00:00+02:00https://gdurisi.github.io/news-post/2021/04/16/code<p>We have just uploaded to our <a href="https://github.com/infotheorychalmers">team’s github repository</a> the numerical routines to reproduce the results reported in two recently published journal papers:</p>
<blockquote>
<p>J. Ostman, A. Lancho, G. Durisi, and L. Sanguinetti, “URLLC with Massive MIMO: Analysis and Design at Finite Blocklength,” <em>IEEE Trans. Wireless Commun.</em>, 2021. [<a href="https://arxiv.org/abs/2009.10550">arXiv</a>], [<a href="https://github.com/infotheorychalmers/URLLC_Massive_MIMO">matlab code</a>]</p>
</blockquote>
<blockquote>
<p>J. Östman, R. Devassy, G. Durisi, and E. G. Ström, “Short-packet Transmission via Variable-Length Codes in the Presence of Noisy Stop Feedback,” <em>IEEE Trans. Wireless Commun</em>, 2021. [<a href="http://arxiv.org/abs/1909.01049">arXiv</a>], [<a href="https://github.com/infotheorychalmers/vlsf-bounds">matlab code</a>]</p>
</blockquote>Giuseppe DurisiWe have just uploaded the matlab code to reproduce the results reported in two recently published papers