Editing Channel capacity (section)

== Channel capacity estimation ==
To determine the channel capacity, it is necessary to find the capacity-achieving distribution <math>p_X(x)</math> and evaluate the [[mutual information]] <math>I(X;Y)</math>. Research has mostly focused on studying additive noise channels under certain power constraints and noise distributions, as analytical methods are not feasible in the majority of other scenarios. Hence, alternative approaches such as, investigation on the input support,<ref>{{Cite journal |last=Smith |first=Joel G. |date=1971 |title=The information capacity of amplitude- and variance-constrained sclar gaussian channels |url=https://linkinghub.elsevier.com/retrieve/pii/S0019995871903469 |journal=Information and Control |language=en |volume=18 |issue=3 |pages=203–219 |doi=10.1016/S0019-9958(71)90346-9}}</ref> relaxations<ref>{{Cite journal |last1=Huang |first1=J. |last2=Meyn |first2=S.P. |date=2005 |title=Characterization and Computation of Optimal Distributions for Channel Coding |url=https://ieeexplore.ieee.org/document/1459046 |journal=IEEE Transactions on Information Theory |language=en |volume=51 |issue=7 |pages=2336–2351 |doi=10.1109/TIT.2005.850108 |s2cid=2560689 |issn=0018-9448}}</ref> and capacity bounds,<ref>{{Cite book |last=McKellips |first=A.L. |chapter=Simple tight bounds on capacity for the peak-limited discrete-time channel |date=2004 |title=International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings. |chapter-url=https://ieeexplore.ieee.org/document/1365385 |publisher=IEEE |pages=348 |doi=10.1109/ISIT.2004.1365385 |isbn=978-0-7803-8280-0|s2cid=41462226 }}</ref> have been proposed in the literature.

The capacity of a discrete memoryless channel can be computed using the [[Blahut–Arimoto algorithm|Blahut-Arimoto algorithm]].

[[Deep learning]] can be used to estimate the channel capacity. In fact, the channel capacity and the capacity-achieving distribution of any discrete-time continuous memoryless vector channel can be obtained using CORTICAL,<ref>{{Cite journal |last1=Letizia |first1=Nunzio A. |last2=Tonello |first2=Andrea M. |last3=Poor |first3=H. Vincent |date=2023 |title=Cooperative Channel Capacity Learning |url=https://ieeexplore.ieee.org/document/10143184 |journal=IEEE Communications Letters |volume=27 |issue=8 |pages=1984–1988 |doi=10.1109/LCOMM.2023.3282307 |issn=1089-7798|arxiv=2305.13493 }}</ref> a cooperative framework inspired by [[Generative adversarial network|generative adversarial networks]]. CORTICAL consists of two cooperative networks: a generator with the objective of learning to sample from the capacity-achieving input distribution, and a discriminator with the objective to learn to distinguish between paired and unpaired channel input-output samples and estimates <math>I(X;Y)</math>.