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== Channel coding rate in the Finite Blocklength Regime ==
[[Finite blocklength information theory]] investigates the maximum channel coding rate achievable at a given block-length and error probability in the finite block-length regime (non-asymptotic regime).<ref>{{Cite conference |last=Mary |first=Philippe |last2=Gorce |first2=Jean-Marie |last3=Unsal |first3=Ayse |last4=Poor |first4=H. Vincent |date=2021-07-20 |title=Finite Blocklength Information Theory: What Is the Practical Impact on Wireless Communications? |url=https://ieeexplore.ieee.org/document/7848909 |conference=IEEE Globecom Workshops |pages=1–6 |doi=10.1109/GLOCOMW.2016.7848909}}</ref><ref>{{Cite journal |last=Polyanskiy |first=Yury |last2=Poor |first2=H. Vincent |last3=Verdu |first3=Sergio |date=2010-05-01 |title=Channel Coding Rate in the Finite Blocklength Regime |url=https://ieeexplore.ieee.org/abstract/document/5452208 |journal=IEEE Transactions on Information Theory |volume=56 |issue=5 |pages=2307–2359 |doi=10.1109/TIT.2010.2043769 |issn=1557-9654}}</ref><ref>{{Cite conference |last=Wijerathna Basnayaka |first=Chathuranga M. |last2=Jayakody |first2=Dushantha Nalin K. |last3=Ponnimbaduge Perera |first3=Tharindu D. |last4=Vidal Ribeiro |first4=Moisés |date=2021-07-20 |title=Age of Information in an URLLC-enabled Decode-and-Forward Wireless Communication System |url=https://ieeexplore.ieee.org/document/9449007 |conference= 2021 IEEE 93rd Vehicular Technology Conference (VTC2021-Spring) |pages=1–6 |doi=10.1109/VTC2021-Spring51267.2021.9449007}}</ref> The maximal achievable channel coding rate <math> \left ( \bar{R} \right ) </math> with given block error probability <math> \left ( \epsilon \right ) </math> and block-length <math> \left ( n \right ) </math> (for binary [[Additive white Gaussian noise]] (AWGN) channels, with short block lengths) , closely approximated by [[Yury Polyanskiy|Polyanskiy]], [[Vincent Poor|Poor]] and [[Sergio Verdú|Verdú]] (PPV) in 2010, is given by
:<math> \bar{R}
where <math> Q^{-1}</math> is the inverse of the complementary [[Normal distribution|Gaussian]] [[cumulative distribution function]], <math> C</math> is the channel capacity and <math> V </math> is a characteristic of the channel referred to as channel dispersion.
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