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One interesting question is the following: how efficient in terms of information transfer can an ECC be that has a negligible decoding error rate? This question was answered by Claude Shannon with his second theorem, which says that the channel capacity is the maximum bit rate achievable by any ECC whose error rate tends to zero:<ref name="shannon paper">{{cite journal|first=C. E.|last=Shannon|title=A mathematical theory of communication|journal=[[Bell System Technical Journal]]|volume=27|issue=3–4|pages=379–423 & 623–656|date=1948|url=http://www.math.harvard.edu/~ctm/home/text/others/shannon/entropy/entropy.pdf|doi=10.1002/j.1538-7305.1948.tb01338.x|hdl=11858/00-001M-0000-002C-4314-2|hdl-access=free}}</ref> His proof relies on Gaussian random coding, which is not suitable to real-world applications. The upper bound given by Shannon's work inspired a long journey in designing ECCs that can come close to the ultimate performance boundary. Various codes today can attain almost the Shannon limit. However, capacity achieving ECCs are usually extremely complex to implement.
The most popular ECCs have a trade-off between performance and computational complexity. Usually, their parameters give a range of possible code rates, which can be optimized depending on the scenario. Usually, this optimization is done in order to achieve a low decoding error probability while minimizing the impact to the data rate. Another criterion for optimizing the code rate is to balance low error rate and retransmissions number in order to the energy cost of the communication.<ref>{{Cite conference |title=Optimizing the code rate for achieving energy-efficient wireless communications |first1=F. |last1=Rosas |first2=G. |last2=Brante |first3=R. D. |last3=Souza |first4=C. |last4=Oberli |url=https://ieeexplore.ieee.org/document/6952166 |date=2014 |pages=775–780 |doi=10.1109/WCNC.2014.6952166 |isbn=978-1-4799-3083-8 |book-title=Proceedings of the IEEE Wireless Communications and Networking Conference (WCNC)|url-access=subscription }}</ref>
==Concatenated ECC codes for improved performance==
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