List of unsolved problems in information theory

• Capacity of a network: The capacity of a general wireless network is not known. There are some specific cases for which the capacity is known, such as the AWGN channel and fading channel.{{cite book|last1=Cover|first1=Thomas|title=Elements of Information Theory|url=https://archive.org/details/elementsofinform0000cove|url-access=registration|publisher=Wiley-Interscience|isbn=978-0471062592|date=1991-08-26}}
• Capacity of the broadcast channel: The capacity of the broadcast channel, or the case in which a single transmitter is sending information to many receivers, is unknown in general, though it is known for several specific cases.{{cite journal|last1=Cover|first1=Thomas|title=Comments on Broadcast Channels|journal=IEEE Trans Inf Theory|date=Oct 1998|volume=44|issue=6|page=2524|doi=10.1109/18.720547|s2cid=8985406 }}{{cite web|last1=Sridharan|first1=Arvind|title=Broadcast Channels|url=https://www3.nd.edu/~jnl/ee698g/materials/summaries/arvind.pdf|website=Notre Dame|accessdate=6 July 2014|archive-date=29 August 2017|archive-url=https://web.archive.org/web/20170829005436/https://www3.nd.edu/~jnl/ee698g/materials/summaries/arvind.pdf|url-status=dead}}
• Capacity of the interference channel (Two User): The capacity of the interference channel, in the case where there are two transmitter and receiver pairs that interfere among each other, is unknown in general. Capacity is known in special cases: strong interference regime, injective-deterministic. Capacity is known in approximate sense or within a range for: injective-semi-deterministic, additive white Gaussian noise with per block power constraint.
• Capacity of the two-way channel: The capacity of the two-way channel (a channel in which information is sent in both directions simultaneously) is unknown.{{cite journal|last1=Shannon|first1=Claude|title=Two-way communication channels|journal=Proc Fourth Berkeley Sump on Mathematical Statistics and Probability|date=1961|volume=1|page=611}}{{cite journal|last1=meeuwissen|first1=Erik|title=The Origin of Two-Way Channels|journal=Proc ISIT|date=16 Aug 1998|volume=I|page=185}}
• Capacity of Aloha: The ALOHAnet used a very simple access scheme for which the capacity is still unknown, though it is known in a few special cases.{{cite journal|last1=Médard|first1=Muriel|author1-link=Muriel Médard|title=Capacity of Time-Slotted ALOHA Packetized Multiple-Access Systems Over the AWGN Channel|journal=IEEE Transactions on Wireless Communications|date=March 2004|volume=3|issue=2|pages=486–499|url=http://colemant.ece.illinois.edu/pubs/capacityALOHAtwireless.pdf|accessdate=11 July 2014|doi=10.1109/TWC.2003.821175|s2cid=791018 |archive-url=https://web.archive.org/web/20111218191542/http://colemant.ece.illinois.edu/pubs/capacityALOHAtwireless.pdf|archive-date=18 December 2011|url-status=dead}}
• Capacity of the queue channel: Under a FIFO policy, whether the feedback capacity of the queue channel is strictly greater than the capacity without feedback is unknown for general service time distributions though it is known that the two quantities are equal when the service time distribution is memoryless.{{cite journal|last1=Anantharam|first1=Venkat|last2=Verdu|first2=Sergio|title=Bits through queues|journal=IEEE Trans Inf Theory|date=1996|volume=42|issue=1|pages=4–18|doi=10.1109/18.481773 }}
• Quantum capacity: The capacity of a quantum channel is in general not known.{{cite book|last=Shor|first=Peter|chapter=Quantum Information Theory: Results and Open Problems |editor=Alon N. |editor2=Bourgain J. |editor3=Connes A. |editor4=Gromov M. |editor5=Milman V.|title=Visions in Mathematics, GAFA 2000 Special Volume: Part II|year=2000|series=Modern Birkhäuser Classics |publisher=Birkhäuser Basel|pages=816–838|chapter-url=http://www-math.mit.edu/~shor/papers/GAFA.pdf|doi=10.1007/978-3-0346-0425-3_9|isbn=978-3-0346-0425-3}}

• Lossy distributed source coding: The best way to compress correlated information sources using encoders that do not communicate with each other, preserving each source to within its distortion metric, is not known.

{{Reflist}}

• {{cite book |last1=Cover |first1=Thomas |last2=Gopinath |first2=B. |title=Open Problems in Communication and Computation |date=1987 |publisher=Springer-Verlag |url=https://raganwald.com/assets/fractran/open-problems-in-communication-and-computation-1987.pdf |access-date=11 February 2021}}
• {{cite book|title=Selected Unsolved Problems in Coding Theory|year=2010|publisher=Springer|location=New York|author=David Joyner|author2=Jon-Lark Kim }}
• {{cite book|last=Longo|first=Giuseppe|title=Information theory: new trends and open problems|year=1975|publisher=Springer |url=https://books.google.com/books?id=ddxfAAAAMAAJ|isbn=9783211813782}}
• {{cite journal|last=Tse|first=David|title=It's Easier to Approximate|journal=Information Theory Society Newsletter|year=1996|url=http://www.eecs.berkeley.edu/~dtse/isit09_plenary.pdf|accessdate=26 June 2013}}

{{unsolved problems}}

information theory