List of unsolved problems in information theory

This article lists some unsolved problems in information theory which are separated into source coding and channel coding. There are also related unsolved problems^[1] in philosophy.

Channel coding

Capacity of a network:^[2] 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.
Capacity of the broadcast channel:^[3]^[4] 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.
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 with in a gap for: injective-semi-deterministic, additive white Gaussian noise with per block power constraint.
Capacity of the two-way channel.^[5]^[6] The capacity of the two-way channel (a channel in which information is sent in both directions simultaneously) is unknown.
The capacity of Aloha:^[7] The ALOHAnet used a very simple access scheme for which the capacity is still unknown, though it is known in a few special cases.
Quantum capacity: The capacity of a quantum channel is in general not known.^[8]

There are many other unsolved problems in coding theory:^[9] and in other areas.^[10]^[11]

Distributed source coding: The best way to compress multiple correlated information sources that do not communicate with each other is not known.