This article lists notable
unsolved problems
List of unsolved problems may refer to several notable conjectures or open problems in various academic fields:
Natural sciences, engineering and medicine
* Unsolved problems in astronomy
* Unsolved problems in biology
* Unsolved problems in chem ...
in
information theory
Information theory is the scientific study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. ...
. These are separated into
source coding
In information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression is either lossy or lossless. Lossless compressi ...
and
channel coding
In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels. The central idea ...
. There are also related unsolved problems in
philosophy
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. ...
.
Channel coding
*Capacity of a network: The capacity of a general
wireless network
A wireless network is a computer network that uses wireless data connections between network nodes.
Wireless networking is a method by which homes, telecommunications networks and business installations avoid the costly process of introducing ...
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: 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 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.
*The capacity of
Aloha
''Aloha'' ( , ) is the Hawaiian word for love, affection, peace, compassion and mercy, that is commonly used as a simple greeting but has a deeper cultural and spiritual significance to native Hawaiians, for whom the term is used to define a f ...
: 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
In the theory of quantum communication, the quantum capacity is the highest rate at which quantum information can be communicated over many independent uses of a noisy quantum channel from a sender to a receiver. It is also equal to the highest ra ...
: The capacity of a quantum channel is in general not known.
Source coding
*
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.
References
Further reading
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{{unsolved problems
information theory
Information theory is the scientific study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. ...