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Each input bit is independently deleted without an erasure marker. The exact capacity is unknown for every nontrivial deletion probability.
Each bit is independently flipped with probability p. This is the canonical finite noisy channel.
A relay assists communication from a source to a destination. Decode-forward and the cut-set bound do not coincide in general.
The power-constrained real Gaussian channel has a closed-form capacity attained by a Gaussian input.
This is the smallest multiple-unicast instance identified by Sun and Jafar where Shannon inequalities do not give the best known converse.
Each transmitted bit is either received correctly or replaced by a visible erasure symbol.
One binary symbol is transmitted perfectly while the other can flip in only one direction.
A sender communicates reliably to a legitimate receiver while keeping the message secret from a degraded eavesdropper.
The general finite memoryless point-to-point channel has a single-letter mutual-information characterization.
One transmitter sends private messages to two receivers whose outputs form a degradation chain.
The transmitted q-ary symbol is correct with probability 1-p and otherwise changes uniformly to one of the other symbols.
Two independent senders communicate to one receiver through a memoryless channel, yielding a polymatroidal capacity region.