Capacity problems

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, giving the canonical finite noisy channel.

An adversary selects a channel state at every use; deterministic capacity exhibits a symmetrizability dichotomy.

The general finite memoryless point-to-point channel has a single-letter mutual-information capacity formula.

Additive Gaussian interference known noncausally to the encoder causes no capacity loss.

A causal relay assists a source, but decode-forward and the cut-set bound do not coincide in general.

The capacity region for two arbitrary broadcast receivers remains unknown outside important ordered subclasses.

Two transmitter-receiver pairs interfere, and the exact capacity region is unknown in general.

The confusability graph is a five-cycle, whose Shannon capacity is exactly the square root of five.

The power-constrained real Gaussian channel has a closed-form capacity attained by a Gaussian input.

A multiple-unicast instance where the exact nonlinear symmetric capacity is separated from the known linear answer.

Ozarow's feedback scheme and converse determine the full two-user Gaussian MAC feedback region.

For a finite confusability graph, the regularized independence number defines capacity but is difficult to compute or characterize.

Noiseless feedback dramatically improves reliability schemes but leaves the ordinary AWGN capacity unchanged.

Each transmitted bit is 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 hiding the message from a degraded eavesdropper.

A power-constrained Gaussian transmitter serves a strong and a weak receiver by superposition coding.

A Gaussian receiver has a lower noise variance than the eavesdropper, yielding a closed-form secrecy capacity.

Common noiseless output feedback lets distributed encoders cooperate, but the general capacity region is unknown.

Two terminals exchange messages while adapting each input to their own past observations.

An iid channel state is revealed causally to the encoder but not to the decoder.

The entire iid state sequence is known noncausally to the encoder but not the decoder.

One unknown channel from a known finite family governs the entire transmission block.

Causal noiseless output feedback changes coding strategies and reliability but not ordinary DMC capacity.

A symbol in a finite group is corrupted by independent additive noise with a known distribution.

A q-symbol input is reproduced exactly, providing the basic normalization for channel capacity.

When the destination is a degraded version of the relay observation, decode-forward meets the cut-set bound.

One transmitter sends private messages to receivers whose outputs form a degradation chain.

A q-ary symbol is correct with probability 1-p and otherwise changes uniformly to another symbol.

Two independent senders communicate to one receiver through a memoryless channel.

Two power-constrained Gaussian users share one receiver, giving an exact pentagonal capacity region.