Capacity problems

Each input bit is independently deleted without an erasure marker; the exact capacity is unknown for every nontrivial deletion probability.

The capacity region of this binary-input broadcast channel remains unknown.

Each bit is independently flipped with probability \(p\).

An adversary selects a channel state at every use; deterministic average-error 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.

A point-to-point Gaussian vector channel under a total covariance trace constraint has a log-determinant water-filling capacity formula.

A relay observes a noisy channel output and sends information over a separate noiseless finite-capacity link, but capacity is unknown in general.

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

The Shannon capacity of the seven-cycle remains unknown.

The linear-encoder symmetric capacity is known, while unrestricted nonlinear capacity remains open.

A six-message, ten-receiver groupcast instance has linear-encoder capacity 5/13 and a non-Shannon nonlinear upper bound 11/28.

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.

A scalar Gaussian channel with a hard amplitude constraint has an optimizing input with finite support.

Noiseless output feedback improves reliability without changing AWGN capacity.

Each transmitted bit is received correctly or replaced by a visible erasure symbol.

Independent stuck-at defects are known noncausally to the encoder but not the decoder.

In the fixed iid random-insertion model, each transmitted bit may be followed by one independent fair inserted bit and exact capacity is unknown.

One binary symbol is transmitted perfectly while the other can flip in only one direction.

The three-input Blackwell channel is a concrete nondegraded deterministic broadcast channel with an exact entropy capacity region.

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.

Each receiver in a directed cycle knows its successor message and requests its own message.

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.

A noiseless legitimate receiver and an erasure eavesdropper have a simple strong-secrecy capacity.

One encoder sends the same message to every receiver in a fixed finite family.

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

A finite DMC under a feasible maximum-codeword average-cost constraint has a constrained mutual-information capacity formula.

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

An independent iid state observed only by the receiver gives a conditional-mutual-information capacity formula.

Stationary irreducible aperiodic Markov noise subtracts its entropy rate from the group alphabet rate.

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

Iid real fading gains known only to the receiver determine ergodic capacity under a fixed power budget.

The unconstrained finite wiretap channel has a single-auxiliary secrecy-capacity characterization without a degradedness assumption.

The capacity regions of all 9,846 nonisomorphic index-coding instances with at most five messages are covered by a finite classification.

A binary erasure channel with no adjacent transmitted ones admits an exact feedback capacity formula.

A less-noisy ordering compares every finite stochastic prefix and yields the exact superposition-coding capacity region.

Independent additive noises allow simultaneous communication in both directions without an adaptation gain.

A more-capable ordering compares the receivers for every input distribution and yields an exact superposition-coding capacity region.

A noiseless binary channel forbids adjacent transmitted ones and has golden-ratio capacity.

A q-symbol input is reproduced exactly.

One source sends a common message to every designated receiver in a finite directed acyclic network.

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.

With causal noiseless output feedback and a known initial state, the binary trapdoor channel has capacity equal to the logarithm of the golden ratio.

The binary trapdoor channel’s exact capacity without feedback remains unknown.

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

Under the two strong-interference information inequalities, both receivers decode both messages and the capacity region is a MAC-region intersection.

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

Each of five receivers knows its two neighbours and asks for its own independent message.