Information Theory.

Shannon's noisy-channel coding theorem defines the hard ceiling on reliable communication: no coding scheme can transmit information faster than a channel's capacity without introducing errors, no matter how sophisticated the encoding.

Second-order approximation to maximal code size at blocklength n and error epsilon.

Capacity of a binary symmetric channel with crossover probability p.

Capacity of a binary erasure channel with erasure probability epsilon.

Capacity per use of a real discrete-time additive white Gaussian noise channel.

Necessary and sufficient length inequality for a binary prefix code.

Exact best error probability for fixed-length almost-lossless coding of a discrete source block.

Squared-error rate-distortion function of an iid zero-mean Gaussian source.

Conditional-entropy bound induced by any estimator's error probability.

Information cannot increase under stochastic post-processing.

Universal Lempel–Ziv coding converges to entropy rate for stationary ergodic finite-alphabet sources.

Rate-distortion function with correlated side information only at the decoder.

Perfect-secrecy capacity of a degraded discrete memoryless wiretap channel.

Lossless separate-encoder rate region for two correlated memoryless sources.

Two-user capacity region for a physically degraded discrete memoryless broadcast channel.

Capacity region of a stationary memoryless multiple-access channel.

Minimum asymptotic lossy coding rate for a memoryless source and single-letter distortion.

Classical sphere-packing upper bound on the reliability exponent above critical rate.

Greedy lower bound on the size of a binary code with prescribed minimum Hamming distance.

Shannon capacity of a finite discrete memoryless channel.

Shannon–Hartley capacity of an ideal band-limited Gaussian channel.

Minimum asymptotic rate for lossless coding of a stationary memoryless source.