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Continuous Information Theory

Definition

Achievable (Continuous)

Theorem

AEP For Continuous IID RVs

Definition

Average Cost Constraint

Definition

Average Power Constraint

Definition

Block Codes for the Gaussian Channel

Theorem

Capacity of Correlated Parallel Gaussian Channels

Theorem

Capacity of Uncorrelated Parallel Gaussian Channels

Theorem

Capacity with Decoder-Side Information (DSI)

Theorem

Capacity with Full-Side Information (FSI)

Theorem

Concavity of Channel Capacity in P

Theorem

Consequence of the AEP

Definition

Continuous Memoryless Source

Definition

Differential Cross-Entropy

Definition

Differential Divergence

Definition

Differential Entropy

Definition

Discrete-Time Continuous Memoryless Channels

Definition

Discrete-Time Memoryless Gaussian Channel (AWGN Channel)

Theorem

Equivalent Properties in Discrete & Continuous IT

Theorem

Estimation Error and differential entropy

Definition

Fading Channel

Theorem

Gaussian Noise Minimizes Capacity of Additive-Noise Channel

Definition

Information Capacity with Input Cost

Theorem

Joint Differential Entropy of Multivariate Gaussian

Definition

Multivariate Gaussian

Definition

Operational Channel Capacity (Continuous)

Theorem

Shannon's Channel Coding Theorem for AWGN

Definition

Typical Set

Theorem

Uniform Quantization of Real-Valued Source

Theorem

Upper Bound on Channel Capacity

Definition

Volume