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Coding

Theorem

Achievability of the Rate Distortion Function

Definition

Achievable

Theorem

Arithmetic-Geometric Mean Inequality

Definition

Average Code Rate

Definition

Average Probability of Error (Channel Code)

Definition

Average Probability of Error (Source-Channel Code)

Definition

Binary Erasure Channel

Definition

Binary Symmetric Channel

Definition

Binary Symmetric Erasure Channel

Definition

Bit Allocation Problem

Definition

Code Rate

Definition

Codebook

Definition

Codeword

Theorem

Dirichlet Mixture Distribution

Definition

Discrete Communication Channel

Definition

Discrete Memoryless Channel

Definition

Distortion

Definition

Distortion Measure

Definition

Distortion Rate Function

Theorem

Divergence Bound on KT

Definition

Fixed-Length (Block) Code

Definition

Fixed-Length Codes for Discrete Channels

Definition

Gain of Transform Coding

Theorem

Gaussian Rate Distortion Function

Theorem

Gaussian Source Maximizes Rate Distortion Function

Theorem

Hadamard's Inequality

Definition

Hamming Distortion

Theorem

Hamming Rate Distortion Function

Theorem

High Resolution Optimality of KLT

Theorem

Huffman Lemma

Definition

Information Capacity

Theorem

Joint AEP

Kac's Lemma (Stationary Ergodic)

Definition

Karhunen-Loeve Transform

Theorem

KL Transform Decorrelates X

Theorem

Kraft Inequality for UD VLCs

Theorem

Krichevsky and Trofimov Coding Distribution

Theorem

Lagrange Multiplier

Lempel-Ziv Coding

Theorem

Lossless Joint Source-Channel Coding Theorem

Theorem

Lossy Source-Channel Coding Theorem

Theorem

Max Redundancy on KT

Definition

Mean Squared Error Distortion

Definition

Nonsingular Code

Theorem

Number of Types

Definition

Operational Channel Capacity

Theorem

Optimal Bit Allocation

Definition

Optimal Distortion

Theorem

Penalty Lemma

Prefix Code

Definition

Prefix Code Redundancy

Definition

Probability of Decoding Error

Definition

Probability Simplex

Theorem

R(D) is Convex in D

Definition

Rate

Definition

Rate Distortion Function

Theorem

Rate Distortion Theorem

Definition

Redundancy

Definition

Reproduction

Definition

Set of Types with Denominator n

Theorem

Shannon Coding Theorem

Definition

Shannon Limit

Shannon-Fano-Elias Code

Theorem

Shannon's Channel Coding Theorem for the DMC

Theorem

Simplification of the Norm

Theorem

Size of Type Class

Definition

Source-Channel Fixed-Length Code

Definition

Symmetric Channel

Theorem

Tangent Plane for LM

Definition

Transform Coding Distortion

Definition

Transform Coding with Scalar Quantization

Definition

Type

Definition

Type Class

Definition

Uniquely Decodable

Definition

Universal Code

Theorem

Universal Code PMF Q

Definition

Variable Length Code

Theorem

Zero Penalty iff Universal Code