The Fundamental Principle

Compression Exploits Patterns

Core Concept

Data compression exploits statistical redundancy and predictable patterns in data. The degree of compressibility is fundamentally limited by the entropy of the source.

Compressible Data

Low entropy - High predictability

  • Repeated sequences
  • Statistical patterns
  • Structural redundancy
  • Non-uniform distribution

AAAAAABBBBCCCC
Contains exploitable patterns

Incompressible Data

High entropy - Maximum randomness

  • Random noise
  • Encrypted data
  • Already compressed data
  • Uniform distribution

3F7A92E1D5B8...
No exploitable patterns

Information Theory

Shannon's Source Coding Theorem: No lossless compression scheme can compress data below its entropy limit. For truly random data with uniform distribution, entropy equals the bit length—compression is impossible.

Kolmogorov Complexity: The shortest possible description of data is its algorithmic information content. Random data has maximum complexity and cannot be described more concisely.

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