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  "slug": "comm-info",
  "title": "Information Theory & Source Coding — Entropy, Huffman, BSC / BEC / Shannon-Hartley — Communication",
  "category": "communication",
  "category_label": "Communication",
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  "description": "The Information Theory workbench covers the source-coding and channel-capacity theorems. Source side: H(X) entropy, Huffman codes, Shannon-Fano codes, comparison of L̄ vs H(X). Channel side: BSC, BEC, Z-channel, generic DMC capacities, Blahut-Arimoto for arbitrary channels, Shannon-Hartley for AWGN. Use it to compute \"how compressible is this source?\" and \"how fast can I send through this channel?\"",
  "keywords": [
    "information theory",
    "entropy",
    "Huffman",
    "Shannon-Fano",
    "source coding",
    "channel capacity",
    "BSC",
    "BEC",
    "DMC",
    "Shannon-Hartley",
    "spectral efficiency",
    "Kraft inequality",
    "mutual information",
    "GATE ECE",
    "communication"
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  "content": {
    "formulas": [
      "Entropy: H(X) = −Σ p_i·log₂(p_i) bits/symbol",
      "Binary entropy: h(p) = −p·log₂(p) − (1−p)·log₂(1−p)",
      "Source coding theorem: H(X) ≤ L̄ < H(X) + 1 (Huffman is optimal)",
      "Kraft inequality: Σ 2^{−l_i} ≤ 1 (prefix code exists)",
      "BSC capacity: C = 1 − h(p)",
      "BEC capacity: C = 1 − ε",
      "Shannon-Hartley: C = B·log₂(1 + S/N) (AWGN)"
    ],
    "citations": [
      "Cover, T. M., Thomas, J. A., \"Elements of Information Theory,\" 2nd ed., Wiley, 2006.",
      "Shannon, C. E., \"A Mathematical Theory of Communication,\" Bell System Tech. J., 1948."
    ],
    "faq": [
      {
        "q": "Why does a binary symmetric channel with p = 0.5 have C = 0?",
        "a": "The output is independent of the input. I(X; Y) = 0. The channel carries no information. The student must understand \"binary symmetric\" means both error directions are equally likely."
      },
      {
        "q": "Huffman is optimal for symbol-by-symbol coding — what about blocks?",
        "a": "For block coding, arithmetic coding is optimal: L̄ approaches H(X) as block length → ∞. Huffman L̄ approaches H(X) + 1/N for block length N."
      }
    ]
  },
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      "TechArticle",
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  },
  "last_updated": "2026-07-05"
}