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  "slug": "comm-ecc",
  "title": "Error Control Coding — Block codes, Hamming, CRC, Viterbi — Communication",
  "category": "communication",
  "category_label": "Communication",
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    "blog_index": "https://siliconverify.com/llms-communication.txt"
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  "description": "The Error Control Coding workbench covers the four canonical ECC families: block codes (Hamming, extended Hamming, repetition, SPC), CRC (4, 8, CCITT, 16 with LFSR state trace), convolutional codes (the (7,5) NASA standard, state diagram, trellis), and Viterbi decoding. It also computes BER vs E_b/N_0 for coded vs uncoded BPSK over AWGN and BSC, with theoretical + Monte-Carlo simulation side-by-side.",
  "keywords": [
    "error control coding",
    "block code",
    "Hamming code",
    "CRC",
    "convolutional code",
    "Viterbi",
    "trellis",
    "syndrome",
    "generator matrix",
    "parity check",
    "BCH",
    "Reed-Solomon",
    "GATE ECE",
    "communication"
  ],
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    "currency": "USDC",
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  "content": {
    "formulas": [
      "Hamming(7,4): corrects any 1-bit error, d_min = 3, rate = 4/7",
      "CRC: detects all 1-bit errors and all burst errors up to r bits (r = deg polynomial)",
      "Convolutional (7,5) NASA standard: constraint K = 3, d_free = 5, ~4 dB coding gain at BER = 10⁻⁵",
      "Viterbi: O(2^K) per bit, finds max-likelihood path",
      "Soft-decision Viterbi: ~2 dB gain over hard decision at same complexity",
      "Channel coding theorem: for R < C, exists code with BER → 0 (Shannon 1948)"
    ],
    "citations": [
      "Lin, S., Costello, D. J., \"Error Control Coding,\" 2nd ed., Prentice Hall, 2004.",
      "Viterbi, A. J., \"Error Bounds for Convolutional Codes and an Asymptotically Optimum Decoding Algorithm,\" IEEE Trans. IT, 1967."
    ],
    "faq": [
      {
        "q": "When should I use CRC vs block code?",
        "a": "CRC for error detection (cheap, just a few extra bits). Block code (Hamming, BCH, Reed-Solomon) for error correction. Storage devices often use CRC + parity for single-error correction; comm channels use block codes."
      },
      {
        "q": "Why is the (7,5) code so popular?",
        "a": "Good free distance (d_free = 5) at low complexity (K = 3, 4 states). Decoded by Viterbi in O(8) per bit. NASA standard for deep-space comm since the 1970s."
      }
    ]
  },
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      "TechArticle",
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  "x402_challenge_example": {
    "request": "curl -A 'GPTBot/1.0' -i https://siliconverify.com/comm-ecc.html",
    "response_headers": [
      "HTTP/1.1 402 Payment Required",
      "X-Siliconverify-Resource-Class: workbench-tool",
      "X-Siliconverify-Price-Atomic: 1000",
      "X-Siliconverify-Price-USD: 0.001"
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    "response_body": "{\n  \"x402Version\": 1,\n  \"accepts\": [\n    {\n      \"scheme\": \"exact\",\n      \"network\": \"base\",\n      \"maxAmountRequired\": \"1000\",\n      \"resource\": \"https://siliconverify.com/comm-ecc.html\",\n      \"description\": \"SiliconVerify workbench tool — interactive browser-based engineering calculator. Client-side computation, no server cost.\",\n      \"mimeType\": \"text/html\",\n      \"payTo\": \"0x97DAA5649Fd7Dfe3e46fCd9f75516e36E750eed7\",\n      \"validAfter\": 1783274656,\n      \"validBefore\": 1783274956\n    }\n  ]\n}",
    "paid_request": "curl -A 'GPTBot/1.0' -H 'X-PAYMENT: 0x<txhash>' -i https://siliconverify.com/comm-ecc.html"
  },
  "last_updated": "2026-07-05"
}