{
  "slug": "code-rate",
  "term": "Code rate",
  "aliases": [
    "coding rate",
    "ECC code rate"
  ],
  "definition": "For a block code encoding k equal-size information symbols into n encoded symbols of the same size, code rate is the dimensionless ratio k/n.",
  "note": "For 0 < k <= n, the redundancy fraction of encoded length is (n-k)/n = 1-R, while extra encoded size relative to the information payload is (n-k)/k = 1/R-1. At R=4/5 these are 20% and 25%, respectively. Neither ratio measures an SSD's complete capacity overhead. [rfc5510]\n\nFor the linear code defined by Hx^T=0, k=n-rank(H), with rank computed over the code's finite field. An m-row matrix gives R=1-m/n only when those checks are independent; duplicate or dependent rows add no independent constraints. [forney2005]\n\nRate alone does not specify correction capability or read cost. In a 2011 NAND simulation, BCH dimensions (n,k)=(9152,8256) and LDPC dimensions (9118,8225) yield different exact rates that both round to 0.9021. The comparison also depends on the selected codes, channel and decoder inputs. [wang2011]",
  "status": "shipping",
  "advantages": [],
  "limitations": [],
  "related": [
    "codeword",
    "error-correcting-code",
    "ldpc",
    "bch-code",
    "reed-solomon-code",
    "soft-decision-decoding"
  ],
  "supersedes": [],
  "supersededBy": [],
  "firstSeen": null,
  "lastSeen": null,
  "citations": [
    {
      "id": "rfc5510",
      "title": "RFC 5510 (2009): Reed-Solomon FEC schemes, sections 3.1-3.2, symbol definitions and code rate",
      "url": "https://www.rfc-editor.org/rfc/rfc5510.html#section-3.1",
      "accessed": "2026-11-07"
    },
    {
      "id": "forney2005",
      "title": "G. D. Forney, MIT 6.451 (2005), sections 6.2.2 and 13.1: dual dimension and dependent parity checks",
      "url": "https://ocw.mit.edu/courses/6-451-principles-of-digital-communication-ii-spring-2005/bb895c1dee9ce0b39d6846e0aa984981_MIT6_451S05_FullLecNotes.pdf",
      "accessed": "2026-11-07"
    },
    {
      "id": "wang2011",
      "title": "Wang et al., GLOBECOM 2011, section IV: BCH and LDPC code dimensions and decoding comparison",
      "url": "https://www.seas.ucla.edu/csl/files/publications/Jiadong_GC2011.pdf",
      "accessed": "2026-11-07"
    },
    {
      "id": "hesela-ldpc",
      "title": "Hesela: LDPC in NAND, the read cost of confidence",
      "url": "https://hesela.com/analyses/ldpc-soft-decoding-read-cost/",
      "accessed": "2026-11-07"
    }
  ],
  "updated": "2026-11-07",
  "provenance": [
    "The denominator identities are arithmetic for fixed-length equal-size symbols; RFC 5510 specifies a packet-erasure scheme, not SSD capacity accounting.",
    "The 2011 comparison is a Gaussian-channel simulation, not measured performance of current NAND devices."
  ]
}