# Low-density generator-matrix (LDGM) code

## Description

\(q\)-ary linear code with a sparse generator matrix. More precisely, a member of an infinite family of \([n,k,d]\) codes for which the number of nonzero entries in each row and column of the generator matrix are both bounded by a constant as \(n\to\infty\). The dual of an LDGM code has a sparse parity-check matrix and is called an LDPC code.

## Rate

Certain LDGM codes come close to achieving Shannon capacity [1].

## Parent

## Child

## Cousins

- Single parity-check (SPC) code — Concatenated SPCs are LDGM [2].
- \(q\)-ary parity-check code — Concatenated parity-check codes are LDGM [2].
- Low-density parity-check (LDPC) code — LDPC and LDGM codes are dual to each other.

## References

- [1]
- J. Garcia-Frias and Wei Zhong, “Approaching Shannon performance by iterative decoding of linear codes with low-density generator matrix”, IEEE Communications Letters 7, 266 (2003) DOI
- [2]
- T. R. Oenning and Jaekyun Moon, “A low-density generator matrix interpretation of parallel concatenated single bit parity codes”, IEEE Transactions on Magnetics 37, 737 (2001) DOI

## Page edit log

- Victor V. Albert (2022-08-15) — most recent

## Cite as:

“Low-density generator-matrix (LDGM) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/ldgm