Evaluation of Gallager Codes for Short Block Length and High Rate Applications

By David John Cameron MacKay, Matthew C. Davey. 2001

347 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Networks and Communications, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/0756c8a5db4635b4c1b787646a7cfdc88d5a4649

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Marc P. C. Fossorier
2. David Declercq
3. David John Cameron MacKay
4. Daniel J. Costello Jr.
5. Arvind Sridharan
6. Matthew C. Davey
7. Graeme J. Mitchison
8. P. L. Mcfadden

In Computer Networks and Communications

1. Marc P. C. Fossorier
2. David Declercq
3. David John Cameron MacKay
4. Daniel J. Costello Jr.
5. Arvind Sridharan
6. Matthew C. Davey
7. William E. Ryan
8. Michael Yang

In Electrical and Electronic Engineering

1. David Declercq
2. Marc P. C. Fossorier
3. Graeme J. Mitchison
4. P. L. Mcfadden
5. David John Cameron MacKay
6. Daniel J. Costello Jr.
7. Arvind Sridharan
8. Matthew C. Davey

Citations in the corpus

• Iterative Decoding Threshold Analysis for LDPC Convolutional Codes (2010, neutral): “The block counterparts of these codes were introduced in the appendix of Gallager’s book [4] and also studied in [11] and [12].”
• Reliable communication over channels with insertions, deletions, and substitutions (2001, methodology): “The code was constructed from a rate‐ low-density parity-check code over GF [ 17 ].”
• LDPC block and convolutional codes based on circulant matrices (2004, methodology): “MacKay and Davey obtained an upper bound on the minimum distance of certain LDPC codes whose parity-check matrices are composed of nonoverlapping blocks of permutation submatrices that all commute with each other [17].”
• Quasicyclic low-density parity-check codes from circulant permutation matrices (2004, background): “V. MINIMUM DISTANCE OF QC LDPC CODES A result of [25] implies that the minimum Hamming distance d H of a (J; L)-regular QC LDPC code is upper-bounded by dH (J + 1)!.”
• Design of efficiently encodable moderate-length high-rate irregular LDPC codes (2004, background): “This is attributable to a somewhat small . We conjecture that low-weight columns in (specifically, the submatrix ) lead to a small . MacKay and Davey [ 17 ] have also made this conjecture.”
• Decoding Algorithms for Nonbinary LDPC Codes Over GF$(q)$ (2007, methodology): “For those high orders, it has been shown that the best LDPC codes decoded with BP should be ultra-sparse [7], [8], that is, with the minimum variable-node connection .”
• Sparse-graph codes for quantum error correction (2003, background): “…(MacKay and Neal 1996; MacKay 1999) and modifications to their construction have turned them into state-of-the-art codes, both at low rates and large blocklengths (Luby et al. 2001; Richardson et al. 2001; Davey and MacKay 1998) and at high rates and short blocklengths (MacKay and Davey 2000).”