More LDPC Codes

Standardized LDPC Codes

StandardNKrateParity Check Matrix
WiFi (802.11)6485405/6alist
ITU G.h3361681/2alist
WiGig (802.11ad)6723361/2alist
WiGig (802.11ad)6724205/8alist
WiGig (802.11ad)6725043/4alist
WiGig (802.11ad)67254613/16alist
WRAN (802.22)3841921/2alist
WRAN (802.22)3842562/3alist
WRAN (802.22)3842883/4alist
WRAN (802.22)3843205/6alist
WRAN (802.22)4802401/2alist
WRAN (802.22)4803202/3alist
WRAN (802.22)4803603/4alist
WRAN (802.22)4804005/6alist


Custom LDPC Codes

NameNKRateSourceParity Check Matrix
LDPC (CCSDS)32161/2[1]alist
TU KL LDPC96481/2 alist
Tanner (3,5)155640.41[3]alist


Multi-Edge Type LDPC Codes

NameNKHRate Parity Check Matrix
Multi-Edge Type10050201/2 alist
Multi-Edge Type v012060241/2 alist
Multi-Edge Type v112060241/2 alist
Multi-Edge Type12864321/2 alist
Multi-Edge Type200100401/2 alist
Multi-Edge Type5122561281/2 alist
Multi-Edge Type576480485/6 alist
Multi-Edge Type8404201681/2 



For basic information on multi-edge type LDPC codes see [4] and [5]. The codes are designed using a quasi cyclic approach, by lifting a small protograph matrix to create a parity check matrix.

In the alist format for multi-edge type codes the number of hidden variable nodes H is indicated by the 3rd number in the 1st row. The hidden nodes are positioned between bit position K and K+H. v0 and v1 correspond to different construction methods, i.e. different protograph.


[1] S. Abu-Surra, D. DeClercq, W. Ryan, and D. Divsalar: Trapping set enumerators for specific LDPC codes. Information Theory Applications Workshop (ITA), 2010

[2] These are codes using WiMAX (802.16) protograph, but permutations are set with a progressive edge growth technique to obtain shorter codes than specified in WiMAX.

[3] Tanner, R. M.; Sridhara, D. & Fuja, T.: A Class of Group-Structured LDPC Codes. International Symposium on Coding Theory and Applications, 2001

[4] T. Richardson and R. Urbanke: Modern Coding Theory. Cambrigde University Press, 2008.

[5] D. Divsalar, S. Dolinar and C. Jones: Construction of Protograph LDPC Codes with Lienar Minimum Distance. 2006 IEEE International Symposium on Information Theory, Seattle, 2006