Channel Codes

Maximum Likelihood (ML) Simulation Results

Here, maximum likelihood decoding (ML) simulation results for various channel codes can be downloaded, including:

  • standardized LDPC (WiMAX, WRAN etc.)
  • LDPC of special interest (MacKay, Tanner etc.)
  • non-binary LDPC
  • Array LDPC
  • LTE Turbo
  • BCH
  • Reed-Solomon
  • Polar Codes
  • Reed-Muller Codes

For some of the codes, we furthermore provide simulation results with LP decoding (LP) and improved LP decoding with adaptive cut generation (LP+ACG). Our software toolbox containing algorithms for ML and LP decoding is available here.

The results on this website are extended continuously.

We gratefully thank the AHRP cluster on which large parts of the computations were performed.

How to Cite

If you use these results in your publication, please cite our website as:

Michael Helmling, Stefan Scholl, Florian Gensheimer, Tobias Dietz, Kira Kraft, Stefan Ruzika, and Norbert Wehn. Database of Channel Codes and ML Simulation Results. www.uni-kl.de/channel-codes, 2019.

BibTex

LDPC Codes

NameNKrate    dmin    IP/ML Code    
WiMAX (802.16)5764805/65sim results
alist

WiMAX (802.16)

6725605/67sim resultsalist
WiMAX (802.16)7686405/67sim resultsalist
WiMAX (802.16)8647205/67sim resultsalist
WiMAX (802.16)9608005/67sim resultsalist
WiMAX (802.16)10568805/67sim resultsalist
LDPC (TU KL)96481/210sim resultsalist
Wimax-like192921/210sim resultsalist
Wimax-like2401201/211sim resultsalist
Wimax-like3361681/215sim resultsalist
Wimax-like3841921/215sim results
alist
WRAN (802.22)3841921/215alist
WRAN (802.22)3842562/38sim resultsalist
WRAN (802.22)3842883/48sim resultsalist
WRAN (802.22)3843205/64sim resultsalist
WRAN (802.22)4802401/216alist
WRAN (802.22)4803202/312alist
WRAN (802.22)4803603/47sim resultsalist
WRAN (802.22)4804005/66sim resultsalist
WiFi (802.11)6485405/68sim results
alist
ITU G.h3361681/213alist
CCSDS32161/24sim resultsalist
CCSDS128641/214sim resultsalist
Tanner (3,5)15564≈0.41320sim resultsalist

MacKay 96.33.964

96481/26sim resultsalist
MacKay 204.33.4842041021/28sim resultsalist

MacKay 408.33.844

4082041/214alist
Multi-Edge Type100501/210sim resultsalist
Multi-Edge Type v0120601/210sim resultsalist
Multi-Edge Type v1120601/210sim resultsalist
Multi-Edge Type128641/2sim resultsalist
Multi-Edge Type2001001/212alist
Multi-Edge Type8404201/218alist

FER charts LDPC

Non-binary LDPC Codes

ML simulation results have been obtained via the binary image representation of the non binary codes. The alists and matrices for the non-binary codes can be found in the non-binary LDPC database.

NameNbinKbinGF  rate    dmin    IP/ML Code    
TU KL Code9648641/2 11ML resultshere

TU KL Code

128642561/2 13ML resultshere
TU KL Code12864161/29ML resultshere
U-NBPB (CCSDS)128642561/2 14ML resultshere
TU KL Code576480645/66ML resultshere
TU KL Code5764802565/67here

FER charts Non-Binary LDPC

Array LDPC Codes

NameNKp    r   rate    dmin    IP/ML Code    
Array4924740.498ML resultsalist

Array

4930730.616ML resultsalist
Array4936720.734ML resultsalist
Array4942710.862ML resultsalist
Array121601160.5016ML resultsalist
Array121701150.5810ML resultsalist
Array121801140.6610ML resultsalist
Array121901130.746ML resultsalist
Array1211001120.834ML resultsalist
Array1211101110.912ML resultsalist
Array169961360.5714alist
Array1691081350.6412ML resultsalist
Array1691201340.7110ML resultsalist
Array1691321330.786ML resultsalist
Array1691441320.854ML resultsalist
Array1691561310.922ML resultsalist
Array3612881940.8016ML resultsalist
Array3613241920.904ML resultsalist
Array5294402340.8310alist
Array136912243740.8910 alist
Array136912963720.954 alist
Array136913323710.972 ML resultsalist

Turbo Codes

NameNKratedminIP/ML Code
LTE132401/311sim resultsalist.xz
LTE156481/313sim resultsalist.xz
LTE180561/313sim resultsalist.xz
LTE204641/3sim resultsalist.xz
LTE228721/3sim resultsalist.xz
LTE252801/3 sim resultsalist.xz
LTE276881/3sim resultsalist.xz
LTE300961/3sim results
alist.xz
LTE3241041/3sim resultsalist.xz
LTE3481121/3sim resultsalist.xz
LTE3721201/3sim resultsalist.xz
LTE3961281/3sim results
alist.xz

FER charts Turbo


BCH Codes

NameNKratet IP/ML Codes
BCH740.57sim results

alist

BCH1570.472sim_resultsalist
BCH15110.731sim_resultsalist
BCH31110.355sim_resultsalist
BCH31160.523sim results
alist
BCH31210.682sim_resultsalist
BCH31260.841sim_resultsalist
BCH63300.486sim_resultsalist
BCH63360.575sim_resultsalist
BCH63390.624sim_resultsalist
BCH63450.713sim_resultsalist
BCH63510.812sim_results
alist
BCH63570.901sim_results
alist
BCH127850.676sim resultsalist
BCH127920.725sim_resultsalist
BCH127990.784sim_resultsalist
BCH1271060.833sim_resultsalist
BCH1271130.892sim_resultsalist
BCH1271200.941sim resultsalist
BCH2552230.884sim resultsalist
BCH2552310.913sim resultsalist
BCH2552390.942sim resultsalist
BCH2552470.971sim resultsalist
BCH5114840.953sim resultsalist
BCH5114930.962sim resultsalist
BCH5115020.981sim resultsalist
BCH10239930.973sim resultsalist
BCH102310030.982sim resultsalist
BCH102310130.991sim resultsalist

FER charts BCH


Reed-Solomon Codes

Name   N     K    rate     t    IP/ML   LPCodes
RS730.432MLbinary image
RS750.711MLbinary image
RS1530.206MLbinary image
RS1550.335MLbinary image
RS1570.47ML
binary image
RS1590.603MLbinary image
RS15110.732MLbinary image
RS15130.871ML
binary image
RS31230.744MLbinary image
RS31250.813ML

LP,

LP+AGC

binary image
RS31270.872

ML

binary image
RS31290.941MLbinary image
RS63550.874

LP,

LP+AGC

binary image

FER charts Reed-Solomon


Polar Codes

Go to our polar codes page for more information about polar codes and their construction. The successive cancellation (SC) list decoding algorithm is described in

Tal, I. & Vardy, A: List decoding of polar codes. Proceedings of the IEEE International Symposium on Information Theory, St. Petersburg, Russia, Jul./Aug. 2011

Name  N     K    rate     dminML   SC List(32)Codes
Polar 128640.58MLSCL

txt

Polar 256163≈0.6378MLSCL

txt

Polar 256219≈0.8554MLSCL

txt

Polar 512466≈0.914MLSCLtxt

FER charts Polar Codes


Reed-Muller Codes

Name  N     K    nrrate     dminML   Codes
RM(3,7)12864730.516MLtxt
RM(4,8)25616384≈0.63716MLtxt
RM(5,8)25621985≈0.8558MLtxt
RM(6,9)51246696≈0.918MLtxt

Other Codes

Name   N     K    rate     dmin    IP/ML   Codes
ex. Golay24121/2ML results
alist
cyclic code48241/212ML resultsalist

Notes and References

Notes and references for the codes and decoding algorithms listed above.

LP Decoding

Feldman, J.; Wainwright, M. J. & Karger, D. R.: Using Linear Programming to Decode Binary Linear Codes. IEEE Transactions on Information Theory, vol. 51, 2005, pp. 954-972

Adaptive Cut Generation

Zhang, X. & Siegel, P. H.: Adaptive Cut Generation Algorithm for Improved Linear Programming Decoding of Binary Linear Codes. IEEE Transactions on Information Theory, vol. 58, 2012, pp. 6581-6594

WRAN Codes (IEEE 802.22)

Codes taken from the WRAN (Wireless Regional Area Networks) standard; see http://www.ieee802.org/22/

MacKay Codes

The matrices and more information about codes by David J. C.  MacKay can be found on his website:

http://www.inference.phy.cam.ac.uk/mackay/codes/data.html

Array LDPC Codes

Fan, John L.: Array codes as low-density parity-check codes. Proceedings of the 2nd International Symposium on Turbo Codes and Related Topics, Brest, France, 2000.

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