Encyclopedia of Sparse Graph Codes

David J.C. MacKay (http://www.inference.phy.cam.ac.uk/mackay/)

Questions about David MacKay's Sparse graph code resources are answered here.

This is a database of sparse graph codes. Properties recorded include the codes' parity check matrices, their rates and minimum distances, their empirical performance on the binary input Gaussian noise channel, and histograms of decoding times.

These Codes and Related Data are made freely available under the conditions that (1) when they are used, the authors of the codes and the data and this archive are acknowledged; (2) the authors of the codes and data are not liable for any inaccuracies in the materials presented here or any failure of the codes to work as hoped.


Please scroll down to enter the archive

Note: there are more codes that I have simulated that have not yet made it into this archive. If you have any requests for additions, email me. With appropriate incentives (eg financial support for my group), I can probably help.

Key for ascii performance files: see this file.
Further information about alist format.

Note on high rate codes:
the following numbers give the highest rate codes I have made with column weights 3 and 4.

   Rate  j N    M
  0.889  4 1998 222 
  0.876  4 3584 444
  0.889  3 999  111
  0.9098 3 998   90  
  0.889  3 900  100
  0.8745 3 494   62
  0.878  3 492   60
  0.927  4 4096 300
  0.936  4 4376 282

Acknowledgements: The work of the inference group is supported by IBM Zurich research laboratory.

Under construction



Gallager codes

Gallager codes with rate 1/2

Column weight t=3

96.3.963 (N=96,K=48,M=48,R=0.5) 96.33.964 (N=96,K=48,M=48,R=0.5)
96.3.965 (N=96,K=48,M=48,R=0.5) 96.33.966 (N=96,K=48,M=48,R=0.5)
96.3.967 (N=96,K=48,M=48,R=0.5) 96.33.968 (N=96,K=48,M=48,R=0.5)
EN/C/204.3.483 (N=204,K=102,M=102,R=0.5) 204.33.484 (N=204,K=102,M=102,R=0.5)
204.3.485 (N=204,K=102,M=102,R=0.5) 204.33.486 (N=204,K=102,M=102,R=0.5)
204.3.487 (N=204,K=102,M=102,R=0.5) 204.33.488 (N=204,K=102,M=102,R=0.5)
408.3.834 (N=408,K=204,M=204,R=0.5) 408.33.844 (N=408,K=204,M=204,R=0.5)
408.3.854 (N=408,K=204,M=204,R=0.5) 408.33.864 (N=408,K=204,M=204,R=0.5)
408.3.874 (N=408,K=204,M=204,R=0.5) 408.33.884 (N=408,K=204,M=204,R=0.5)
816.3.134 (N=816,K=408,M=408,R=0.5) 816.33.144 (N=816,K=408,M=408,R=0.5)
816.3.154 (N=816,K=408,M=408,R=0.5) 816.33.164 (N=816,K=408,M=408,R=0.5)
816.3.174 (N=816,K=408,M=408,R=0.5) 816.33.184 (N=816,K=408,M=408,R=0.5)
252.252.3.252 (N=504,K=252,M=252,R=0.5) 504.504.3.504 (N=1008,K=504,M=504,R=0.5)
Margulis2640.1320.3 (N=2640,K=1320,M=1320,R=0.5) ram17.5 (N=4896,K=2448,M=2448,R= 0.5053)
ram13.11.5 (N=,K=,M=,R=) 4000.2000.3.243 (N=4000,K=2000,M=2000,R=0.5)
8000.4000.3.483 (N=8000,K=4000,M=4000,R=0.5) 10000.10000.3.631 (N=20000,K=10000,M=10000,R=0.5)

Column weight t=4

816.4.383 (N=816,K=408,M=408,R=0.5) 816.44.434 (N=816,K=408,M=408,R=0.5)
816.4.545 (N=816,K=408,M=408,R=0.5) 816.44.656 (N=816,K=408,M=408,R=0.5)
816.4.767 (N=816,K=408,M=408,R=0.5) 816.44.878 (N=816,K=408,M=408,R=0.5)
4000.2000.4.244 (N=4000,K=2000,M=2000,R=0.5) 8000.4000.4.484 (N=8000,K=4000,M=4000,R=0.5)
assorted small codes
96.44.443 (N=,K=,M=,R=) 96.44.665 (N=,K=,M=,R=)
96.44.887 (N=,K=,M=,R=) 60.44.246 (N=,K=,M=,R=)

Column weight t=5

816.55.134 (N=816,K=408,M=408,R=0.5) 816.55.156 (N=816,K=408,M=408,R=0.5)
816.55.178 (N=816,K=408,M=408,R=0.5)
204.55.187 (N=204,K=102,M=102,R=0.5) 204.55.165 (N=204,K=102,M=102,R=0.5)
204.55.153 (N=204,K=102,M=102,R=0.5)

Column weight t=6

816.66.634 (N=816,K=408,M=408,R=0.5) 816.66.656 (N=816,K=408,M=408,R=0.5)
816.66.678 (N=816,K=408,M=408,R=0.5)

Irregular codes with rate 1/2

4986.93xb.329 (N=9972 ,K=4986,M=4986,R= 0.5) 4986.93y.654 (N=9972 ,K=4986,M=4986,R= 0.5)
4986.l3u.306 (N=9972 ,K=4986,M=4986,R= 0.5) 4986.l93.193 (N=9972 ,K=4986,M=4986,R= 0.5)
4986.93.128 (N=9972 ,K=4986,M=4986,R= 0.5) 4986.93i.939 (N=9972 ,K=4986,M=4986,R= 0.5)
4986.3.333 (N=9972 ,K=4986,M=4986,R= 0.5) 4986.33.330 (N=9972 ,K=4986,M=4986,R= 0.5)

Regular and Irregular codes with rate 1/2, Progressive Edge Growth (PEG) construction

PEGReg252x504 (N=504 ,K=252,M=252,R= 0.5) PEGReg504x1008 (N=1008 ,K=504,M=504,R= 0.5)
PEGirReg252x504 (N=504 ,K=252,M=252,R= 0.5) PEGirReg504x1008 (N=1008 ,K=504,M=504,R= 0.5)
PEGirUppTriang1030x2048 (N=2048 ,K=1018,M=1030,R= 0.4971) PEGirUppTriang518x1024 (N=1024 ,K=506,M=518,R= 0.4941)

Gallager codes with rate 1/3

Column weight t=2,3 or 3

1920.1280.3.303 (N=1920,K=640,M=1280,R= 0.3333) 816.1A3.833 (N=,K=,M=,R=)
816.2A3.344 (N=,K=,M=,R=) 816.1A3.455 (N=,K=,M=,R=)
816.2A3.566 (N=,K=,M=,R=) 816.1A3.677 (N=,K=,M=,R=)
816.2A3.788 (N=,K=,M=,R=)

408.1A3.832 (N=,K=,M=,R=) 408.2A3.342 (N=,K=,M=,R=)
408.1A3.452 (N=,K=,M=,R=) 408.2A3.564 (N=,K=,M=,R=)
408.1A3.675 (N=,K=,M=,R=) 408.2A3.786 (N=,K=,M=,R=)

Column weight t=4

408.1A4.482 (N=,K=,M=,R=) 408.1A4.483 (N=,K=,M=,R=)
408.1A4.485 (N=,K=,M=,R=)

816.1A4.842 (N=,K=,M=,R=) 816.1A4.843 (N=816 ,K=272,M=544,R= 0.3346)
816.1A4.845 (N=816,K=272,M=544,R= 0.3333)

Column weight 4, tiny block length

60.1A4.246 (N=,K=,M=,R=) 60.1A4.245 (N=,K=,M=,R=)
54.1A4.254 (N=,K=,M=,R=) 54.1A4.253 (N=,K=,M=,R=)
48.1A4.153 (N=,K=,M=,R=) 48.1A4.154 (N=,K=,M=,R=)
48.1A4.158 (N=,K=,M=,R=)

Column weight t=6

204.1A6.138 (N=,K=,M=,R=) 204.1A6.139 (N=,K=,M=,R=)
204.1A6.338 (N=,K=,M=,R=)
96.1A3.838 (N=,K=,M=,R=) 96.2A3.343 (N=,K=,M=,R=)
96.1A3.454 (N=,K=,M=,R=) 96.2A3.565 (N=,K=,M=,R=)
96.1A3.676 (N=,K=,M=,R=) 96.2A3.787 (N=,K=,M=,R=)

Assorted Regular Gallager codes

120.64.3.109 (N=120,K=56,M=64,R= 0.4667) 120.64.3.110 (N=120,K=56,M=64,R= 0.4667)
120.64.3.111 (N=120,K=56,M=64,R= 0.4667)
271.127.3.112 (N=271,K=144,M=127,R= 0.5314) 271.127.3.113 (N=271,K=144,M=127,R= 0.5314)
271.127.3.114 (N=271,K=144,M=127,R= 0.5314)

Gallager codes with Rate 1/4

10002.3.333e (N=13298,K=3296,M=10002,R=0.5)

High rate Gallager codes (R=0.7,0.77)

These codes were created for comparison with 2 DSC codes (273,191) (R~0.7) and (1057,813) (R~0.77).

(273,191) (R~0.7)

273.82.3.353 (N=,K=,M=,R=) 273.82.3.364 (N=,K=,M=,R=)
273.82.3.378 (N=,K=,M=,R=) 273.82.4.556 (N=,K=,M=,R=)
273.82.4.2763 (N=,K=,M=,R=) 273.82.4.3065 (N=,K=,M=,R=)

(1057,813) (R~0.77)

Very high rate Gallager codes (R~=0.89,0.94)

Column Weight 3, N=495, Rate=0.87

Note, high rate Gallager codes with column weight 3 are not expected to be good codes.
1057.244.3.352 (N=,K=,M=,R=) 1057.244.3.353 (N=,K=,M=,R=)
1057.244.3.457 (N=,K=,M=,R=) 1057.244.4.360 (N=,K=,M=,R=)
1057.244.4.364 (N=,K=,M=,R=) 1057.244.4.389 (N=,K=,M=,R=)
495.62.3.2915 (N=495,K=433,M=62,R= 0.8747)

Column Weight 3, N=999, Rate=0.89

Note, high rate Gallager codes with column weight 3 are not expected to be good codes. These codes were made for use in Gallager codes over GF(16), where column weight 3 is OK.
999.111.3.5543 (N=999,K=888,M=111,R= 0.8889) 999.111.3.5555 (N=999,K=888,M=111,R= 0.8889)
999.111.3.5565 (N=999,K=888,M=111,R= 0.8889)

Column Weight 4, N~=1998, Rate=0.89

1908.212.4.1383 (N=1908,K=1696,M=212,R= 0.8889) 1998.5.3.2665 (N=1998,K=1776,M=222,R= 0.8889)
1998.5.3.1392 (N=1998,K=1776,M=222,R= 0.8889) 1998.5.3.1500 (N=1998,K=1776,M=222,R= 0.8889)
s2.94.594 (N=1998,K=1776,M=222,R= 0.8889) s2.94.494 (N=1998,K=1776,M=222,R= 0.8889)

Column Weight 4, N~=4000, Rate~=0.9

4376.282.4.9598 (N=4376,K=4094,M=282,R= 0.9356) 3584.5.3.4326 (N=3584,K=3140,M=444,R=0.876)

Column Weights less than 4, N=1998, Rate=0.89

s2.943.349 (N=1998,K=1776,M=222,R= 0.8889) s2.94c.194 (N=1998,K=1776,M=222,R= 0.8889)

More high rate codes (R=.82-.93)

Note, very high rate Gallager codes with column weight j=3 are not expected to be good codes. For each (N,R), a pair of codes are provided, one with j=3 and one with j=4.

Length 4095 with Rate=0.82

4095.737.3.101 (N=4095,K=3358,M=737,R= 0.82) 4095.738.4.102 (N=4095,K=3357,M=738,R= 0.82)
4161.731.4.352 (N=4095,K=3364,M=731,R= 0.8215) 4161.731.4.356 (N=4095,K=3364,M=731,R= 0.8215)

Length 16383 with rate=0.87

16383.2130.3.103 (N=16383,K=14253,M=2130,R= 0.87) 16383.2131.4.104 (N=16383,K=14252,M=2131,R= 0.87)

Length 32000 with rate=0.93.

32000.2240.3.105 (N=32000,K=29760,M=2240,R= 0.93) 32000.2241.4.106 (N=32000,K=29759,M=2241,R= 0.93)

Gallager-like codes and Algebraically constructed codes

Tiny regular codes

algebraic/monodec10.3 (N=15,K=5,M=10,R= 0.4)

DSC codes

DSC.273.82.A (N=273,K=0,M=273,R= 0.6996)

Repeat-accumulate codes (Divsalar, D., Jin, H., and McEliece, R. J., 1998)

Nothing here at the moment (under construction)
Here are the details of individual codes:

96.3.963 (N=96,K=48,M=48,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 96
M: 48
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=963 N=96 GH/spec3 > GHC/96.3.963
comment: Notes in READEN

96.33.964 (N=96,K=48,M=48,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 96
M: 48
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=964 N=96 GH/spec33 > GHC/96.33.964

96.3.965 (N=96,K=48,M=48,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 96
M: 48
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=965 N=96 GH/spec3 > GHC/96.3.965

96.33.966 (N=96,K=48,M=48,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 96
M: 48
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=966 N=96 GH/spec33 > GHC/96.33.966

96.3.967 (N=96,K=48,M=48,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 96
M: 48
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=967 N=96 GH/spec3 > GHC/96.3.967

96.33.968 (N=96,K=48,M=48,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 96
M: 48
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=968 N=96 GH/spec33 > GHC/96.33.968

EN/C/204.3.483 (N=204,K=102,M=102,R=0.5)
Gaussian channel: postscript
Gaussian channel: ascii
N: 204
M: 102
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=483 N=204 GH/spec3 > GHC/204.3.483

204.33.484 (N=204,K=102,M=102,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 204
M: 102
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=484 N=204 GH/spec33 > GHC/204.33.484

204.3.485 (N=204,K=102,M=102,R=0.5)
Gaussian channel: postscript
Gaussian channel: ascii
N: 204
M: 102
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=485 N=204 GH/spec3 > GHC/204.3.485

204.33.486 (N=204,K=102,M=102,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 204
M: 102
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=486 N=204 GH/spec33 > GHC/204.33.486

204.3.487 (N=204,K=102,M=102,R=0.5)
Gaussian channel: postscript
Gaussian channel: ascii
N: 204
M: 102
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=487 N=204 GH/spec3 > GHC/204.3.487

204.33.488 (N=204,K=102,M=102,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 204
M: 102
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=488 N=204 GH/spec33 > GHC/204.33.488

408.3.834 (N=408,K=204,M=204,R=0.5)
Gaussian channel: postscript
Gaussian channel: ascii
N: 408
M: 204
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=834 N=408 GH/spec3 > GHC/408.3.834

408.33.844 (N=408,K=204,M=204,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 408
M: 204
author: D.J.C. MacKay (recreated March 2009)
R: 0.5
created: GHG.p seed=844 N=408 GH/spec33 > GHC/408.33.844

408.3.854 (N=408,K=204,M=204,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 408
M: 204
author: D.J.C. MacKay (recreated March 2009)
R: 0.5
created: GHG.p seed=854 N=408 GH/spec3 > GHC/408.3.854

408.33.864 (N=408,K=204,M=204,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 408
M: 204
author: D.J.C. MacKay (recreated March 2009)
R: 0.5
created: GHG.p seed=864 N=408 GH/spec33 > GHC/408.33.864

408.3.874 (N=408,K=204,M=204,R=0.5)
Gaussian channel: postscript
Gaussian channel: ascii
N: 408
M: 204
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=874 N=408 GH/spec3 > GHC/408.3.874

408.33.884 (N=408,K=204,M=204,R=0.5)
Gaussian channel: postscript
Gaussian channel: ascii
N: 408
M: 204
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=884 N=408 GH/spec33 > GHC/408.33.884

816.3.134 (N=816,K=408,M=408,R=0.5)
Gaussian channel: postscript
Gaussian channel: ascii
N: 816
M: 408
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=134 N=816 GH/spec3 > GHC/816.3.134

816.33.144 (N=816,K=408,M=408,R=0.5)
Gaussian channel: postscript
Gaussian channel: ascii
N: 816
M: 408
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=144 N=816 GH/spec33 > GHC/816.33.144

816.3.154 (N=816,K=408,M=408,R=0.5)
Gaussian channel: postscript
Gaussian channel: ascii
N: 816
M: 408
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=154 N=816 GH/spec3 > GHC/816.3.154

816.33.164 (N=816,K=408,M=408,R=0.5)
Gaussian channel: postscript
Gaussian channel: ascii
N: 816
M: 408
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=164 N=816 GH/spec33 > GHC/816.33.164

816.3.174 (N=816,K=408,M=408,R=0.5)
Gaussian channel: postscript
Gaussian channel: ascii
Alist file: parity check matrix
N: 816
M: 408
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=174 N=816 GH/spec3 > GHC/816.3.174

816.33.184 (N=816,K=408,M=408,R=0.5)
Gaussian channel: postscript
Gaussian channel: ascii
N: 816
M: 408
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=184 N=816 GH/spec33 > GHC/816.33.184

252.252.3.252 (N=504,K=252,M=252,R=0.5)
Alist file: parity check matrix
N: 504
M: 252
author: D.J.C. MacKay
R: 0.5
created: code4r -cheap 1 -n 252 -t1 3 -v 0 -rho 1 -hd 3 -seed 252

504.504.3.504 (N=1008,K=504,M=504,R=0.5)
Alist file: parity check matrix
N: 1008
M: 504
author: D.J.C. MacKay
R: 0.5
t: 3
created: code4r -cheap 1 -n 504 -t1 3 -v 0 -rho 1 -hd 3 -seed 504

Margulis2640.1320.3 (N=2640,K=1320,M=1320,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 2640
M: 1320
t: 3
R: 0.5
author: Mike Postol + David MacKay
created: This is Margulis's Cayley graph construction with p=11. It has distance <= 220. It has a (12,4) near-codeword.

ram17.5 (N=4896,K=2448,M=2448,R= 0.5053)
Alist file: parity check matrix
N: 4896
M: 2448
Mtrue: 2422
Ktrue: 2474
t: 3
author: Pascal Vontobel and Joachim Rosenthal.
created: Constructed using Ramanujan graphs and ideas from Margulis. (q=17, p=5) (Allerton 2000)

ram13.11.5 (N=,K=,M=,R=)

4000.2000.3.243 (N=4000,K=2000,M=2000,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 4000
M: 2000
author: D.J.C. MacKay
R: 0.5
t: 3
created: code6 -n1 0 -n 4000 -t2 3 -t1 3 -v 0 -m 2000 -seed 243 -o GHC/4000.2000.3.243

8000.4000.3.483 (N=8000,K=4000,M=4000,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 8000
M: 4000
author: D.J.C. MacKay
R: 0.5
t: 3
created: code6 -n1 0 -n 8000 -t2 3 -t1 3 -v 0 -m 4000 -seed 483 -o GHC/8000.4000.3.483

10000.10000.3.631 (N=20000,K=10000,M=10000,R=0.5)
Alist file: parity check matrix
N: 20000
M: 10000
author: D.J.C. MacKay
R: 0.5
t: 3
created:

816.4.383 (N=816,K=408,M=408,R=0.5)
Gaussian channel: postscript
Gaussian channel: ascii
N: 816
M: 408
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=383 N=816 GH/spec4 > GHC/816.4.383

816.44.434 (N=816,K=408,M=408,R=0.5)
Gaussian channel: postscript
Gaussian channel: ascii
N: 816
M: 408
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=434 N=816 GH/spec44 > GHC/816.44.434

816.4.545 (N=816,K=408,M=408,R=0.5)
Gaussian channel: postscript
Gaussian channel: ascii
N: 816
M: 408
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=545 N=816 GH/spec4 > GHC/816.4.545

816.44.656 (N=816,K=408,M=408,R=0.5)
Gaussian channel: postscript
Gaussian channel: ascii
N: 816
M: 408
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=656 N=816 GH/spec44 > GHC/816.44.656

816.4.767 (N=816,K=408,M=408,R=0.5)
Gaussian channel: postscript
Gaussian channel: ascii
N: 816
M: 408
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=767 N=816 GH/spec4 > GHC/816.4.767

816.44.878 (N=816,K=408,M=408,R=0.5)
Gaussian channel: postscript
Gaussian channel: ascii
N: 816
M: 408
t: 4
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=878 N=816 GH/spec44 > GHC/816.44.878

4000.2000.4.244 (N=4000,K=2000,M=2000,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 4000
M: 2000
author: D.J.C. MacKay
R: 0.5
t: 4
created: code6 -n1 0 -n 4000 -t2 4 -t1 4 -v 0 -m 2000 -seed 244 -o GHC/4000.2000.4.244

8000.4000.4.484 (N=8000,K=4000,M=4000,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 8000
M: 4000
author: D.J.C. MacKay
R: 0.5
t: 4
created: code6 -n1 0 -n 8000 -t2 4 -t1 4 -v 0 -m 4000 -seed 484 -o GHC/8000.4000.4.484

96.44.443 (N=,K=,M=,R=)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=548 N=96 GH/spec44 > GHC/96.44.443

96.44.665 (N=,K=,M=,R=)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=665 N=96 GH/spec44 > GHC/96.44.665

96.44.887 (N=,K=,M=,R=)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=887 N=96 GH/spec44 > GHC/96.44.887

60.44.246 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=548 N=60 GH/spec44 > GHC/60.44.246

816.55.134 (N=816,K=408,M=408,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 816
M: 408
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=434 N=816 GH/spec55 > GHC/816.55.134

816.55.156 (N=816,K=408,M=408,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 816
M: 408
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=656 N=816 GH/spec55 > GHC/816.55.156

816.55.178 (N=816,K=408,M=408,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 816
M: 408
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=878 N=816 GH/spec55 > GHC/816.55.178

204.55.187 (N=204,K=102,M=102,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 204
M: 102
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=837 N=204 GH/spec55 > GHC/204.55.187

204.55.165 (N=204,K=102,M=102,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 204
M: 102
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=521679 N=204 GH/spec55 > GHC/204.55.165

204.55.153 (N=204,K=102,M=102,R=0.5)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 204
M: 102
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=41627 N=204 GH/spec55 > GHC/204.55.153

816.66.634 (N=816,K=408,M=408,R=0.5)
Gaussian channel: postscript
Gaussian channel: ascii
N: 816
M: 408
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=434 N=816 GH/spec66 > GHC/816.66.634

816.66.656 (N=816,K=408,M=408,R=0.5)
Gaussian channel: postscript
Gaussian channel: ascii
N: 816
M: 408
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=656 N=816 GH/spec66 > GHC/816.66.656

816.66.678 (N=816,K=408,M=408,R=0.5)
Gaussian channel: postscript
Gaussian channel: ascii
N: 816
M: 408
author: D.J.C. MacKay
R: 0.5
created: GHG.p seed=878 N=816 GH/spec66 > GHC/816.66.678

4986.93xb.329 (N=9972 ,K=4986,M=4986,R= 0.5)
Alist file: parity check matrix
author: D.J.C. MacKay
N: 9972
M: 4986
t: 3,9
comment: "Super Poisson" code labelled '93x'. Simulations reported in "Comparison of Construction of Irregular Gallager Codes" in Trans. on Comm. vol 47, oct. 1999 used up to a maximum of 200 iterations.
created: GH.p file=GH93xb.p spec93xb
GH93xb.p seed=329 M=4986 > ../GHC/4986.93xb.329

4986.93y.654 (N=9972 ,K=4986,M=4986,R= 0.5)
Alist file: parity check matrix
author: D.J.C. MacKay
N: 9972
M: 4986
t: 3,9
comment: "Super Poisson code" labelled '93y'. Simulations reported in "Comparison of Construction of Irregular Gallager Codes" in Trans. on Comm. vol 47, oct. 1999 used up to a maximum of 200 iterations.
created: GH.p file=GH93y.p spec93y
GH93y.p seed=654 M=4986 > ../GHC/4986.93y.654

4986.l3u.306 (N=9972 ,K=4986,M=4986,R= 0.5)
Alist file: parity check matrix
author: D.J.C. MacKay
N: 9972
M: 4986
t: 3,9
comment: 4986.l3u.306 Linear-time encodeable 'l3'
created:

4986.l93.193 (N=9972 ,K=4986,M=4986,R= 0.5)
Alist file: parity check matrix
author: D.J.C. MacKay
N: 9972
M: 4986
t: 3,9
comment: 4986.l93.193 Linear-time encodeable 'l93y'. Note this file name contains the characters l(L) and 1(one).
created:

4986.93.128 (N=9972 ,K=4986,M=4986,R= 0.5)
Alist file: parity check matrix
author: D.J.C. MacKay
N: 9972
M: 4986
t: 3,9
comment: 4986.93.128 "Sub-Poisson code" is labelled '93a'
created: GH93b.p seed=128 M=4986 > ../GHC/4986.93.128

4986.93i.939 (N=9972 ,K=4986,M=4986,R= 0.5)
Alist file: parity check matrix
author: D.J.C. MacKay
N: 9972
M: 4986
t: 3,9
comment: 4986.93i.939 "Poisson" code, is labelled '93p'
created: Using Matthew Davey's "irreg" software: irreg -i ispec/93 -c > ../GHC/4986.93i.939

4986.3.333 (N=9972 ,K=4986,M=4986,R= 0.5)
Alist file: parity check matrix
author: D.J.C. MacKay
N: 9972
M: 4986
t: 3
comment: 4986.3.333 Regular weight 3 code is labelled '3'
created: GH3.p seed=333 M=4986 > ../GHC/4986.3.333

4986.33.330 (N=9972 ,K=4986,M=4986,R= 0.5)
Alist file: parity check matrix
author: D.J.C. MacKay
N: 9972
M: 4986
t: 3
comment: 4986.33.330 Regular weight 3 code is labelled '33'
created: GH33.p seed=330 M=4986 > ../GHC/4986.33.330

PEGReg252x504 (N=504 ,K=252,M=252,R= 0.5)
Alist file: parity check matrix
author: Xiao-Yu Hu, IBM Zurich research labs
N: 504
M: 252
t: 3
comment: Progressive Edge Growth construction attempts to maximize girth, and empirically gives very good codes. This is the best known regular Gallager code with these parameters (M,N,t) [Best in the sense of perfromance on AWGN, Wed 11/5/05]. The code is not quite regular in row-degree.
created: MainPEG

PEGReg504x1008 (N=1008 ,K=504,M=504,R= 0.5)
Alist file: parity check matrix
author: Xiao-Yu Hu, IBM Zurich research labs
N: 1008
M: 504
t: 3
comment: Progressive Edge Growth construction attempts to maximize girth, and empirically gives very good codes. This is the best known regular Gallager code with these parameters (M,N,t) [Best in the sense of perfromance on AWGN, Wed 11/5/05]. The code is not quite regular in row-degree.
created: MainPEG

PEGirReg252x504 (N=504 ,K=252,M=252,R= 0.5)
Alist file: parity check matrix
author: Xiao-Yu Hu, IBM Zurich research labs
N: 504
M: 252
comment: Progressive Edge Growth construction attempts to maximize girth, and empirically gives very good codes. This is the best known code with these parameters (N,M). [Best in the sense of perfromance on AWGN, Wed 11/5/05]
created: MainPEG

PEGirReg504x1008 (N=1008 ,K=504,M=504,R= 0.5)
Alist file: parity check matrix
author: Xiao-Yu Hu, IBM Zurich research labs
N: 1008
M: 504
comment: Progressive Edge Growth construction attempts to maximize girth, and empirically gives very good codes. The best known code with these parameters (N,M). [Best in the sense of perfromance on AWGN, Wed 11/5/05]
created: MainPEG

PEGirUppTriang1030x2048 (N=2048 ,K=1018,M=1030,R= 0.4971)
Alist file: parity check matrix
author: Xiao-Yu Hu, IBM Zurich research labs
N: 2048
M: 1030
comment: Progressive Edge Growth construction attempts to maximize girth, and empirically gives very good codes. This code is upper triangular, so fast-encodeable.
created: MainPEG

PEGirUppTriang518x1024 (N=1024 ,K=506,M=518,R= 0.4941)
Alist file: parity check matrix
author: Xiao-Yu Hu, IBM Zurich research labs
N: 1024
M: 518
comment: Progressive Edge Growth construction attempts to maximize girth, and empirically gives very good codes. This code is upper triangular, so fast-encodeable.
created: MainPEG

1920.1280.3.303 (N=1920,K=640,M=1280,R= 0.3333)
Alist file: parity check matrix
author: D.J.C. MacKay
N: 1920
M: 1280
t: 3
comment: For proposed international standard for cellular telephones
created:

816.1A3.833 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=833 N=816 GH/spec1A3 > GHC/816.1A3.833

816.2A3.344 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=344 N=816 GH/spec2A3 > GHC/816.2A3.344

816.1A3.455 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=455 N=816 GH/spec1A3 > GHC/816.1A3.455

816.2A3.566 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=566 N=816 GH/spec2A3 > GHC/816.2A3.566

816.1A3.677 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=677 N=816 GH/spec1A3 > GHC/816.1A3.677

816.2A3.788 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=788 N=816 GH/spec2A3 > GHC/816.2A3.788

408.1A3.832 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=832 N=408 GH/spec1A3 > GHC/408.1A3.832

408.2A3.342 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=342 N=408 GH/spec2A3 > GHC/408.2A3.342

408.1A3.452 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=452 N=408 GH/spec1A3 > GHC/408.1A3.452

408.2A3.564 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=564 N=408 GH/spec2A3 > GHC/408.2A3.564

408.1A3.675 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=675 N=408 GH/spec1A3 > GHC/408.1A3.675

408.2A3.786 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=786 N=408 GH/spec2A3 > GHC/408.2A3.786

408.1A4.482 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=482 N=408 GH/spec1A4 > GHC/408.1A4.482

408.1A4.483 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=483 N=408 GH/spec1A4 > GHC/408.1A4.483

408.1A4.485 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=485 N=408 GH/spec1A4 > GHC/408.1A4.485

816.1A4.842 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=842 N=816 GH/spec1A4 > GHC/816.1A4.842

816.1A4.843 (N=816 ,K=272,M=544,R= 0.3346)
Gaussian channel: postscript
Gaussian channel: ascii
N: 816
M: 544
Mtrue: 543
Ktrue: 273
author: D.J.C. MacKay
R:
comment: Obviously, since this code has all columns of even weight, it must have not-full rank.
created: GHG.p seed=843 N=816 GH/spec1A4 > GHC/816.1A4.843

816.1A4.845 (N=816,K=272,M=544,R= 0.3333)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 816
M: 544
author: D.J.C. MacKay
R:
created: GHG.p seed=845 N=816 GH/spec1A4 > GHC/816.1A4.845

60.1A4.246 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=548 N=60 GH/spec1A4 > GHC/60.1A4.246

60.1A4.245 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=545 N=60 GH/spec1A4 > GHC/60.1A4.245
comment: has a weight 9 codeword (and none smaller)

54.1A4.254 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=142 N=54 GH/spec1A4 > GHC/54.1A4.254

54.1A4.253 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=140 N=54 GH/spec1A4 > GHC/54.1A4.253

48.1A4.153 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=1153 N=48 GH/spec1A4 > GHC/48.1A4.153
comment: has distance 8. This is an example of a code with (rate,distance) beyond the Gilbert bound: R_GV(8) = 1.0 - H(8.0/48.0) = 0.34997.
Ktrue: 17

48.1A4.154 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
Ktrue: 17
created: GHG.p seed=1163 N=48 tries=1000 GH/spec1A4 > GHC/48.1A4.154
comment: has distance 8 This is an example of a code with (rate,distance) beyond the Gilbert bound: R_GV(8) = 1.0 - H(8.0/48.0) = 0.34997.

48.1A4.158 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
Ktrue: 17
created: GHG.p seed=1400 N=48 tries=1000 GH/spec1A4 > GHC/48.1A4.158
comment: has distance greater than 8 This is an example of a code with (rate,distance) beyond the Gilbert bound: R_GV(8) = 1.0 - H(8.0/48.0) = 0.34997.

204.1A6.138 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=6245399 N=204 GH/spec1A6 > GHC/204.1A6.138

204.1A6.139 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=46245399 N=204 GH/spec1A6 > GHC/204.1A6.139

204.1A6.338 (N=,K=,M=,R=)
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=263438 N=204 GH/spec1A6 > GHC/204.1A6.338

96.1A3.838 (N=,K=,M=,R=)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=838 N=96 GH/spec1A3 > GHC/96.1A3.838

96.2A3.343 (N=,K=,M=,R=)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=343 N=96 GH/spec2A3 > GHC/96.2A3.343

96.1A3.454 (N=,K=,M=,R=)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=454 N=96 GH/spec1A3 > GHC/96.1A3.454

96.2A3.565 (N=,K=,M=,R=)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=565 N=96 GH/spec2A3 > GHC/96.2A3.565

96.1A3.676 (N=,K=,M=,R=)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=676 N=96 GH/spec1A3 > GHC/96.1A3.676

96.2A3.787 (N=,K=,M=,R=)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: GHG.p seed=787 N=96 GH/spec2A3 > GHC/96.2A3.787

120.64.3.109 (N=120,K=56,M=64,R= 0.4667)
Alist file: parity check matrix
N: 120
M: 64
t: 3
author: D J C MacKay
created: code5 -n 120 -t1 3 -v 0 -m 64 -hd 3 -seed 1912 -o GHC/120.64.3.109
comment: This code has no 4-cycles in its graph.

120.64.3.110 (N=120,K=56,M=64,R= 0.4667)
Alist file: parity check matrix
N: 120
M: 64
t: 3
author: D J C MacKay
created: code5 -n 120 -t1 3 -v 0 -m 64 -hd 3 -seed 1091 -o GHC/120.64.3.110
comment: This code has no 4-cycles in its graph.

120.64.3.111 (N=120,K=56,M=64,R= 0.4667)
Alist file: parity check matrix
N: 120
M: 64
t: 3
author: D J C MacKay
created: code5 -n 120 -t1 3 -v 0 -m 64 -hd 3 -seed 1093 -o GHC/120.64.3.111
comment: This code has no 4-cycles in its graph.

271.127.3.112 (N=271,K=144,M=127,R= 0.5314)
Alist file: parity check matrix
N: 271
M: 127
t: 3
author: D J C MacKay
created: code5 -n 271 -t1 3 -v 0 -m 127 -hd 3 -seed 1094 -o GHC/271.127.3.112
comment: This code has no 4-cycles in its graph.

271.127.3.113 (N=271,K=144,M=127,R= 0.5314)
Alist file: parity check matrix
N: 271
M: 127
t: 3
author: D J C MacKay
created: code5 -n 271 -t1 3 -v 0 -m 127 -hd 3 -seed 1095 -o GHC/271.127.3.113
comment: This code has no 4-cycles in its graph.

271.127.3.114 (N=271,K=144,M=127,R= 0.5314)
Alist file: parity check matrix
N: 271
M: 127
t: 3
author: D J C MacKay
created: code5 -n 271 -t1 3 -v 0 -m 127 -hd 3 -seed 10916 -o GHC/271.127.3.114
comment: This code has no 4-cycles in its graph.

10002.3.333e (N=13298,K=3296,M=10002,R=0.5)
Alist file: parity check matrix
N: 13298
M: 10002
author: D.J.C. MacKay
R: 0.5
t: 3
created:

273.82.3.353 (N=,K=,M=,R=)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: beckmann.p w=3 N=273 M=82 verbose=1 docodemod=0 T=3000 s0=50

273.82.3.364 (N=,K=,M=,R=)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: beckmann.p w=3 N=273 M=82 verbose=1 docodemod=0 T=3000 s0=50

273.82.3.378 (N=,K=,M=,R=)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: beckmann.p w=3 N=273 M=82 verbose=1 docodemod=0 T=3000 s0=50

273.82.4.556 (N=,K=,M=,R=)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: beckmann.p w=4 N=273 M=82 verbose=1 docodemod=0 T=3000 s0=50

273.82.4.2763 (N=,K=,M=,R=)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: beckmann.p w=4 N=273 M=82 verbose=1 docodemod=0 T=3000 s0=50

273.82.4.3065 (N=,K=,M=,R=)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: beckmann.p w=4 N=273 M=82 verbose=1 docodemod=0 T=3000 s0=50

1057.244.3.352 (N=,K=,M=,R=)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: beckmann.p w=3 N=1057 M=244 verbose=1 docodemod=0 T=200 s0=50

1057.244.3.353 (N=,K=,M=,R=)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: beckmann.p w=3 N=1057 M=244 verbose=1 docodemod=0 T=200 s0=50

1057.244.3.457 (N=,K=,M=,R=)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: beckmann.p w=3 N=1057 M=244 verbose=1 docodemod=0 T=200 s0=50

1057.244.4.360 (N=,K=,M=,R=)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: beckmann.p w=4 N=1057 M=244 verbose=1 docodemod=0 T=200 s0=50

1057.244.4.364 (N=,K=,M=,R=)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: beckmann.p w=4 N=1057 M=244 verbose=1 docodemod=0 T=200 s0=50

1057.244.4.389 (N=,K=,M=,R=)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N:
M:
author: D.J.C. MacKay
R:
created: beckmann.p w=4 N=1057 M=244 verbose=1 docodemod=0 T=200 s0=50


495.62.3.2915 (N=495,K=433,M=62,R= 0.8747)
Alist file: parity check matrix
N: 495
M: 62
t: 3
author: D.J.C. MacKay
comment: has one 4-cycle
created: see code/IBM.

999.111.3.5543 (N=999,K=888,M=111,R= 0.8889)
Alist file: parity check matrix
N: 999
M: 111
t: 3
author: D.J.C. MacKay
created:

999.111.3.5555 (N=999,K=888,M=111,R= 0.8889)
Alist file: parity check matrix
N: 999
M: 111
t: 3
author: D.J.C. MacKay
created:

999.111.3.5565 (N=999,K=888,M=111,R= 0.8889)
Alist file: parity check matrix
N: 999
M: 111
t: 3
author: D.J.C. MacKay
created:

1908.212.4.1383 (N=1908,K=1696,M=212,R= 0.8889)
Alist file: parity check matrix
N: 1908
M: 212
t: 4
author: D.J.C. MacKay
comment: has no 4-cycles
created: see code/IBM. Used beckmann.p.

1998.5.3.2665 (N=1998,K=1776,M=222,R= 0.8889)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 1998
M: 222
t: 4
author: D.J.C. MacKay
created:

1998.5.3.1392 (N=1998,K=1776,M=222,R= 0.8889)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 1998
M: 222
t: 4
author: D.J.C. MacKay
created:

1998.5.3.1500 (N=1998,K=1776,M=222,R= 0.8889)
Gaussian channel: postscript
Gaussian channel: ascii
N: 1998
M: 222
t: 4
author: D.J.C. MacKay
created: READGHG has details of how this file was created. The code's been deleted in the move from SF.

s2.94.594 (N=1998,K=1776,M=222,R= 0.8889)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 1998
M: 222
t: 4
author: D.J.C. MacKay
created:

s2.94.494 (N=1998,K=1776,M=222,R= 0.8889)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 1998
M: 222
t: 4
author: D.J.C. MacKay
created:

4376.282.4.9598 (N=4376,K=4094,M=282,R= 0.9356)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 4376
M: 282
t: 4
author: D.J.C. MacKay
comment: This code was found by an intensive search using construction method 1A followed by manual pruning of two columns to remove the remaining overlaps greater than 1. It is the highest rate code I was able to make with column weight 4 and blocklength near 4376. It may be that this code is sailing too close to the wind, i.e., that its asymptotic performance for high snr is not as good as other Gallager codes. Nevertheless, in experiments so far this code competes well with RS and BCH codes.

3584.5.3.4326 (N=3584,K=3140,M=444,R=0.876)
Alist file: parity check matrix
Gaussian channel: postscript
Gaussian channel: ascii
N: 3584
K: 3140
R: 0.876
t: 4
comment: Construction 1A was used.
author: D.J.C. MacKay
created:

s2.943.349 (N=1998,K=1776,M=222,R= 0.8889)
Gaussian channel: postscript
Gaussian channel: ascii
N: 1998
M: 222
t: 3-4
author: D.J.C. MacKay
created:
comment: This code has a few weight 3 columns and they spoil its performance

s2.94c.194 (N=1998,K=1776,M=222,R= 0.8889)
Gaussian channel: postscript
Gaussian channel: ascii
N: 1998
M: 222
t: 3-4
author: D.J.C. MacKay
created:
comment: This code has a few weight 3 columns and they spoil its performance

4095.737.3.101 (N=4095,K=3358,M=737,R= 0.82)
Alist file: parity check matrix
N: 4095
M: 737
t: 3
Mtrue: <= 737
Ktrue: 3358
author: D J C MacKay
created: code5 -n 4095 -t1 3 -v 0 -m 737 -hd 3 -seed 101 -o GHC/4095.737.3.101
comment: This code has no 4-cycles in its graph.

4095.738.4.102 (N=4095,K=3357,M=738,R= 0.82)
Alist file: parity check matrix
N: 4095
M: 738
t: 4
Mtrue: <= 737
Ktrue: 3358
author: D J C MacKay
created: code5 -n 4095 -t1 4 -v 0 -m 738 -hd 3 -seed 104 -o GHC/4095.738.4.102
comment: This code has no 4-cycles in its graph.

4161.731.4.352 (N=4095,K=3364,M=731,R= 0.8215)
Alist file: parity check matrix
N: 4095
M: 731
t: 4
comment: Alist file is gzipped

4161.731.4.356 (N=4095,K=3364,M=731,R= 0.8215)
Alist file: parity check matrix
N: 4095
M: 731
t: 4
comment: Alist file is gzipped

16383.2130.3.103 (N=16383,K=14253,M=2130,R= 0.87)
Alist file: parity check matrix
N: 16383
M: 2130
t: 3
Mtrue: <= 2130
Ktrue: 14253
author: D J C MacKay
created: code5 -n 16383 -t1 3 -v 0 -m 2130 -hd 3 -seed 101 -o GHC/16383.2130.3.103
comment: This code has no 4-cycles in its graph.

16383.2131.4.104 (N=16383,K=14252,M=2131,R= 0.87)
Alist file: parity check matrix
N: 16383
M: 2131
t: 4
Mtrue: <= 2130
Ktrue: 14253
author: D J C MacKay
created: code5 -n 16383 -t1 4 -v 0 -m 2131 -hd 3 -seed 104 -o GHC/16383.2131.4.104
comment: This code has no 4-cycles in its graph.

32000.2240.3.105 (N=32000,K=29760,M=2240,R= 0.93)
Alist file: parity check matrix
N: 32000
M: 2240
t: 3
Mtrue: <= 2240
Ktrue: 29760
author: D J C MacKay
created: code5 -n 32000 -t1 3 -v 0 -m 2240 -hd 3 -seed 101 -o GHC/32000.2240.3.105
comment: This code has no 4-cycles in its graph.

32000.2241.4.106 (N=32000,K=29759,M=2241,R= 0.93)
Alist file: parity check matrix
N: 32000
M: 2241
t: 4
Mtrue: <= 2240
Ktrue: 29760
author: D J C MacKay
created: code5 -n 32000 -t1 4 -v 0 -m 2241 -hd 3 -seed 108 -o GHC/32000.2241.4.106
comment: This code has no 4-cycles in its graph.

algebraic/monodec10.3 (N=15,K=5,M=10,R= 0.4)
N: 15
M: 10
tr: 3
Mtrue: 9
Ktrue: 6
d: 5
Gaussian channel: postscript
Gaussian channel: ascii
author: David MacKay
comment: This code is presented on page 221 of D J C MacKay (2003), and eq 13.41. I call it the pentagonful low-density parity-check code. The graph is called the Petersen graph, so maybe a good name for this code would be the (15,6) Petersen code. It has 12 words of weight 5.

DSC.273.82.A (N=273,K=0,M=273,R= 0.6996)
N: 273
M: 273
tr: 17
Mtrue: 82
Ktrue: 191
d: 18
author: Rainer Lucas and Marc Fossorier
comment: This code has no 4-cycles in its graph. It has many 6-cycles (as does any cyclic code). Its true value of M is 3.3 times smaller than its apparent value of M. Has distance 18.