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3 changed files with 618 additions and 717 deletions

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@ -1,6 +1,6 @@
@ARTICLE{ADMM, @ARTICLE{ADMM,
author={Barman, Siddharth and Liu, Xishuo and Draper, Stark C. and Recht, Benjamin}, author={Barman, Siddharth and Liu, Xishuo and Draper, Stark C. and Recht, Benjamin},
journal={Trans. Inf. Theory}, journal={IEEE Transactions on Information Theory},
title={Decomposition Methods for Large Scale LP Decoding}, title={Decomposition Methods for Large Scale LP Decoding},
year={2013}, year={2013},
volume={59}, volume={59},
@ -11,7 +11,7 @@
@ARTICLE{feldman_paper, @ARTICLE{feldman_paper,
author={Feldman, J. and Wainwright, M.J. and Karger, D.R.}, author={Feldman, J. and Wainwright, M.J. and Karger, D.R.},
journal={IEEE Trans. Inf. Theory}, journal={IEEE Transactions on Information Theory},
title={Using linear programming to Decode Binary linear codes}, title={Using linear programming to Decode Binary linear codes},
year={2005}, year={2005},
volume={51}, volume={51},
@ -22,7 +22,7 @@
@ARTICLE{ml_in_the_list, @ARTICLE{ml_in_the_list,
author={Geiselhart, Marvin and Elkelesh, Ahmed and Ebada, Moustafa and Cammerer, Sebastian and Brink, Stephan ten}, author={Geiselhart, Marvin and Elkelesh, Ahmed and Ebada, Moustafa and Cammerer, Sebastian and Brink, Stephan ten},
journal={IEEE Trans. Commun.}, journal={IEEE Transactions on Communications},
title={Automorphism Ensemble Decoding of ReedMuller Codes}, title={Automorphism Ensemble Decoding of ReedMuller Codes},
year={2021}, year={2021},
volume={69}, volume={69},
@ -33,7 +33,7 @@
@ARTICLE{mackay99, @ARTICLE{mackay99,
author={MacKay, D.J.C.}, author={MacKay, D.J.C.},
journal={IEEE Trans. Inf. Theory}, journal={IEEE Transactions on Information Theory},
title={Good error-correcting codes based on very sparse matrices}, title={Good error-correcting codes based on very sparse matrices},
year={1999}, year={1999},
volume={45}, volume={45},
@ -46,10 +46,10 @@
author = {MacKay, David J.C.}, author = {MacKay, David J.C.},
title = {Encyclopedia of Sparse Graph Codes}, title = {Encyclopedia of Sparse Graph Codes},
date = {2023-04}, date = {2023-04},
url = {www.inference.org.uk/mackay/codes/data.html} url = {http://www.inference.org.uk/mackay/codes/data.html}
} }
@book{proximal_algorithms, @article{proximal_algorithms,
title={Proximal algorithms}, title={Proximal algorithms},
author={Parikh, Neal and Boyd, Stephen and others}, author={Parikh, Neal and Boyd, Stephen and others},
journal={Foundations and trends{\textregistered} in Optimization}, journal={Foundations and trends{\textregistered} in Optimization},
@ -72,7 +72,7 @@
@INPROCEEDINGS{adaptive_lp_decoding, @INPROCEEDINGS{adaptive_lp_decoding,
author={Taghavi, Mohammad H. and Siegel, Paul H.}, author={Taghavi, Mohammad H. and Siegel, Paul H.},
booktitle={IEEE Proc. ISIT}, booktitle={2006 IEEE International Symposium on Information Theory},
title={Adaptive Linear Programming Decoding}, title={Adaptive Linear Programming Decoding},
year={2006}, year={2006},
volume={}, volume={},
@ -83,7 +83,7 @@
@INPROCEEDINGS{interior_point_decoding, @INPROCEEDINGS{interior_point_decoding,
author={Vontobel, Pascal O.}, author={Vontobel, Pascal O.},
booktitle={Proc. ITA}, booktitle={2008 Information Theory and Applications Workshop},
title={Interior-point algorithms for linear-programming decoding}, title={Interior-point algorithms for linear-programming decoding},
year={2008}, year={2008},
volume={}, volume={},
@ -102,14 +102,3 @@
% doi={10.1587/transfun.2022TAP0002} % doi={10.1587/transfun.2022TAP0002}
} }
@ARTICLE{chase_decoding,
author={Chase, D.},
journal={IEEE Trans. Inf. Theory},
title={Class of algorithms for decoding block codes with channel measurement information},
year={1972},
% volume={18},
% number={1},
% pages={170-182},
% keywords={},
% doi={10.1109/TIT.1972.1054746}}
}

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@ -1,205 +1,205 @@
index,p_error index,p_error
0,0.001972541 0,0.00196649
1,0.00184933 1,0.00184247
2,0.001619784 2,0.0016156
3,0.000671981 3,0.00066842
4,0.000330856 4,0.00033188
5,0.000186121 5,0.00018416
6,0.000117411 6,0.00011708
7,8.0073e-05 7,8.057e-05
8,5.7761e-05 8,5.825e-05
9,4.3332e-05 9,4.342e-05
10,3.3405e-05 10,3.424e-05
11,2.6124e-05 11,2.667e-05
12,2.102e-05 12,2.035e-05
13,1.7142e-05 13,1.79e-05
14,1.425e-05 14,1.413e-05
15,1.1871e-05 15,1.173e-05
16,9.983e-06 16,1.013e-05
17,8.707e-06 17,8.33e-06
18,7.293e-06 18,7.16e-06
19,6.256e-06 19,6.06e-06
20,5.442e-06 20,5.49e-06
21,4.955e-06 21,5.25e-06
22,4.34e-06 22,3.93e-06
23,3.781e-06 23,3.75e-06
24,3.306e-06 24,3.44e-06
25,3.026e-06 25,3.04e-06
26,2.752e-06 26,2.69e-06
27,2.458e-06 27,2.67e-06
28,2.208e-06 28,2.16e-06
29,2.104e-06 29,2.46e-06
30,1.84e-06 30,1.87e-06
31,1.628e-06 31,1.7e-06
32,1.538e-06 32,1.46e-06
33,1.447e-06 33,1.62e-06
34,1.354e-06 34,1.54e-06
35,1.175e-06 35,1.26e-06
36,1.089e-06 36,1.09e-06
37,1.049e-06 37,1.1e-06
38,9.17e-07 38,8e-07
39,8.59e-07 39,8.9e-07
40,8.42e-07 40,8e-07
41,7.75e-07 41,6.1e-07
42,6.93e-07 42,7.1e-07
43,7.08e-07 43,6.6e-07
44,6.11e-07 44,5.9e-07
45,6.12e-07 45,7.2e-07
46,5.98e-07 46,6e-07
47,5.86e-07 47,5.8e-07
48,4.91e-07 48,4.4e-07
49,4.63e-07 49,5.2e-07
50,4.57e-07 50,4.2e-07
51,4.11e-07 51,4.2e-07
52,4.13e-07 52,4.3e-07
53,4.15e-07 53,4.8e-07
54,3.85e-07 54,4.6e-07
55,3.76e-07 55,3.6e-07
56,3.77e-07 56,4.5e-07
57,3.58e-07 57,3e-07
58,3.18e-07 58,3.3e-07
59,2.86e-07 59,3.4e-07
60,2.94e-07 60,2.4e-07
61,3.11e-07 61,3.4e-07
62,2.8e-07 62,2.8e-07
63,2.61e-07 63,2e-07
64,2.56e-07 64,2.8e-07
65,2.48e-07 65,2.7e-07
66,2.73e-07 66,3.2e-07
67,2.28e-07 67,1.8e-07
68,2.33e-07 68,2.7e-07
69,2.26e-07 69,1.9e-07
70,2.01e-07 70,1.7e-07
71,1.88e-07 71,1.6e-07
72,2.11e-07 72,2e-07
73,2.14e-07 73,2.8e-07
74,1.86e-07 74,1.4e-07
75,2.03e-07 75,1.5e-07
76,1.89e-07 76,2.6e-07
77,2.07e-07 77,2.4e-07
78,2.02e-07 78,1.1e-07
79,1.91e-07 79,2.2e-07
80,2.01e-07 80,2.1e-07
81,1.88e-07 81,2.6e-07
82,2.15e-07 82,2e-07
83,1.68e-07 83,1.9e-07
84,1.88e-07 84,1.8e-07
85,1.86e-07 85,1.8e-07
86,1.82e-07 86,1.9e-07
87,1.8e-07 87,2e-07
88,2.01e-07 88,2e-07
89,1.88e-07 89,1.7e-07
90,1.84e-07 90,1.8e-07
91,1.92e-07 91,2e-07
92,1.88e-07 92,2.3e-07
93,1.85e-07 93,1.5e-07
94,1.71e-07 94,1.7e-07
95,1.78e-07 95,1.4e-07
96,1.44e-07 96,1.1e-07
97,1.4e-07 97,1.6e-07
98,1.65e-07 98,2.2e-07
99,1.33e-07 99,1.1e-07
100,1.67e-07 100,1.8e-07
101,1.56e-07 101,1.4e-07
102,1.42e-07 102,1.6e-07
103,1.35e-07 103,9e-08
104,1.4e-07 104,1e-07
105,1.22e-07 105,1.3e-07
106,1.42e-07 106,9e-08
107,1.43e-07 107,1.1e-07
108,1.19e-07 108,1.3e-07
109,1.25e-07 109,1.2e-07
110,1.02e-07 110,9e-08
111,1.06e-07 111,1.7e-07
112,1.19e-07 112,1.3e-07
113,1.2e-07 113,7e-08
114,1.19e-07 114,1.2e-07
115,1.03e-07 115,6e-08
116,9.8e-08 116,1.4e-07
117,1.15e-07 117,1.3e-07
118,1.01e-07 118,1.3e-07
119,1e-07 119,8e-08
120,1.01e-07 120,8e-08
121,9.6e-08 121,8e-08
122,8.6e-08 122,1.1e-07
123,7.8e-08 123,2e-08
124,9.6e-08 124,1e-07
125,7.7e-08 125,1e-07
126,8.6e-08 126,9e-08
127,9.9e-08 127,9e-08
128,7.9e-08 128,1.1e-07
129,8.4e-08 129,6e-08
130,9.1e-08 130,5e-08
131,8.3e-08 131,5e-08
132,7.7e-08 132,6e-08
133,8.4e-08 133,6e-08
134,6.1e-08 134,6e-08
135,6.7e-08 135,6e-08
136,6.6e-08 136,5e-08
137,7.6e-08 137,9e-08
138,7e-08 138,7e-08
139,7.4e-08 139,9e-08
140,6.9e-08 140,9e-08
141,6.4e-08 141,5e-08
142,6.6e-08 142,6e-08
143,6.5e-08 143,1e-08
144,6.9e-08 144,9e-08
145,5.5e-08 145,8e-08
146,5.8e-08 146,5e-08
147,6.2e-08 147,7e-08
148,6.4e-08 148,3e-08
149,6.4e-08 149,3e-08
150,6.4e-08 150,3e-08
151,5.3e-08 151,6e-08
152,5.7e-08 152,6e-08
153,4.9e-08 153,9e-08
154,6.1e-08 154,6e-08
155,5.6e-08 155,7e-08
156,4.2e-08 156,5e-08
157,5.6e-08 157,2e-08
158,4e-08 158,3e-08
159,5.7e-08 159,5e-08
160,6.3e-08 160,7e-08
161,7.5e-08 161,4e-08
162,3.3e-08 162,3e-08
163,5.7e-08 163,7e-08
164,4.5e-08 164,1e-08
165,5.1e-08 165,7e-08
166,6e-08 166,6e-08
167,4.3e-08 167,6e-08
168,3.8e-08 168,5e-08
169,4.3e-08 169,4e-08
170,4.2e-08 170,5e-08
171,5.1e-08 171,8e-08
172,6.4e-08 172,5e-08
173,3.9e-08 173,7e-08
174,4.3e-08 174,4e-08
175,3.5e-08 175,5e-08
176,2.9e-08 176,3e-08
177,4.3e-08 177,4e-08
178,4e-08 178,3e-08
179,5.1e-08 179,1e-08
180,4.8e-08 180,4e-08
181,6e-08 181,5e-08
182,5.1e-08 182,5e-08
183,4.2e-08 183,2e-08
184,3.9e-08 184,3e-08
185,3.4e-08 185,1e-08
186,4.7e-08 186,5e-08
187,2.4e-08 187,0.0
188,3.9e-08 188,6e-08
189,5.2e-08 189,9e-08
190,6.7e-08 190,6e-08
191,3.2e-08 191,2e-08
192,4e-08 192,6e-08
193,3.3e-08 193,4e-08
194,3.9e-08 194,3e-08
195,4.5e-08 195,5e-08
196,5e-08 196,6e-08
197,5.3e-08 197,4e-08
198,7.4e-08 198,4e-08
199,6.8e-08 199,5e-08
200,8.3e-08 200,7e-08
201,1.2e-07 201,1e-07
202,1.94e-07 202,1.4e-07
203,2.52e-07 203,3.2e-07

1 index p_error
2 0 0.001972541 0.00196649
3 1 0.00184933 0.00184247
4 2 0.001619784 0.0016156
5 3 0.000671981 0.00066842
6 4 0.000330856 0.00033188
7 5 0.000186121 0.00018416
8 6 0.000117411 0.00011708
9 7 8.0073e-05 8.057e-05
10 8 5.7761e-05 5.825e-05
11 9 4.3332e-05 4.342e-05
12 10 3.3405e-05 3.424e-05
13 11 2.6124e-05 2.667e-05
14 12 2.102e-05 2.035e-05
15 13 1.7142e-05 1.79e-05
16 14 1.425e-05 1.413e-05
17 15 1.1871e-05 1.173e-05
18 16 9.983e-06 1.013e-05
19 17 8.707e-06 8.33e-06
20 18 7.293e-06 7.16e-06
21 19 6.256e-06 6.06e-06
22 20 5.442e-06 5.49e-06
23 21 4.955e-06 5.25e-06
24 22 4.34e-06 3.93e-06
25 23 3.781e-06 3.75e-06
26 24 3.306e-06 3.44e-06
27 25 3.026e-06 3.04e-06
28 26 2.752e-06 2.69e-06
29 27 2.458e-06 2.67e-06
30 28 2.208e-06 2.16e-06
31 29 2.104e-06 2.46e-06
32 30 1.84e-06 1.87e-06
33 31 1.628e-06 1.7e-06
34 32 1.538e-06 1.46e-06
35 33 1.447e-06 1.62e-06
36 34 1.354e-06 1.54e-06
37 35 1.175e-06 1.26e-06
38 36 1.089e-06 1.09e-06
39 37 1.049e-06 1.1e-06
40 38 9.17e-07 8e-07
41 39 8.59e-07 8.9e-07
42 40 8.42e-07 8e-07
43 41 7.75e-07 6.1e-07
44 42 6.93e-07 7.1e-07
45 43 7.08e-07 6.6e-07
46 44 6.11e-07 5.9e-07
47 45 6.12e-07 7.2e-07
48 46 5.98e-07 6e-07
49 47 5.86e-07 5.8e-07
50 48 4.91e-07 4.4e-07
51 49 4.63e-07 5.2e-07
52 50 4.57e-07 4.2e-07
53 51 4.11e-07 4.2e-07
54 52 4.13e-07 4.3e-07
55 53 4.15e-07 4.8e-07
56 54 3.85e-07 4.6e-07
57 55 3.76e-07 3.6e-07
58 56 3.77e-07 4.5e-07
59 57 3.58e-07 3e-07
60 58 3.18e-07 3.3e-07
61 59 2.86e-07 3.4e-07
62 60 2.94e-07 2.4e-07
63 61 3.11e-07 3.4e-07
64 62 2.8e-07
65 63 2.61e-07 2e-07
66 64 2.56e-07 2.8e-07
67 65 2.48e-07 2.7e-07
68 66 2.73e-07 3.2e-07
69 67 2.28e-07 1.8e-07
70 68 2.33e-07 2.7e-07
71 69 2.26e-07 1.9e-07
72 70 2.01e-07 1.7e-07
73 71 1.88e-07 1.6e-07
74 72 2.11e-07 2e-07
75 73 2.14e-07 2.8e-07
76 74 1.86e-07 1.4e-07
77 75 2.03e-07 1.5e-07
78 76 1.89e-07 2.6e-07
79 77 2.07e-07 2.4e-07
80 78 2.02e-07 1.1e-07
81 79 1.91e-07 2.2e-07
82 80 2.01e-07 2.1e-07
83 81 1.88e-07 2.6e-07
84 82 2.15e-07 2e-07
85 83 1.68e-07 1.9e-07
86 84 1.88e-07 1.8e-07
87 85 1.86e-07 1.8e-07
88 86 1.82e-07 1.9e-07
89 87 1.8e-07 2e-07
90 88 2.01e-07 2e-07
91 89 1.88e-07 1.7e-07
92 90 1.84e-07 1.8e-07
93 91 1.92e-07 2e-07
94 92 1.88e-07 2.3e-07
95 93 1.85e-07 1.5e-07
96 94 1.71e-07 1.7e-07
97 95 1.78e-07 1.4e-07
98 96 1.44e-07 1.1e-07
99 97 1.4e-07 1.6e-07
100 98 1.65e-07 2.2e-07
101 99 1.33e-07 1.1e-07
102 100 1.67e-07 1.8e-07
103 101 1.56e-07 1.4e-07
104 102 1.42e-07 1.6e-07
105 103 1.35e-07 9e-08
106 104 1.4e-07 1e-07
107 105 1.22e-07 1.3e-07
108 106 1.42e-07 9e-08
109 107 1.43e-07 1.1e-07
110 108 1.19e-07 1.3e-07
111 109 1.25e-07 1.2e-07
112 110 1.02e-07 9e-08
113 111 1.06e-07 1.7e-07
114 112 1.19e-07 1.3e-07
115 113 1.2e-07 7e-08
116 114 1.19e-07 1.2e-07
117 115 1.03e-07 6e-08
118 116 9.8e-08 1.4e-07
119 117 1.15e-07 1.3e-07
120 118 1.01e-07 1.3e-07
121 119 1e-07 8e-08
122 120 1.01e-07 8e-08
123 121 9.6e-08 8e-08
124 122 8.6e-08 1.1e-07
125 123 7.8e-08 2e-08
126 124 9.6e-08 1e-07
127 125 7.7e-08 1e-07
128 126 8.6e-08 9e-08
129 127 9.9e-08 9e-08
130 128 7.9e-08 1.1e-07
131 129 8.4e-08 6e-08
132 130 9.1e-08 5e-08
133 131 8.3e-08 5e-08
134 132 7.7e-08 6e-08
135 133 8.4e-08 6e-08
136 134 6.1e-08 6e-08
137 135 6.7e-08 6e-08
138 136 6.6e-08 5e-08
139 137 7.6e-08 9e-08
140 138 7e-08
141 139 7.4e-08 9e-08
142 140 6.9e-08 9e-08
143 141 6.4e-08 5e-08
144 142 6.6e-08 6e-08
145 143 6.5e-08 1e-08
146 144 6.9e-08 9e-08
147 145 5.5e-08 8e-08
148 146 5.8e-08 5e-08
149 147 6.2e-08 7e-08
150 148 6.4e-08 3e-08
151 149 6.4e-08 3e-08
152 150 6.4e-08 3e-08
153 151 5.3e-08 6e-08
154 152 5.7e-08 6e-08
155 153 4.9e-08 9e-08
156 154 6.1e-08 6e-08
157 155 5.6e-08 7e-08
158 156 4.2e-08 5e-08
159 157 5.6e-08 2e-08
160 158 4e-08 3e-08
161 159 5.7e-08 5e-08
162 160 6.3e-08 7e-08
163 161 7.5e-08 4e-08
164 162 3.3e-08 3e-08
165 163 5.7e-08 7e-08
166 164 4.5e-08 1e-08
167 165 5.1e-08 7e-08
168 166 6e-08
169 167 4.3e-08 6e-08
170 168 3.8e-08 5e-08
171 169 4.3e-08 4e-08
172 170 4.2e-08 5e-08
173 171 5.1e-08 8e-08
174 172 6.4e-08 5e-08
175 173 3.9e-08 7e-08
176 174 4.3e-08 4e-08
177 175 3.5e-08 5e-08
178 176 2.9e-08 3e-08
179 177 4.3e-08 4e-08
180 178 4e-08 3e-08
181 179 5.1e-08 1e-08
182 180 4.8e-08 4e-08
183 181 6e-08 5e-08
184 182 5.1e-08 5e-08
185 183 4.2e-08 2e-08
186 184 3.9e-08 3e-08
187 185 3.4e-08 1e-08
188 186 4.7e-08 5e-08
189 187 2.4e-08 0.0
190 188 3.9e-08 6e-08
191 189 5.2e-08 9e-08
192 190 6.7e-08 6e-08
193 191 3.2e-08 2e-08
194 192 4e-08 6e-08
195 193 3.3e-08 4e-08
196 194 3.9e-08 3e-08
197 195 4.5e-08 5e-08
198 196 5e-08 6e-08
199 197 5.3e-08 4e-08
200 198 7.4e-08 4e-08
201 199 6.8e-08 5e-08
202 200 8.3e-08 7e-08
203 201 1.2e-07 1e-07
204 202 1.94e-07 1.4e-07
205 203 2.52e-07 3.2e-07