-
Notifications
You must be signed in to change notification settings - Fork 20
/
hgen.m
305 lines (265 loc) · 11 KB
/
hgen.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
function [H,exactRate,nk,ERROR_FLAG] = hgen(R,N,Lambda,Deg_Lambda,Rho,Deg_Rho,seed,DEBUG_FLAG,FileName_sparse);
% [H_SPARSE,EXACT_RATE,NK,ERROR_FLAG] = HGEN(R,N,LAMBDA,DEG_LAMBDA,RHO,DEG_RHO,SEED,DEBUG_FLAG, FILENAME_SPARSE)
% generates a random Parity-Check Matrix of rate R and length N for a given
% profile
% LAMBDA = [LAMBDA(1),...,LAMBDA(.)] is the polynomial representing the proportion of edges LAMBDA(i) connected to
% variables nodes of degree DEG_LAMBDA(i)
% DEG_LAMBDA = [2,3,...] is the vector representing all degrees of the variables-nodes in the code
% RHO = [RHO(1),...,RHO(.)] is the polynomial representing the proportion of edges RHO(i) connected to
% check nodes of degree DEG_RHO(i)
% DEG_RHO = [2,3,...] is the vector representing all degrees of the check-nodes in the code
% SEED seed number to initialize the random generator
% DEBUG_FLAG 0 to desactive it, 1 to print some crucial variables
% FILENAME to use the default name (gallager.n.nk.rate.dat), use []
% EXACT_RATE the exact rate given by the parity-check matrix (as close as
% possible of R)
% NK dimension of the parity-check equation H (nk x n)
% EXAMPLE:
%R = .6;N = 6500;Lambda = [0.2096540000 0.4024980000 0.3878480000];Deg_Lambda = [2 3 10];Rho = [1];Deg_Rho = [9];seed = 0;DEBUG_FLAG = 1;FileName = [];
ERROR_FLAG = 0;
FALSE_ = 0;
TRUE_ = 1;
rand('state',seed);
if (R-floor(100*R)/100<2e-2);
R = floor(100*R)/100;
end;
CodeNumber = 0;
Int_0_1_Lambda = sum(Lambda./Deg_Lambda);
Int_0_1_Rho = sum(Rho./Deg_Rho);
M = round(N*(1-round(1e16*(1-Int_0_1_Rho/Int_0_1_Lambda))/1e16));
Proportion_Lambda = (Int_0_1_Lambda)*Lambda./Deg_Lambda/sum((Int_0_1_Lambda)*Lambda./Deg_Lambda);
Proportion_Rho = (Int_0_1_Rho)*Rho./Deg_Rho/sum((Int_0_1_Rho)*Rho./Deg_Rho);
Nb_Variable_Nodes = round((N/Int_0_1_Lambda)*Lambda./Deg_Lambda);
Nb_Check_Nodes = round((M/Int_0_1_Rho)*Rho./Deg_Rho);
% First step: add nb_row_toaddtoright rows of the lowest connection degree;
nb_row_toaddtoright = M-sum(Nb_Check_Nodes);
Nb_Check_Nodes(1) = Nb_Check_Nodes(1)+nb_row_toaddtoright;
% Update the total number of ones on the right side
nb1_right = sum(Nb_Check_Nodes.*Deg_Rho);
nb1_left = sum(Nb_Variable_Nodes.*Deg_Lambda);
nb_col_toaddtoleft = N-sum(Nb_Variable_Nodes);
if length(Lambda)==1 & nb_col_toaddtoleft~=0;
disp('Cannot generate this matrix');
return;
else;
if (nb1_right ~= nb1_left | nb_col_toaddtoleft ~= 0);
x = [Deg_Lambda(1),Deg_Lambda(2);1,1]\[nb1_right-nb1_left;nb_col_toaddtoleft];
Nb_Variable_Nodes(1) = Nb_Variable_Nodes(1)+x(1);
Nb_Variable_Nodes(2) = Nb_Variable_Nodes(2)+x(2);
end;
end;
exactRate = (sum(Nb_Variable_Nodes)-sum(Nb_Check_Nodes))/sum(Nb_Variable_Nodes)
KK = sum(Nb_Variable_Nodes)-sum(Nb_Check_Nodes);
nk = M;
if sum(Nb_Variable_Nodes.*Deg_Lambda) ~= sum(Nb_Check_Nodes.*Deg_Rho);
disp('Cannot generate this matrix');
return;
end;
if DEBUG_FLAG;
String = [];
for l = 1:length(Deg_Lambda);
String = [String,'+',num2str(Deg_Lambda(l)),'*',num2str(Nb_Variable_Nodes(l))];
end;
String = [String,' (',num2str(sum(Nb_Variable_Nodes.*Deg_Lambda)),')','~='];
for l = 1:length(Deg_Rho);
String = [String,'+',num2str(Deg_Rho(l)),'*',num2str(Nb_Check_Nodes(l))];
end;
String = [String,' (',num2str(sum(Nb_Check_Nodes.*Deg_Rho)),')'];
disp(String);
disp(['Add ',num2str(N-sum(Nb_Variable_Nodes)),' columns and ',num2str(M-sum(Nb_Check_Nodes)),' rows']);
disp('Press any key to continue and adjust the weights by hands if necessary');pause;
%end;
end;
CumSum_Nb_Variable_Nodes = cumsum(Nb_Variable_Nodes);
Nb_Elements_Per_Column = zeros(1,N);
Nb_Elements_Per_Column(1:CumSum_Nb_Variable_Nodes(1)) = Deg_Lambda(1);
for l = 1:length(Deg_Lambda)-1;
Nb_Elements_Per_Column(CumSum_Nb_Variable_Nodes(l)+1:CumSum_Nb_Variable_Nodes(l+1)) = Deg_Lambda(l+1);
end;
CumSum_Nb_Check_Nodes = cumsum(Nb_Check_Nodes);
Nb_Elements_Per_Row = zeros(1,M);
Nb_Elements_Per_Row(1:CumSum_Nb_Check_Nodes(1)) = Deg_Rho(1);
for l = 1:length(Deg_Rho)-1;
Nb_Elements_Per_Row(CumSum_Nb_Check_Nodes(l)+1:CumSum_Nb_Check_Nodes(l+1)) = Deg_Rho(l+1);
end;
Random_Nb_Elements_Per_Row = Nb_Elements_Per_Row(randperm(length(Nb_Elements_Per_Row)));
% disp('---------------------- Parity-check matrix (Hr) generation... ------------------');
CYCLESREMOVAL_ = FALSE_;
while ~CYCLESREMOVAL_;
Max_Deg_Rho = max(Deg_Rho);
Index_Temp = 0;
Vec_Temp = zeros(sum(Nb_Check_Nodes.*Deg_Rho),1);
Vec_Temp(Index_Temp+1:Index_Temp+Deg_Lambda(1)*Nb_Variable_Nodes(1)) = repmat([1:CumSum_Nb_Variable_Nodes(1)],1,Deg_Lambda(1));
Index_Temp = Index_Temp+Deg_Lambda(1)*Nb_Variable_Nodes(1);
for l=2:length(Deg_Lambda);
Vec_Temp(Index_Temp+1:Index_Temp+Deg_Lambda(l)*Nb_Variable_Nodes(l)) = repmat([CumSum_Nb_Variable_Nodes(l-1)+1:CumSum_Nb_Variable_Nodes(l)],1,Deg_Lambda(l));
Index_Temp = Index_Temp+Deg_Lambda(l)*Nb_Variable_Nodes(l);
end;
Random_Columns_Index = Vec_Temp(randperm(length(Vec_Temp)));
Hr = zeros(M,max(Deg_Rho));
Index = 1;
for n = 1:M;
Hr(n,1:Random_Nb_Elements_Per_Row(n)) = Random_Columns_Index(Index:Index+Random_Nb_Elements_Per_Row(n)-1).';
Index = Index+Random_Nb_Elements_Per_Row(n);
end;
%Hr = reshape(Vec_Temp(randperm(length(Vec_Temp))),M,Deg_Rho);
% disp('---------- Parity-check matrix (Hr) generation done ------------');
% ---------- Removal of cycles of length 2... --------------------
% Validation
for n = 1:M;
if DEBUG_FLAG;
if mod(n,floor(M/100))==0;disp([num2str(round(n/M*100)),'%']);end;
end;
Hrn = Hr(n,1:Random_Nb_Elements_Per_Row(n));
[B,In,Jn] = unique(Hrn);
IndicesToSwitch = setdiff([1:Random_Nb_Elements_Per_Row(n)],In);
NbIndicesToSwitch = length(IndicesToSwitch);
if n+NbIndicesToSwitch<=M;
for d = 1:NbIndicesToSwitch;
IndexToSwitch = IndicesToSwitch(d);
IndexToSwitch2 = floor(Random_Nb_Elements_Per_Row(n+d)*rand)+1;
tmp = Hr(n,IndexToSwitch);
Hr(n,IndexToSwitch) = Hr(n+d,IndexToSwitch2);
Hr(n+d,IndexToSwitch2) = tmp;
end;
else;
for d = 1:NbIndicesToSwitch;
IndexToSwitch = IndicesToSwitch(d);
IndexToSwitch2 = floor(Random_Nb_Elements_Per_Row(n-d)*rand)+1;
tmp = Hr(n,IndexToSwitch);
Hr(n,IndexToSwitch) = Hr(n-d,IndexToSwitch2);
Hr(n-d,IndexToSwitch2) = tmp;
end;
end;
% if Diff ~= 0;
% switch Diff;
% case 1;
% %disp('Attempt to remove cycle(s) of length 2');
% [B,In,Jn] = unique(Hr(n,1:Random_Nb_Elements_Per_Row(n)));
%
% for l = 1:Random_Nb_Elements_Per_Row(n);
% if length(find(In==l))==0;
% l_eliminate = l;
% end;
% end;
% if ~l_eliminate;
% disp('FAILURE --- Matrix is too full -- Please restart the program');
% CYCLESREMOVAL_ = FALSE_
% end;
% temp = Hr(n,l_eliminate);
% if n<M;
% l_switch = floor(Random_Nb_Elements_Per_Row(n+1)*rand)+1;
% Hr(n,l_eliminate) = Hr(n+1,l_switch);
% Hr(n+1,l_switch) = temp;
% else;
% l_switch = floor(Random_Nb_Elements_Per_Row(n-1)*rand)+1;
% Hr(n,l_eliminate) = Hr(n-1,l_switch);
% Hr(n-1,l_switch) = temp;
% end;
% case {2,3,4,5};
% [B,In,Jn] = unique(Hr(n,1:Random_Nb_Elements_Per_Row(n)));
% l_eliminate = [];
% for l = 1:Deg_Rho;
% if length(find(In==l))==0;
% l_eliminate = [l_eliminate,l];
% end;
% end;
% if length(l_eliminate) < Diff;
% disp('FAILURE --- Matrix is too full -- Please restart the program');
% CYCLESREMOVAL_ = FALSE_
% end;
%
% otherwise;
% CYCLESREMOVAL_ = FALSE_
% Diff
% %disp('Bad draw. Restart the program');
% end;
end;
%disp('Second pass for checking removal of cycle of length 2');
counter = 0;
for n = 1:M;
%if DEBUG_FLAG;
if mod(n,floor(M/100))==0;disp([num2str(round(n/M*100)),'%']);end;
%end;
Diff = length(Hr(n,1:Random_Nb_Elements_Per_Row(n)))-length(unique(Hr(n,1:Random_Nb_Elements_Per_Row(n))));
if Diff ~= 0;
counter = counter+1;
CYCLESREMOVAL_ = FALSE_;
disp('Cycle of length 2 still here. The program will automatically restart');pause(2);
end;
end;
if counter==0;
disp('Succeed. No more cycles of length 2.')
CYCLESREMOVAL_ = TRUE_;
end;
end; % end of while ~CYCLESREMOVAL_;
%disp('---------------------- Removal of cycles of length 2 done-------------------------');
if DEBUG_FLAG;
disp('---------------------- Check out the profile of Hr... ----------------------------');
profilec = zeros(1,N);
for n = 1:N;
if mod(n*10,N) == 0;disp([num2str(n*100/N),'%']);end;
[I,J] = find(Hr==n);
profilec(n) = length(I);
end;
figure(1);plot(profilec,'k-');hold on;
disp('---------------------- Check out the profile of Hr done---------------------------');
end; % end of DEBUG_FLAG;
%disp('---------------------- Generation of Hc... ---------------------------------------');
Hc = zeros(N,max(Deg_Lambda));
for n = 1:N;
%if DEBUG_FLAG;
if mod(n,floor(N/100))==0;disp([num2str(round(n/N*100)),'%']);end;
%end;
[I,J] = find(Hr==n);
Hc(n,1:length(I))=I.';
end;
%disp('---------------------- Generation of Hc done --------------------------------------');
if DEBUG_FLAG;
disp('---------------------- Check out the profile of Hc... ----------------------------');
profiler = zeros(1,N);
for n = 1:M;
if mod(n*10,M) == 0;disp([num2str(n*100/(M)),'%']);end;
[I,J] = find(Hc==n);
profiler(n) = length(I);
end;
plot(profiler,'r-');hold on;
disp('---------------------- Check out the profile of Hc done---------------------------');
end;% end of DEBUG_FLAG;
if DEBUG_FLAG;
disp('---------------------- Check the rank of H...--------------------------------------');
if N<=1152;
Hnonsparse = zeros(M,N);
for ink = 1:M;
Hnonsparse(ink,Hr(ink,:)) = 1;
end;
Hnonsparsegf = gf(Hnonsparse);
disp('H gf done');
rankH = rank(Hnonsparsegf);
disp(['rank(H,',num2str(length(Hnonsparse(:,1))),'x',num2str(length(Hnonsparse(1,:))),') = ',num2str(rankH)]);
else;
disp('Dimensions of the PCM are too large');
end;
disp('---------------------- Check the rank of H done--------------------------------------');
end;
%disp('---------------------- Printing H in file (matlab sparse format)...--------------------------------------');
if length(FileName_sparse) == 0;
FileName_sparse = ['gallager.sparse.',num2str(N),'.',num2str(KK),'.',num2str(CodeNumber),'.mat'];
end;
ii = zeros(1,sum(Nb_Elements_Per_Column));
jj = ii;
kkk = 1;
for iii=1:N;
%if DEBUG_FLAG;
if mod(iii,floor(N/100))==0;disp([num2str(round(iii/N*100)),'%']);end;
%end;
for jjj=1:Nb_Elements_Per_Column(iii);
jj(kkk) = iii;
ii(kkk) = Hc(iii,jjj);
ss = 1;
kkk = kkk+1 ;
end
end
H = sparse(ii,jj,ss,M,N);
save(FileName_sparse,'H');
%disp('---------------------- Printing H in file done -------------------------------------');