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err_coeff_pac4_parfor.m
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err_coeff_pac4_parfor.m
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N = 2^8; % Code length
R = 0.75; % Code rate
K = N * R; % code dimention: the number of information bits
design_snr_db = 4; % for the optimized code
g = [1 0 1 1 0 1 1];%[1 0 1 1];% 0 1 1 0 1 1];%[1 0 0 0 0 1 1];%[1 0 1 0 1 0 1];%
I = construct_dega(design_snr_db, N, K); % the indices of K information bits
% Rem = [56,52];%[60,58,57]; For (64,32)
% Add = [22,25];%[27,29,30];
% I0 = I;
% j = 1;
% for i = Rem
% idx = find(I==i);
% I(idx) = Add(j);
% j = j + 1;
% end
% I = sort(I);
% find_set_M1(3,[5,10],5)
tic
[d_min,A_dmin,A_dminPAC] = err_coeff(I,N,g)
toc
%set_Ki = find_Ki(7,5)
% returns the minimum distance of the code and the number of codewords with minumum distance (error coefficient)
function [dmin, A_dmin, A_dminPAC] = err_coeff(I,N,g)
d = min(sum(dec2bin(I)-'0',2));
dmin = 2^d; n = log2(N); A_dmin = 0; A_dminPAC = 0; A_dminPAC2 = 0;
B = find(sum(dec2bin(I)-'0',2)==d);
set_F = find_F(I); % F indicator
cosetsAdmin = zeros(length(B),4);
cosetsAdmin(:,1) = I(B);
for i = B' % a set of indices of elements in I, not elements of I
%i=find(I==205); % for jumoping to the test coset
Ki_size = n - d;
for x = find(dec2bin(I(i),n)-'0'==1) % support of I(i): positions of 1's in the binary representation of the sub-channel index
ii = dec2bin(bitxor(N-1,I(i)),n)-'0';
Ki_size = Ki_size + sum(ii(1:x-1));
end
%set_Kix = find_Kix(I(i),set_F,n); Ki_size = Ki_size - length(set_Kix); %For modified codes. To find rozen rows that could be member of Ki.
A_dmin = A_dmin + 2^Ki_size;
cosetsAdmin(find(B==i),2) = 2^Ki_size;
A_dminPAC = A_dminPAC + 2^Ki_size;
set_Fxi = find_Fxi(I(i),set_F,n); % elements in F that differ more than one element with I(i)
if isempty(set_Fxi)
A_dminPAC2 = A_dminPAC2 + 2^Ki_size;
continue;
end
i_lead = I(i);
max_f = max(set_Fxi);
set_KiRed = find_KiRed(i_lead,max_f,n); %reduced Ki set up to max(Fxi)
set_KiRed_gen = find_KiRed_gen(i_lead,max_f,n); %generalized
% Subtracting the removed min_weight codewords by precoding
%M_subKiRed = zeros(2^length(set_KiRed), max_f-i_lead);
%M_subKiRed = find_ones_full(i_lead,max_f,set_KiRed_gen,n);
cnt_comb = 0; cnt_comb_1 = 0; cnt_comb_2 = 0;
A_dmin_minus = 0;
A_Kif = 0;
A_dmin_minus_f = 0;
for x = 0:length(set_KiRed)
A = nchoosek(set_KiRed,x); %each row, one combination
if x==0
A=[0];
%A=[A,0];
end
%[n_combs,~] = size(A); %size(A,1)
for y = 1:size(A,1) %parfor
discounted = false;
cnt_comb = cnt_comb + 1;
u_supp = [i_lead];
J = [];
F1 = []; % the idex set of positions where u_i=1 in Ki
F1xi = []; % the idex set of positions where u_i=1 not in Ki
v = zeros(N,1); u = zeros(N,1);
cur_state = zeros(1,length(g)-1);
v(i_lead+1) = 1;
[u(i_lead+1),cur_state] = conv_1bit_nxtState(v(i_lead+1),cur_state,g); %the i-th bit first, +1 is due to starting index in MATLAB.
if A(y,:)==0
J0 = []; % different with moving J.
else
J0 = A(y,:);
end
%[M_subKiRed, ones] = find_ones(i_lead,max_f,J0,set_KiRed,M_subKiRed,n);
%ones = M_subKiRed(get_idx_MsubKiRed(J0,set_KiRed_gen),:); % retruns partial set M only for Ki, not Ki_gen.
ones = zeros(1,max_f-i_lead);
M = [];
cnt_i = 1; cnt_f = 1;
for j = i_lead+1:max_f
if set_F(j+1) == 0
if A(y,cnt_i)==j
u_supp = [u_supp j];
%ones = M_subKiRed(get_idx_MsubKiRed(J,set_KiRed_gen),:);
%ones = bitxor(ones, find_ones_Fx(i_lead,max_f,J,[j],n));
[M, ones1] = find_ones_1R(i_lead,max_f,J,M,j,n);
ones = bitxor(ones, ones1);
J = [J j];
if conv_1bit(v(j+1),cur_state,g) == 0
v(j+1) = 1;
end
%[u(j+1),cur_state] = conv_1bit_nxtState(v(j+1),cur_state,g);
if cnt_i<x
cnt_i = cnt_i + 1;
end
else
if ones(j-i_lead)==1
u_supp = [u_supp j];
if conv_1bit(v(j+1),cur_state,g) == 0
v(j+1) = 1;
end
else
if conv_1bit(v(j+1),cur_state,g) == 1
v(j+1) = 1;
end
end
% if conv_1bit(v(j+1),cur_state,g) == 1 && x>1
% if sum(dec2bin(bitxor(i_lead,bitor(j,i_lead)),n)-'0'==1)>1
% if ((length(J)>1 && ismember(j,find_set_M(i_lead,J,n)) ~= 1) || length(J)<=1)
% v(j+1) = 1;
% else
% u_supp = [u_supp j];
% end
% else
% v(j+1) = 1;
% end
% elseif sum(dec2bin(bitxor(i_lead,bitor(j,i_lead)),n)-'0'==1)>1 && x>1
% if (length(J)>1 && ismember(j,find_set_M(i_lead,J,n)) == 1)
% v(j+1) = 1;
% u_supp = [u_supp j];
% end
% end
%[u(j+1),cur_state] = conv_1bit_nxtState(v(j+1),cur_state,g);
end
[u(j+1),cur_state] = conv_1bit_nxtState(v(j+1),cur_state,g);
else
[u(j+1),cur_state] = conv_1bit_nxtState(v(j+1),cur_state,g);
if set_Fxi(cnt_f)==j
if u(j+1)==1
F1xi = [F1xi j];
u_supp = [u_supp j];
%set_M0 = find_set_M(i_lead,J,n);
%if isempty(F1) || ((length(J)>0 && ~isempty(F1)) && ismember(j,find_set_M(i_lead,J,n)) ~= 1)
if ones(j-i_lead)==0
%discounted = true;
%cnt_comb_1 = cnt_comb_1 + 1;
A_dmin_minus = A_dmin_minus + 2^(Ki_size-length(set_KiRed));
A_Kif = A_Kif + 1;
break;
end
else
if ones(j-i_lead)==1
%discounted = true;
%cnt_comb_1 = cnt_comb_1 + 1;
A_dmin_minus = A_dmin_minus + 2^(Ki_size-length(set_KiRed));
A_Kif = A_Kif + 1;
break;
end
end
if cnt_f<length(set_Fxi)
cnt_f = cnt_f + 1;
end
else
if u(j+1)==1
F1 = [F1 j];
%ones = bitxor(ones, find_ones_Fx(i_lead,max_f,J,[j],n));
[M, ones1] = find_ones_1R(i_lead,max_f,J,M,j,n);
ones = bitxor(ones, ones1);
J = [J j];
u_supp = [u_supp j];
%ones = M_subKiRed(get_idx_MsubKiRed(J,set_KiRed_gen),:);
end
end
end
end
%%{
% intersect(set_M,J) always empty?It is possible when |J|=1
% if discounted == false %&& length(J)>1 % After max_f, J might get larger by including more from F and then it might require Fxi members as well
% set_M = find_set_M(i_lead,J,n);
% F11 = union(F1,F1xi);
% %len_M = length(set_M)
% %len_M_I = length(intersect(set_M,I))
% if length(intersect(set_M,set_Fxi)) > length(F1xi) || (isempty(intersect(set_M,F1xi)) && ~isempty(F1xi)) % intersection with F
% %if length(intersect(set_M,set_Fxi)) > length(F1xi) || (isempty(intersect(set_M,F1xi)) && ~isempty(F1xi)) % intersection with F
% %if length(intersect(set_M,I))<length(set_M) &&
% %length(intersect(set_M,J)) ~= length(set_M) %
% %intersection with F, intersect(set_M,J) always empty?
% %It is possible when |J|=1
% %if nnz(set_M>max_f)==0
% A_dmin_minus_f = A_dmin_minus_f + 2^(Ki_size-length(set_KiRed));
% discounted = true;
% cnt_comb_2 = cnt_comb_2 + 1;
% %end
% end
% end
% if discounted == false
% discounted = false;
% end
end
end
%A_Kif
%set_KiRed
A_dminPAC2 = A_dminPAC2 + (2^length(set_KiRed) - A_Kif) * 2^(Ki_size-length(set_KiRed));
A_dminPAC = A_dminPAC - A_dmin_minus - A_dmin_minus_f;
cosetsAdmin(find(B==i),3) = A_dmin_minus + A_dmin_minus_f;
cosetsAdmin(find(B==i),4) = cosetsAdmin(find(B==i),2) - cosetsAdmin(find(B==i),3);
%i_lead
%Ki_size
%A_dmin_minus
%A_dmin_minus_f
%A_dminPAC
end
cosetsAdmin(:,4) = cosetsAdmin(:,2) - cosetsAdmin(:,3);
cosetsAdmin
A_dminPAC2
end
function set_Fxi = find_Fxi(index,F,n)
i = index + 2;
set_Fxi = [];
while i < 2^n
if F(i) == 1 && sum(dec2bin(bitxor(index,bitor(i-1,index)),n)-'0'==1)>1
set_Fxi = [set_Fxi, i-1];
end
i = i + 1;
end
end
function set_Kix = find_Kix(index,F,n)
i = index + 2;
set_Kix = [];
while i < 2^n
if F(i) == 1 && sum(dec2bin(bitxor(index,bitor(i-1,index)),n)-'0'==1)==1
set_Kix = [set_Kix, i-1];
end
i = i + 1;
end
end
function set_F = find_F(I) % indicator vector, not index vector
N = max(I)+1;
set_F = ones(N,1);
j=1;
for i = 1:N
if I(j)==i-1
set_F(i) = 0;
j = j + 1;
end
end
end
function set_KiRed = find_KiRed(index,max_Fxi,n)
set_KiRed = [];
Ki = find_Ki(index,n);
for j = 1:length(Ki)
if Ki(j) < max_Fxi
set_KiRed = [set_KiRed, Ki(j)];
end
end
end
function set_KiRed_gen = find_KiRed_gen(i_lead,max_f,n)
set_KiRed_gen = [];
for j = i_lead+1:max_f
if sum(dec2bin(bitxor(i_lead,bitor(j,i_lead)),n)-'0'==1) == 1
set_KiRed_gen = [set_KiRed_gen, j];
end
end
end
function set_Ki = find_Ki(index,n)
set_Ki = [];
supp_index = find_supp(index,n);
supp_zeros = find(dec2bin(bitxor(2^n-1,index),n)-'0'==1); %complement of supp
%Ki_size = n - length(supp_index); %due to signle-bit addition
index_bin = dec2bin(index, n);
for j = supp_zeros
index_add = index_bin;
index_add(j) = '1';
set_Ki = [set_Ki, bin2dec(index_add)];
end
for x = supp_index
for j = supp_zeros
if j<x
index_leftSW = index_bin;
index_leftSW(x) = '0';
index_leftSW(j) = '1';
set_Ki = [set_Ki, bin2dec(index_leftSW)];
end
end
end
set_Ki = sort(set_Ki);
end
function M = find_set_M(index,J,n)
M = [];
supp_index = find_supp(index,n);
supp_zeros = find(dec2bin(bitxor(2^n-1,index),n)-'0'==1); %complement of supp
%Sm_Si = set(supp_index)
Sm_Ti = supp_zeros;
for s = 2:length(J)
row_sets = nchoosek(J, s);
for row_idx = 1:size(row_sets,1)
valid_set_for_M = true;
Sm_S = supp_index;
Sm_T = [];
column_elmnt_cnt = zeros(length(supp_zeros),1);
for r = row_sets(row_idx,:)
r_bin = dec2bin(r,n);
supp_r = find_supp(r,n);
Sm_S = intersect(Sm_S, supp_r);
if ~isempty(intersect(Sm_T,intersect(Sm_Ti, supp_r)))
valid_set_for_M = false;
break;
end
Sm_T = union(Sm_T,intersect(Sm_Ti, supp_r));
cnt=1;
for t = supp_zeros
if r_bin(t)=='1' %%%%%%%% 1 WAS INCORRECT. %%%%%%%%%%
column_elmnt_cnt(cnt) = column_elmnt_cnt(cnt) + 1;
if column_elmnt_cnt(cnt) > 1
valid_set_for_M = false;
break;
end
end
cnt = cnt + 1;
end
if valid_set_for_M == false
break;
end
end
if valid_set_for_M == true
Sm = union(Sm_T,Sm_S);
M = [M supp2dec(Sm,n)];
end
end
end
% Removeing the repeated elements by even times.
M1 = unique(M);
count_M = histc(M,M1);
indices = [];
for cnt = 1:length(count_M)
if mod(count_M(cnt),2) == 0
indices = [indices cnt];
end
end
M1(indices) = [];
M = M1;
end
%%
function [M_subKiRed,ones] = find_ones(i_lead,max_f,J,set_KiRed,M_subKiRed,n)
ones = zeros(1,max_f-i_lead);
x = size(J,1);
if x == 2
M = find_set_M1(i_lead,J,n);
if ~isempty(M)
ones(1,M(1)-i_lead) = 1;
end
elseif x > 2
M = find_set_M1(i_lead,J,n);
if ~isempty(M)
ones(1,M(1)-i_lead) = 1;
end
B = nchoosek(J,x-1);
for z = 1:size(B,1)
ones = bitxor(ones, M_subKiRed(get_idx_MsubKiRed(B(z,:),set_KiRed),:));
end
M_subKiRed(get_idx_MsubKiRed(J,set_KiRed),:) = ones;
end
for z=1:x
ones(1,J(z)-i_lead) = 1;
end
end
function M_subKiRed = find_ones_full0(i_lead,max_f,set_KiRed_gen,n)
M_subKiRed = zeros(2^length(set_KiRed_gen), max_f-i_lead);
for x = 2:length(set_KiRed_gen)
A = nchoosek(set_KiRed_gen,x); %each row, one combination
for y = 1:size(A,1)
J = A(y,:);
%[M_subKiRed, ones] = find_ones(i_lead,max_f,J0,set_KiRed_gen,M_subKiRed,n);
ones = zeros(1,max_f-i_lead);
%ones = zeros(1,2^n);
if x == 2
M = find_set_M1(i_lead,J,n);
if ~isempty(M) && M(1) <= max_f
ones(1,M(1)-i_lead) = 1;
%M_subKiRed(get_idx_MsubKiRed(J,set_KiRed_gen),:) = ones;
end
elseif x > 2
M = find_set_M1(i_lead,J,n);
if ~isempty(M) && M(1) <= max_f
ones(1,M(1)-i_lead) = 1;
end
for xx=x-1:2
%B = nchoosek(J,x-1);
B = nchoosek(J,xx);
for z = 1:size(B,1)
ones = bitxor(ones, M_subKiRed(get_idx_MsubKiRed(B(z,:),set_KiRed_gen),:));
end
end
end
M_subKiRed(get_idx_MsubKiRed(J,set_KiRed_gen),:) = ones;
%for z=1:x
%ones(1,J(z)-i_lead) = 1;
%end
end
end
%%%%%%%%%%%%
end
function M_subKiRed = find_ones_full(i_lead,max_f,set_KiRed_gen,n)
M_subKiRed_base = zeros(2^length(set_KiRed_gen), max_f-i_lead);
M_subKiRed = zeros(2^length(set_KiRed_gen), max_f-i_lead);
for x = 2:length(set_KiRed_gen)
A = nchoosek(set_KiRed_gen,x); %each row, one combination
for y = 1:size(A,1)
J = A(y,:);
%[M_subKiRed, ones] = find_ones(i_lead,max_f,J0,set_KiRed_gen,M_subKiRed,n);
ones = zeros(1,max_f-i_lead);
%ones = zeros(1,2^n);
M = find_set_M1(i_lead,J,n);
if ~isempty(M) && M(1) <= max_f
ones(1,M(1)-i_lead) = 1;
%M_subKiRed(get_idx_MsubKiRed(J,set_KiRed_gen),:) = ones;
end
M_subKiRed_base(get_idx_MsubKiRed(J,set_KiRed_gen),:) = ones;
if x == 2
M_subKiRed(get_idx_MsubKiRed(J,set_KiRed_gen),:) = ones;
end
end
end
for x = 3:length(set_KiRed_gen)
A = nchoosek(set_KiRed_gen,x); %each row, one combination
for y = 1:size(A,1)
J = A(y,:);
%[M_subKiRed, ones] = find_ones(i_lead,max_f,J0,set_KiRed_gen,M_subKiRed,n);
ones = zeros(1,max_f-i_lead);
M = find_set_M1(i_lead,J,n);
if ~isempty(M) && M(1) <= max_f
ones(1,M(1)-i_lead) = 1;
end
for xx=x-1:-1:2
%B = nchoosek(J,x-1);
B = nchoosek(J,xx);
for z = 1:size(B,1)
ones = bitxor(ones, M_subKiRed_base(get_idx_MsubKiRed(B(z,:),set_KiRed_gen),:));
end
end
M_subKiRed(get_idx_MsubKiRed(J,set_KiRed_gen),:) = ones;
%for z=1:x
%ones(1,J(z)-i_lead) = 1;
%end
end
end
%%%%%%%%%%%%
end
function ones = find_ones_Fx(i_lead,max_f,J,F1,n)
ones = zeros(1,max_f-i_lead);
for x = 1:length(F1)
A = nchoosek(F1,x); %each row, one combination
for y = 1:size(A,1)
F = A(y,:);
for xx=1:length(J)
B = nchoosek(J,xx);
for z = 1:size(B,1)
JF = union(B(z,:),F);
M = find_set_M1(i_lead,JF,n);
if ~isempty(M) && M(1) <= max_f
ones(1,M(1)-i_lead) = bitxor(ones(1,M(1)-i_lead), 1);
end
end
end
end
end
end
function [M, ones] = find_ones_1R(i_lead,max_f,J,M,j,n) %Progressively
ones = zeros(1,max_f-i_lead);
for x=1:length(M)
%Mj = union(M(x),j);
m = find_set_M1R(i_lead,M(x),j,n);
if m>0 && m <= max_f
M = [M m]; %Make sure M will not have a repetitive elements. It will cancelled in the next line anyways.
ones(1,m-i_lead) = bitxor(ones(1,m-i_lead), 1);
end
end
for x=1:length(J)
Jj = union(J(x),j);
m = find_set_M1(i_lead,Jj,n);
if m>0 && m <= max_f
M = [M m];
ones(1,m-i_lead) = bitxor(ones(1,m-i_lead), 1);
end
end
end
function m = find_set_M1(index,J,n)
%M = [];
m = 0;
supp_index = find_supp(index,n);
supp_zeros = find(dec2bin(bitxor(2^n-1,index),n)-'0'==1); %complement of supp
%Sm_Si = set(supp_index)
Sm_Ti = supp_zeros;
%for s = 2:length(J)
row_sets = J; %nchoosek(J, s);
%for row_idx = 1:size(row_sets,1)
valid_set_for_M = true;
Sm_S = supp_index;
Sm_T = [];
%column_elmnt_cnt = zeros(length(supp_zeros),1);
for r = row_sets %(row_idx,:)
%r_bin = dec2bin(r,n);
supp_r = find_supp(r,n);
Sm_S = intersect(Sm_S, supp_r);
if ~isempty(intersect(Sm_T,intersect(Sm_Ti, supp_r))) %distinctness condition
valid_set_for_M = false; % No need to set M.
break;
end
Sm_T = union(Sm_T,intersect(Sm_Ti, supp_r));
%{
cnt=0;
for t = supp_zeros % The difference with the upper if block?
if r_bin(t)=='1'
column_elmnt_cnt(cnt) = column_elmnt_cnt(cnt) + 1;
if column_elmnt_cnt(cnt) > 1 % No memebr of J would satisfy this condition.
valid_set_for_M = false; % No need to set M.
break;
end
end
cnt = cnt + 1;
end
%}
%if valid_set_for_M == false
%break;
%end
end
if valid_set_for_M == true
Sm = union(Sm_T,Sm_S);
m = supp2dec(Sm,n);
end
%end
%end
% Removeing the repeated elements by even times.
%{
M1 = unique(M); %It should be done with the previous summation on level elements and this Sm.
count_M = histc(M,M1);
indices = [];
for cnt = 1:length(count_M)
if mod(count_M(cnt),2) == 0
indices = [indices cnt];
end
end
M1(indices) = [];
M = M1;
%}
end
function m1 = find_set_M1R(index,m,j,n)
%M = [];
m1 = 0;
supp_index = find_supp(index,n);
supp_zeros = find(dec2bin(bitxor(2^n-1,index),n)-'0'==1); %complement of supp
Ti = supp_zeros;
Si = supp_index;
supp_j = find_supp(j,n);
supp_m = find_supp(m,n);
Sm_S = intersect(intersect(Si, supp_j), supp_m);
Tj = intersect(Ti, supp_j);
if isempty(intersect(intersect(Ti, supp_m), Tj)) %distinctness condition
Sm_T = union(Tj,intersect(Ti, supp_m));
Sm = union(Sm_T,Sm_S);
m1 = supp2dec(Sm,n);
end
end
function supp = find_supp(i,n)
supp = find(dec2bin(i,n)-'0'==1);
end
function decimal = supp2dec(indices,n)
decimal = 0;
for i = indices
decimal = decimal + 2^(n-i);
end
end
function decimal = get_idx_MsubKiRed(row_indices,KiRed)
%n = size(KiRed,1);
decimal = 0;
for i = row_indices
decimal = decimal + 2^(find(KiRed==i)-1);
end
decimal = decimal + 1;
end
%%
% retruns Mean-LLRs (a measure for sub-channels' reliability) obtained from Density Evolution by Gaussian Approximation (DEGA)
function I = construct_dega(design_snr_db, N, K)
mllr = zeros(N,1);
sigma_sq = 1/(2*K/N*power(10,design_snr_db/10));
mllr(1) = 2/sigma_sq;
for level = 1:log2(N)
B = 2^level;
for j = 1:B / 2
T = mllr(j);
mllr(j) = calc_phi_inv(T);
mllr(B / 2 + j) = 2 * T;
end
end
mask = zeros(N,3);
nat = bitrevorder(0:N-1);
for i = 1:N
mask(i,:) = [nat(i), mllr(i), 1];
end
% sort sub-channels by mllr
mask = sortrows(mask,2); %direction: ascend (default)
% set info bits to 1 for sub-channels with K largest mllr values
for i = 1:N-K
mask(i,3) = 0;
end
% sort channels with respect to index (in bitreversal order; line 42
mask = sortrows(mask,1); %direction: ascend (default)
I = find(mask(:,3)==1)-1;
end
% returns Phi inverse based on piece-wise linear approximation
function phi_inv = calc_phi_inv(x)
if (x>12)
phi_inv = 0.9861 * x - 2.3152;
elseif (x<=12 && x>3.5)
phi_inv = x*(0.009005 * x + 0.7694) - 0.9507;
elseif (x<=3.5 && x>1)
phi_inv = x*(0.062883*x + 0.3678)- 0.1627;
else
phi_inv = x*(0.2202*x + 0.06448);
end
end
function u = conv_1bit(in_bit,cur_state,g)
u = in_bit * g(1); % by convention, we have always g(1)=1
for i = 2:length(g)
if g(i)==1
u = bitxor(u,cur_state(i-1));
end
end
end
function [u,state] = conv_1bit_nxtState(in_bit,cur_state,g)
u = in_bit * g(1); % by convention, we have always g(1)=1
for i = 2:length(g)
if g(i)==1
u = bitxor(u,cur_state(i-1));
end
end
m = length(cur_state);
if in_bit == 0
state = [0,cur_state(1:m-1)];
else
state = [1,cur_state(1:m-1)];
end
end