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ldpc_encode_optimized.m
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ldpc_encode_optimized.m
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% 5g ldpc encoding
% input: s, bit sequence of dimension K * 1
% output: encoded_bits, bit sequence
% reference: 3GPP TS 38.212 section 5.3.2
% author: Xiao, Shaoning 萧少宁
% license: MIT
function [encoded_bits, H, Z_c, encoded_bits_original] = ldpc_encode_optimized(s, base_graph_index)
K = length(s);
encoded_bits = zeros(3*K, 1);
if base_graph_index == 1
a = 4;
b = 22;
c = 26;
d = 42;
e = 46;
z = K/b;
Z_c = z;
N = 66 * Z_c;
z = K/b;
set_index = lifting_size_table_lookup(z);
load parity_check_matrices_protocol_1
BG = parity_check_matrices_protocol_1(:, :, set_index); %#ok<NODEF>
elseif base_graph_index == 2
a = 4;
b = 10;
c = 14;
d = 38;
e = 42;
z = K/b;
Z_c = z;
N = 50 * Z_c;
set_index = lifting_size_table_lookup(z);
load parity_check_matrices_protocol_2
BG = parity_check_matrices_protocol_2(:, :, set_index); %#ok<NODEF>
else
error('wrong base graph index in ldpc encoding.');
end
BG(BG ~= -1) = mod(BG(BG ~= -1), Z_c);
for k = (2*Z_c):(K-1)
if s(k+1) ~= -1
encoded_bits(k-2*Z_c+1) = s(k+1);
else
s(k+1) = 0;
encoded_bits(k-2*Z_c+1) = -1;
end
end
% set_index = lifting_size_table_lookup(Z_c);
% BG = parity_check_matrices_protocol(:, :, set_index);
A_prime = BG(1:a, 1:b);
B_prime = BG(1:a, (b+1):c);
C_prime = BG((a+1):e, 1:b);
D_prime = BG((a+1):e, (b+1):c);
z = Z_c;
a_row_list = [];
a_column_list = [];
a_none_zero_entry_number = 0;
for row_index = 1:a
for column_index = 1:b
if A_prime(row_index, column_index) ~= -1
a_none_zero_entry_number = a_none_zero_entry_number + 1;
a_row_list = [a_row_list, (row_index-1)*z+1:row_index*z];
a_column_list = [a_column_list, (column_index-1)*z+1+mod(A_prime(row_index, column_index), z):column_index*z, (column_index-1)*z+1:(column_index-1)*z+mod(A_prime(row_index, column_index), z)];
end
end
end
A = sparse(a_row_list, a_column_list, ones(1, z * a_none_zero_entry_number), z * a, z * b);
b_row_list = [];
b_column_list = [];
b_none_zero_entry_number = 0;
for row_index = 1:a
for column_index = 1:a
if B_prime(row_index, column_index) ~= -1
b_none_zero_entry_number = b_none_zero_entry_number + 1;
b_row_list = [b_row_list, (row_index-1)*z+1:row_index*z];
b_column_list = [b_column_list, (column_index-1)*z+1+mod(B_prime(row_index, column_index), z):column_index*z, (column_index-1)*z+1:(column_index-1)*z+mod(B_prime(row_index, column_index), z)];
end
end
end
B = sparse(b_row_list, b_column_list, ones(1, z * b_none_zero_entry_number), z * a, z * a);
c_row_list = [];
c_column_list = [];
c_none_zero_entry_number = 0;
for row_index = 1:d
for column_index = 1:b
if C_prime(row_index, column_index) ~= -1
c_none_zero_entry_number = c_none_zero_entry_number + 1;
c_row_list = [c_row_list, (row_index-1)*z+1:row_index*z];
c_column_list = [c_column_list, (column_index-1)*z+1+mod(C_prime(row_index, column_index), z):column_index*z, (column_index-1)*z+1:(column_index-1)*z+mod(C_prime(row_index, column_index), z)];
end
end
end
C = sparse(c_row_list, c_column_list, ones(1, z * c_none_zero_entry_number), z * d, z * b);
d_row_list = [];
d_column_list = [];
d_none_zero_entry_number = 0;
for row_index = 1:d
for column_index = 1:a
if D_prime(row_index, column_index) ~= -1
d_none_zero_entry_number = d_none_zero_entry_number + 1;
d_row_list = [d_row_list, (row_index-1)*z+1:row_index*z];
d_column_list = [d_column_list, (column_index-1)*z+1+mod(D_prime(row_index, column_index), z):column_index*z, (column_index-1)*z+1:(column_index-1)*z+mod(D_prime(row_index, column_index), z)];
end
end
end
D = sparse(d_row_list, d_column_list, ones(1, z * d_none_zero_entry_number), z * d, z * a);
B_inv = spalloc(a*z, a*z, 20*z);
if (base_graph_index == 1) && (set_index ~= 7)
B_inv(1:z, 1:z) = speye(z);
B_inv(1:z, 1+z:2*z) = speye(z);
B_inv(1:z, 1+2*z:3*z) = speye(z);
B_inv(1:z, 1+3*z:4*z) = speye(z);
B_inv(1+z:2*z, 1:z) = speye(z) + sparse(1:z, [2:z, 1], ones(1, z), z, z);
B_inv(1+z:2*z, 1+z:2*z) = sparse(1:z, [2:z, 1], ones(1, z), z, z);
B_inv(1+z:2*z, 1+2*z:3*z) = sparse(1:z, [2:z, 1], ones(1, z), z, z);
B_inv(1+z:2*z, 1+3*z:4*z) = sparse(1:z, [2:z, 1], ones(1, z), z, z);
B_inv(1+2*z:3*z, 1:z) = sparse(1:z, [2:z, 1], ones(1, z), z, z);
B_inv(1+2*z:3*z, 1+z:2*z) = sparse(1:z, [2:z, 1], ones(1, z), z, z);
B_inv(1+2*z:3*z, 1+2*z:3*z) = speye(z) + sparse(1:z, [2:z, 1], ones(1, z), z, z);
B_inv(1+2*z:3*z, 1+3*z:4*z) = speye(z) + sparse(1:z, [2:z, 1], ones(1, z), z, z);
B_inv(1+3*z:4*z, 1:z) = sparse(1:z, [2:z, 1], ones(1, z), z, z);
B_inv(1+3*z:4*z, 1+z:2*z) = sparse(1:z, [2:z, 1], ones(1, z), z, z);
B_inv(1+3*z:4*z, 1+2*z:3*z) = sparse(1:z, [2:z, 1], ones(1, z), z, z);
B_inv(1+3*z:4*z, 1+3*z:4*z) = speye(z) + sparse(1:z, [2:z, 1], ones(1, z), z, z);
elseif (base_graph_index == 2) && ((set_index ~= 4) && (set_index ~= 8))
B_inv(1:z, 1:z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1:z, 1+z:2*z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1:z, 1+2*z:3*z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1:z, 1+3*z:4*z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+z:2*z, 1:z) = speye(z) + sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+z:2*z, 1+z:2*z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+z:2*z, 1+2*z:3*z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+z:2*z, 1+3*z:4*z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+2*z:3*z, 1:z) = speye(z) + sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+2*z:3*z, 1+z:2*z) = speye(z) + sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+2*z:3*z, 1+2*z:3*z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+2*z:3*z, 1+3*z:4*z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+3*z:4*z, 1:z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+3*z:4*z, 1+z:2*z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+3*z:4*z, 1+2*z:3*z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+3*z:4*z, 1+3*z:4*z) = speye(z) + sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
elseif (base_graph_index == 1) && (z == 208)
B_inv(1:z, 1:z) = sparse(circshift(eye(208), 105));
B_inv(1:z, 1+z:2*z) = sparse(circshift(eye(208), 105));
B_inv(1:z, 1+2*z:3*z) = sparse(circshift(eye(208), 105));
B_inv(1:z, 1+3*z:4*z) = sparse(circshift(eye(208), 105));
B_inv(1+z:2*z, 1:z) = speye(208) + sparse(circshift(eye(208), 105));
B_inv(1+z:2*z, 1+z:2*z) = sparse(circshift(eye(208), 105));
B_inv(1+z:2*z, 1+2*z:3*z) = sparse(circshift(eye(208), 105));
B_inv(1+z:2*z, 1+3*z:4*z) = sparse(circshift(eye(208), 105));
B_inv(1+2*z:3*z, 1:z) = sparse(circshift(eye(208), 105));
B_inv(1+2*z:3*z, 1+z:2*z) = sparse(circshift(eye(208), 105));
B_inv(1+2*z:3*z, 1+2*z:3*z) = speye(208) + sparse(circshift(eye(208), 105));
B_inv(1+2*z:3*z, 1+3*z:4*z) = speye(208) + sparse(circshift(eye(208), 105));
B_inv(1+3*z:4*z, 1:z) = sparse(circshift(eye(208), 105));
B_inv(1+3*z:4*z, 1+z:2*z) = sparse(circshift(eye(208), 105));
B_inv(1+3*z:4*z, 1+2*z:3*z) = sparse(circshift(eye(208), 105));
B_inv(1+3*z:4*z, 1+3*z:4*z) = speye(208) + sparse(circshift(eye(208), 105));
elseif (base_graph_index == 1) && ((z ~= 208) && (set_index == 7))
B_inv(1:z, 1:z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1:z, 1+z:2*z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1:z, 1+2*z:3*z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1:z, 1+3*z:4*z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+z:2*z, 1:z) = speye(z) + sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+z:2*z, 1+z:2*z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+z:2*z, 1+2*z:3*z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+z:2*z, 1+3*z:4*z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+2*z:3*z, 1:z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+2*z:3*z, 1+z:2*z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+2*z:3*z, 1+2*z:3*z) = speye(z) + sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+2*z:3*z, 1+3*z:4*z) = speye(z) + sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+3*z:4*z, 1:z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+3*z:4*z, 1+z:2*z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+3*z:4*z, 1+2*z:3*z) = sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
B_inv(1+3*z:4*z, 1+3*z:4*z) = speye(z) + sparse(1:z, [z, 1:(z-1)], ones(1, z), z, z);
elseif (base_graph_index == 2) && ((set_index == 4) || (set_index == 8))
B_inv(1:z, 1:z) = speye(z);
B_inv(1:z, 1+z:2*z) = speye(z);
B_inv(1:z, 1+2*z:3*z) = speye(z);
B_inv(1:z, 1+3*z:4*z) = speye(z);
B_inv(1+z:2*z, 1:z) = speye(z) + sparse(1:z, [2:z, 1], ones(1, z), z, z);
B_inv(1+z:2*z, 1+z:2*z) = sparse(1:z, [2:z, 1], ones(1, z), z, z);
B_inv(1+z:2*z, 1+2*z:3*z) = sparse(1:z, [2:z, 1], ones(1, z), z, z);
B_inv(1+z:2*z, 1+3*z:4*z) = sparse(1:z, [2:z, 1], ones(1, z), z, z);
B_inv(1+2*z:3*z, 1:z) = speye(z) + sparse(1:z, [2:z, 1], ones(1, z), z, z);
B_inv(1+2*z:3*z, 1+z:2*z) = speye(z) + sparse(1:z, [2:z, 1], ones(1, z), z, z);
B_inv(1+2*z:3*z, 1+2*z:3*z) = sparse(1:z, [2:z, 1], ones(1, z), z, z);
B_inv(1+2*z:3*z, 1+3*z:4*z) = sparse(1:z, [2:z, 1], ones(1, z), z, z);
B_inv(1+3*z:4*z, 1:z) = sparse(1:z, [2:z, 1], ones(1, z), z, z);
B_inv(1+3*z:4*z, 1+z:2*z) = sparse(1:z, [2:z, 1], ones(1, z), z, z);
B_inv(1+3*z:4*z, 1+2*z:3*z) = sparse(1:z, [2:z, 1], ones(1, z), z, z);
B_inv(1+3*z:4*z, 1+3*z:4*z) = speye(z) + sparse(1:z, [2:z, 1], ones(1, z), z, z);
end
s = s(:);
p_1 = mod(B_inv * (A * s), 2);
p_2 = mod(C * s + D * p_1, 2);
w = [p_1; p_2];
for k = K:(N+2*Z_c-1)
encoded_bits(k-2*Z_c+1) = w(k-K+1);
end
H = [A, B, spalloc(a*z, d*z, 0); C, D, speye(d*z)];
encoded_bits_original = [s; w];
% mod(H * [s; p_1; p_2]) = 0
clear A
clear B
clear C
clear D
clear B_inv
clear A_prime
clear B_prime
clear C_prime
clear D_prime
end