void print_bitstring(unsigned char * _x,
unsigned char _n)
{
unsigned int i;
// compute number of elements in _x
div_t d = div(_n, 8);
unsigned int N = d.quot + (d.rem ? 1 : 0);
// print leader
printf(" ");
if (d.rem == 0) printf(" ");
for (i=0; i<8-d.rem-1; i++)
printf(" ");
// print bitstring
for (i=0; i<N; i++) {
if (i==0 && d.rem)
print_bitstring_short(_x[i], d.rem);
else
print_bitstring_short(_x[i], 8);
printf(" ");
}
printf("\n");
}
int main(int argc, char*argv[])
{
unsigned int i;
// error vector [22 x 1]
unsigned char err[3] = {0x00, 0x0000, 0x0001};
// original message [16 x 1]
unsigned char m[2] = {0x0000, 0x0001};
m[0] = rand() & 0xffff;
m[1] = rand() & 0xffff;
// derived values
unsigned char v[3]; // encoded/transmitted message
unsigned char e[3]; // error vector
unsigned char r[3]; // received vector
unsigned char s; // syndrome vector
unsigned char e_hat[3] = {0,0,0}; // estimated error vector
unsigned char v_hat[3]; // estimated transmitted message
unsigned char m_hat[2]; // estimated original message
#if 0
// print P matrix
printf("P : \n");
print_bitstring(&P[ 0],16);
print_bitstring(&P[ 2],16);
print_bitstring(&P[ 4],16);
print_bitstring(&P[ 6],16);
print_bitstring(&P[ 8],16);
print_bitstring(&P[10],16);
#endif
// original message
printf("m (original message): ");
print_bitstring(m,16);
// compute encoded/transmitted message: v = m*G
v[0] = 0;
for (i=0; i<6; i++) {
v[0] <<= 1;
unsigned int p = liquid_c_ones[P[2*i+0] & m[0]] +
liquid_c_ones[P[2*i+1] & m[1]];
printf("p = %u\n", p);
v[0] |= p & 0x01;
}
v[1] = m[0];
v[2] = m[1];
printf("v (encoded message): ");
print_bitstring(v,22);
// use pre-determined error vector
e[0] = err[0];
e[1] = err[1];
e[2] = err[2];
printf("e (error vector): ");
print_bitstring(e,22);
// compute received vector: r = v + e
r[0] = v[0] ^ e[0];
r[1] = v[1] ^ e[1];
r[2] = v[2] ^ e[2];
printf("r (received vector): ");
print_bitstring(r,22);
// compute syndrome vector, s = r*H^T = ( H*r^T )^T
s = 0;
for (i=0; i<6; i++) {
s <<= 1;
unsigned int p =
( (r[0] & (1<<(6-i-1))) ? 1 : 0 )+
liquid_count_ones(P[2*i+0] & r[1]) +
liquid_count_ones(P[2*i+1] & r[2]);
//printf("p = %u\n", p);
s |= p & 0x01;
}
printf("s (syndrome vector): ");
print_bitstring(&s,6);
// compute weight of s
unsigned int ws = liquid_count_ones(s);
printf("weight(s) = %u\n", ws);
if (ws == 0) {
printf("no errors detected\n");
} else {
// estimate error location
unsigned char e_test[3] = {0x00, 0x0000, 0x0001};
int syndrome_match = 0;
// TODO : these can be pre-computed
unsigned int n;
for (n=0; n<22; n++) {
// compute syndrome
unsigned int s_test = 0;
for (i=0; i<6; i++) {
s_test <<= 1;
unsigned int p =
( (e_test[0] & (1<<(6-i-1))) ? 1 : 0 )+
liquid_count_ones(P[2*i+0] & e_test[1]) +
liquid_count_ones(P[2*i+1] & e_test[2]);
s_test |= p & 0x01;
}
#if 1
// print results
//printf("e_test:"); print_bitstring(e_test, 72);
printf("%3u : e = ", n);
print_bitstring_short(e_test[0],6); printf(" ");
print_bitstring_short(e_test[1],8); printf(" ");
print_bitstring_short(e_test[2],8); printf(" ");
printf(", s = ");
print_bitstring_short(s_test,6);
if (s == s_test) printf(" *");
printf("\n");
#else
// print output array (secded2216_syndrome_w1[])
printf("0x%.2x\n", s_test);
#endif
if (s == s_test) {
memmove(e_hat, e_test, sizeof(e_test));
syndrome_match = 1;
}
// shift e_test
e_test[0] = (e_test[0] << 1) | ((e_test[1] & 0x80) ? 1 : 0);
e_test[1] = (e_test[1] << 1) | ((e_test[2] & 0x80) ? 1 : 0);
e_test[2] <<= 1;
}
if (syndrome_match) {
printf("syndrome match!\n");
} else {
printf("no syndrome match; expected multiple errors\n");
}
}
// compute estimated transmitted message: v_hat = r + e_hat
printf("e-hat (estimated error):");
print_bitstring(e_hat,22);
printf("v-hat (estimated tx): ");
v_hat[0] = r[0] ^ e_hat[0];
v_hat[1] = r[1] ^ e_hat[1];
v_hat[2] = r[2] ^ e_hat[2];
print_bitstring(v_hat,22);
// compute estimated original message: (last 16 bits of encoded message)
m_hat[0] = v_hat[1];
m_hat[1] = v_hat[2];
printf("m-hat (estimated orig.):");
print_bitstring(m_hat,16);
// compute errors between v, v_hat
unsigned int num_errors_encoded = count_bit_errors(v[0], v_hat[0]) +
count_bit_errors(v[1], v_hat[1]) +
count_bit_errors(v[2], v_hat[2]);
printf("decoding errors (encoded) : %2u / 22\n", num_errors_encoded);
// compute errors between m, m_hat
unsigned int num_errors_decoded = count_bit_errors(m[0], m_hat[0]) +
count_bit_errors(m[1], m_hat[1]);
printf("decoding errors (original) : %2u / 16\n", num_errors_decoded);
return 0;
}
int main(int argc, char*argv[])
{
unsigned int i;
// error vector [72 x 1]
unsigned char e[9] = {0,0,0,0,0,0,0,0,2};
// original message [64 x 1]
unsigned char m[8] = {0,0,0,0,0,0,0,1};
// derived values
unsigned char v[9]; // encoded/transmitted message
unsigned char r[9]; // received vector
unsigned char s; // syndrome vector
unsigned char v_hat[9]; // estimated transmitted message
unsigned char m_hat[8]; // estimated original message
// original message
printf("m (original message):\n ");
print_bitstring(m,64);
// compute encoded/transmitted message: v = m*G
v[0] = 0;
for (i=0; i<8; i++) {
v[0] <<= 1;
unsigned int p = liquid_c_ones[ P[8*i+0] & m[0] ] +
liquid_c_ones[ P[8*i+1] & m[1] ] +
liquid_c_ones[ P[8*i+2] & m[2] ] +
liquid_c_ones[ P[8*i+3] & m[3] ] +
liquid_c_ones[ P[8*i+4] & m[4] ] +
liquid_c_ones[ P[8*i+5] & m[5] ] +
liquid_c_ones[ P[8*i+6] & m[6] ] +
liquid_c_ones[ P[8*i+7] & m[7] ];
//printf("p = %u\n", p);
v[0] |= p & 0x01;
}
for (i=0; i<8; i++)
v[i+1] = m[i];
printf("v (encoded/transmitted message):\n");
print_bitstring(v,72);
// use pre-determined error vector
printf("e (error vector):\n");
print_bitstring(e,72);
// compute received vector: r = v + e
for (i=0; i<9; i++)
r[i] = v[i] ^ e[i];
printf("r (received vector):\n");
print_bitstring(r,72);
// compute syndrome vector, s = r*H^T = ( H*r^T )^T
s = 0;
for (i=0; i<8; i++) {
s <<= 1;
unsigned int p =
( (r[0] & (1<<(8-i-1))) ? 1 : 0 )+
liquid_c_ones[ P[8*i+0] & r[1] ] +
liquid_c_ones[ P[8*i+1] & r[2] ] +
liquid_c_ones[ P[8*i+2] & r[3] ] +
liquid_c_ones[ P[8*i+3] & r[4] ] +
liquid_c_ones[ P[8*i+4] & r[5] ] +
liquid_c_ones[ P[8*i+5] & r[6] ] +
liquid_c_ones[ P[8*i+6] & r[7] ] +
liquid_c_ones[ P[8*i+7] & r[8] ];
printf("p = %u\n", p);
s |= p & 0x01;
}
printf("s (syndrome vector):\n");
print_bitstring(&s,8);
// compute weight of s
unsigned int ws = liquid_count_ones(s);
printf("w(s) = %u\n", ws);
// estimated error vector
unsigned char e_hat[9] = {0,0,0,0,0,0,0,0,0};
if (ws == 0) {
printf("no errors detected\n");
} else {
// estimate error location
int syndrome_match = 0;
// TODO : these can be pre-computed
unsigned int n;
for (n=0; n<72; n++) {
// compute syndrome
unsigned char e_test[9] = {0,0,0,0,0,0,0,0,0};
unsigned char s_hat = 0;
div_t d = div(n,8);
e_test[9-d.quot-1] = 1 << d.rem;
for (i=0; i<8; i++) {
s_hat <<= 1;
unsigned int p =
( (e_test[0] & (1<<(8-i-1))) ? 1 : 0 )+
liquid_c_ones[ P[8*i+0] & e_test[1] ] +
liquid_c_ones[ P[8*i+1] & e_test[2] ] +
liquid_c_ones[ P[8*i+2] & e_test[3] ] +
liquid_c_ones[ P[8*i+3] & e_test[4] ] +
liquid_c_ones[ P[8*i+4] & e_test[5] ] +
liquid_c_ones[ P[8*i+5] & e_test[6] ] +
liquid_c_ones[ P[8*i+6] & e_test[7] ] +
liquid_c_ones[ P[8*i+7] & e_test[8] ];
s_hat |= p & 0x01;
}
// print results
//printf("e_test:"); print_bitstring(e_test, 72);
printf("%2u e=", n);
for (i=0; i<9; i++) {
print_bitstring_short(e_test[i],8);
printf(" ");
}
printf("s=");
print_bitstring_short(s_hat,8);
if (s == s_hat) printf("*");
printf("\n");
if (s == s_hat) {
memmove(e_hat, e_test, 9*sizeof(unsigned char));
syndrome_match = 1;
}
}
if (syndrome_match) {
printf("syndrome match!\n");
} else {
printf("no syndrome match; expected multiple errors\n");
}
}
// compute estimated transmitted message: v_hat = r + e_hat
printf("e-hat (estimated error vector):\n");
print_bitstring(e_hat,72);
printf("v-hat (estimated transmitted vector):\n");
for (i=0; i<9; i++)
v_hat[i] = r[i] ^ e_hat[i];
print_bitstring(v_hat,72);
//print_bitstring(v, 72);
// compute errors between v, v_hat
unsigned int num_errors_encoded = count_bit_errors_array(v, v_hat, 9);
printf("decoding errors (encoded) : %2u / 72\n", num_errors_encoded);
// compute estimated original message: (last 64 bits of encoded message)
for (i=0; i<9; i++)
m_hat[i] = v_hat[i+1];
printf("m-hat (estimated original vector):\n ");
print_bitstring(m_hat,64);
//print_bitstring(m, 64);
// compute errors between m, m_hat
unsigned int num_errors_decoded = count_bit_errors_array(m, m_hat, 8);
printf("decoding errors (original) : %2u / 64\n", num_errors_decoded);
return 0;
}
