/**
* Compute the syndrome of the input [parity, message]
*
* @param data [parity, message]
* @param syndrome The syndromes (checksums) of the data
* @return true If syndromes are all zeros
*/
private boolean computeSyndrome(int[] data, int[] syndrome) {
boolean corruptionFound = false;
for (int i = 0; i < paritySize; i++) {
syndrome[i] = GF.substitute(data, primitivePower[i]);
if (syndrome[i] != 0) {
corruptionFound = true;
}
}
return !corruptionFound;
}
@Override
public void decode(int[] data, int[] erasedLocation, int[] erasedValue) {
if (erasedLocation.length == 0) {
return;
}
assert (erasedLocation.length == erasedValue.length);
for (int i = 0; i < erasedLocation.length; i++) {
data[erasedLocation[i]] = 0;
}
for (int i = 0; i < erasedLocation.length; i++) {
errSignature[i] = primitivePower[erasedLocation[i]];
erasedValue[i] = GF.substitute(data, primitivePower[i]);
}
GF.solveVandermondeSystem(errSignature, erasedValue, erasedLocation.length);
}
/**
* Given parity symbols followed by message symbols, return the locations of symbols that are
* corrupted. Can resolve up to (parity length / 2) error locations.
*
* @param data The message and parity. The parity should be placed in the first part of the array.
* In each integer, the relevant portion is present in the least significant bits of each int.
* The number of elements in data is stripeSize() + paritySize(). <b>Note that data may be
* changed after calling this method.</b>
* @param errorLocations The set to put the error location results
* @return true If the locations can be resolved, return true.
*/
public boolean computeErrorLocations(int[] data, Set<Integer> errorLocations) {
assert (data.length == paritySize + stripeSize && errorLocations != null);
errorLocations.clear();
int maxError = paritySize / 2;
int[][] syndromeMatrix = new int[maxError][];
for (int i = 0; i < syndromeMatrix.length; ++i) {
syndromeMatrix[i] = new int[maxError + 1];
}
int[] syndrome = new int[paritySize];
if (computeSyndrome(data, syndrome)) {
// Parity check OK. No error location added.
return true;
}
for (int i = 0; i < maxError; ++i) {
for (int j = 0; j < maxError + 1; ++j) {
syndromeMatrix[i][j] = syndrome[i + j];
}
}
GF.gaussianElimination(syndromeMatrix);
int[] polynomial = new int[maxError + 1];
polynomial[0] = 1;
for (int i = 0; i < maxError; ++i) {
polynomial[i + 1] = syndromeMatrix[maxError - 1 - i][maxError];
}
for (int i = 0; i < paritySize + stripeSize; ++i) {
int possibleRoot = GF.divide(1, primitivePower[i]);
if (GF.substitute(polynomial, possibleRoot) == 0) {
errorLocations.add(i);
}
}
// Now recover with error locations and check the syndrome again
int[] locations = new int[errorLocations.size()];
int k = 0;
for (int loc : errorLocations) {
locations[k++] = loc;
}
int[] erasedValue = new int[locations.length];
decode(data, locations, erasedValue);
for (int i = 0; i < locations.length; ++i) {
data[locations[i]] = erasedValue[i];
}
return computeSyndrome(data, syndrome);
}
/**
* A "bulk" version of the substitute. Tends to be 2X faster than the "int" substitute in a loop.
*
* @param p input polynomial
* @param q store the return result
* @param x input field
*/
public void substitute(byte[][] p, byte[] q, int x) {
substitute(p, q, x, 0, p[0].length);
}