/** * 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); }