private void init(int stripeSize, int paritySize) {
assert (stripeSize + paritySize < GF.getFieldSize());
this.stripeSize = stripeSize;
this.paritySize = paritySize;
this.errSignature = new int[paritySize];
this.paritySymbolLocations = new int[paritySize];
this.dataBuff = new int[paritySize + stripeSize];
for (int i = 0; i < paritySize; i++) {
paritySymbolLocations[i] = i;
}
this.primitivePower = new int[stripeSize + paritySize];
// compute powers of the primitive root
for (int i = 0; i < stripeSize + paritySize; i++) {
primitivePower[i] = GF.power(PRIMITIVE_ROOT, i);
}
// compute generating polynomial
int[] gen = {1};
int[] poly = new int[2];
for (int i = 0; i < paritySize; i++) {
poly[0] = primitivePower[i];
poly[1] = 1;
gen = GF.multiply(gen, poly);
}
// generating polynomial has all generating roots
generatingPolynomial = gen;
}
@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);
}
/**
* 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 encode(int[] message, int[] parity) {
assert (message.length == stripeSize && parity.length == paritySize);
for (int i = 0; i < paritySize; i++) {
dataBuff[i] = 0;
}
for (int i = 0; i < stripeSize; i++) {
dataBuff[i + paritySize] = message[i];
}
GF.remainder(dataBuff, generatingPolynomial);
for (int i = 0; i < paritySize; i++) {
parity[i] = dataBuff[i];
}
}
public class ReedSolomonCode extends ErasureCode {
public static final Log LOG = LogFactory.getLog(ReedSolomonCode.class);
private int stripeSize;
private int paritySize;
private int[] generatingPolynomial;
private int PRIMITIVE_ROOT = 2;
private int[] primitivePower;
private GaloisField GF = GaloisField.getInstance();
private int[] errSignature;
private int[] paritySymbolLocations;
private int[] dataBuff;
@Deprecated
public ReedSolomonCode(int stripeSize, int paritySize) {
init(stripeSize, paritySize);
}
public ReedSolomonCode() {}
@Override
public void init(Codec codec) {
init(codec.stripeLength, codec.parityLength);
LOG.info(
"Initialized "
+ ReedSolomonCode.class
+ " stripeLength:"
+ codec.stripeLength
+ " parityLength:"
+ codec.parityLength);
}
private void init(int stripeSize, int paritySize) {
assert (stripeSize + paritySize < GF.getFieldSize());
this.stripeSize = stripeSize;
this.paritySize = paritySize;
this.errSignature = new int[paritySize];
this.paritySymbolLocations = new int[paritySize];
this.dataBuff = new int[paritySize + stripeSize];
for (int i = 0; i < paritySize; i++) {
paritySymbolLocations[i] = i;
}
this.primitivePower = new int[stripeSize + paritySize];
// compute powers of the primitive root
for (int i = 0; i < stripeSize + paritySize; i++) {
primitivePower[i] = GF.power(PRIMITIVE_ROOT, i);
}
// compute generating polynomial
int[] gen = {1};
int[] poly = new int[2];
for (int i = 0; i < paritySize; i++) {
poly[0] = primitivePower[i];
poly[1] = 1;
gen = GF.multiply(gen, poly);
}
// generating polynomial has all generating roots
generatingPolynomial = gen;
}
@Override
public void encode(int[] message, int[] parity) {
assert (message.length == stripeSize && parity.length == paritySize);
for (int i = 0; i < paritySize; i++) {
dataBuff[i] = 0;
}
for (int i = 0; i < stripeSize; i++) {
dataBuff[i + paritySize] = message[i];
}
GF.remainder(dataBuff, generatingPolynomial);
for (int i = 0; i < paritySize; i++) {
parity[i] = dataBuff[i];
}
}
@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);
}
@Override
public int stripeSize() {
return this.stripeSize;
}
@Override
public int paritySize() {
return this.paritySize;
}
@Override
public int symbolSize() {
return (int) Math.round(Math.log(GF.getFieldSize()) / Math.log(2));
}
/**
* 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);
}
/**
* 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 int symbolSize() {
return (int) Math.round(Math.log(GF.getFieldSize()) / Math.log(2));
}
