4 Commits

Author SHA1 Message Date
lwvmobile
fbe7fcab0e Merge pull request #376 from grantsavill/ras-fixes
DMR: Prevent false RAS detection on non-RAS data bursts
2026-11-14 23:51:43 -05:00
lwvmobile
138a48ad31 Merge pull request #375 from grantsavill/bptc-fixes
DMR: Improve BPTC(196,96), BPTC(128,77), and BPTC(16x2) FEC decoding
2026-11-14 20:16:00 -05:00
Grant Savill
cd6ce80124 DMR: Prevent false RAS detection and latching on non-RAS data bursts
Check standard 24-bit Full LC and 16-bit CCITT CRCs before treating a flipped bptc_res_bits[2] bit as RAS, require PF/Reserved bits to be 0 for embedded LC RAS detection, and require two RAS bursts (or a key-verified RAS burst) to latch state->dmr_is_ras while clearing it on valid non-RAS BPTC bursts.
2026-11-15 00:18:03 +00:00
Grant Savill
edf97e26b8 DMR: Improve BPTC(196,96), BPTC(128,77), and BPTC(16x2) FEC decoding
Decode parity rows/columns and re-inject corrected parity bits in BPTC_196x96_Extract_Data with post-pass syndrome convergence verification, include row 7 and 2-column parity-guided repair in BPTC_128x77_Extract_Data, and apply Hamming(16,11,4) decoding to both rows in BPTC_16x2_Extract_Data.
2026-11-15 00:15:46 +00:00
2 changed files with 208 additions and 59 deletions

View File

@@ -213,8 +213,8 @@ uint32_t BPTC_196x96_Extract_Data(uint8_t InputDeInteleavedData[196],
} }
} }
/* ========== Pass 1: row Hamming(15,11) on rows 0..8 ========== */ /* ========== Pass 1: row Hamming(15,11) on rows 0..12 ========== */
for (i = 0; i < 9; i++) for (i = 0; i < 13; i++)
{ {
for (j = 0; j < 15; j++) for (j = 0; j < 15; j++)
{ {
@@ -232,8 +232,8 @@ uint32_t BPTC_196x96_Extract_Data(uint8_t InputDeInteleavedData[196],
fprintf(stderr, "%u", LineBefore[j] & 1); fprintf(stderr, "%u", LineBefore[j] & 1);
fprintf(stderr, "\n"); fprintf(stderr, "\n");
#endif #endif
/* Keep original data bits on failure */ /* Keep original bits on failure */
for (j = 0; j < 11; j++) for (j = 0; j < 15; j++)
DataMatrix[i][j] = LineBefore[j]; DataMatrix[i][j] = LineBefore[j];
} }
else else
@@ -253,8 +253,9 @@ uint32_t BPTC_196x96_Extract_Data(uint8_t InputDeInteleavedData[196],
#endif #endif
} }
} }
for (j = 0; j < 11; j++) /* Re-inject the full line (including corrected parity bits) in the matrix */
DataMatrix[i][j] = LineCorrected[j]; for (j = 0; j < 15; j++)
DataMatrix[i][j] = LineUncorrected[j];
} }
} }
#if BPTC_196x96_DEBUG #if BPTC_196x96_DEBUG
@@ -282,7 +283,7 @@ uint32_t BPTC_196x96_Extract_Data(uint8_t InputDeInteleavedData[196],
fprintf(stderr, "%u", ColumnBefore[j] & 1); fprintf(stderr, "%u", ColumnBefore[j] & 1);
fprintf(stderr, "\n"); fprintf(stderr, "\n");
#endif #endif
for (j = 0; j < 9; j++) for (j = 0; j < 13; j++)
DataMatrix[j][i] = ColumnBefore[j]; DataMatrix[j][i] = ColumnBefore[j];
} }
else else
@@ -301,8 +302,9 @@ uint32_t BPTC_196x96_Extract_Data(uint8_t InputDeInteleavedData[196],
#endif #endif
} }
} }
for (j = 0; j < 9; j++) /* Re-inject the full column (including corrected parity bits) in the matrix */
DataMatrix[j][i] = ColumnCorrected[j]; for (j = 0; j < 13; j++)
DataMatrix[j][i] = ColumnUncorrected[j];
} }
} }
#if BPTC_196x96_DEBUG #if BPTC_196x96_DEBUG
@@ -315,7 +317,7 @@ uint32_t BPTC_196x96_Extract_Data(uint8_t InputDeInteleavedData[196],
HammingIrrecoverableErrorNb = 0; HammingIrrecoverableErrorNb = 0;
/* ========== Pass 2: rows ========== */ /* ========== Pass 2: rows ========== */
for (i = 0; i < 9; i++) for (i = 0; i < 13; i++)
{ {
for (j = 0; j < 15; j++) for (j = 0; j < 15; j++)
{ {
@@ -333,7 +335,7 @@ uint32_t BPTC_196x96_Extract_Data(uint8_t InputDeInteleavedData[196],
fprintf(stderr, "%u", LineBefore[j] & 1); fprintf(stderr, "%u", LineBefore[j] & 1);
fprintf(stderr, "\n"); fprintf(stderr, "\n");
#endif #endif
for (j = 0; j < 11; j++) for (j = 0; j < 15; j++)
DataMatrix[i][j] = LineBefore[j]; DataMatrix[i][j] = LineBefore[j];
} }
else else
@@ -352,8 +354,9 @@ uint32_t BPTC_196x96_Extract_Data(uint8_t InputDeInteleavedData[196],
#endif #endif
} }
} }
for (j = 0; j < 11; j++) /* Re-inject the full line (including corrected parity bits) in the matrix */
DataMatrix[i][j] = LineCorrected[j]; for (j = 0; j < 15; j++)
DataMatrix[i][j] = LineUncorrected[j];
} }
} }
#if BPTC_196x96_DEBUG #if BPTC_196x96_DEBUG
@@ -381,7 +384,7 @@ uint32_t BPTC_196x96_Extract_Data(uint8_t InputDeInteleavedData[196],
fprintf(stderr, "%u", ColumnBefore[j] & 1); fprintf(stderr, "%u", ColumnBefore[j] & 1);
fprintf(stderr, "\n"); fprintf(stderr, "\n");
#endif #endif
for (j = 0; j < 9; j++) for (j = 0; j < 13; j++)
DataMatrix[j][i] = ColumnBefore[j]; DataMatrix[j][i] = ColumnBefore[j];
} }
else else
@@ -400,8 +403,58 @@ uint32_t BPTC_196x96_Extract_Data(uint8_t InputDeInteleavedData[196],
#endif #endif
} }
} }
for (j = 0; j < 9; j++) /* Re-inject the full column (including corrected parity bits) in the matrix */
DataMatrix[j][i] = ColumnCorrected[j]; for (j = 0; j < 13; j++)
DataMatrix[j][i] = ColumnUncorrected[j];
}
}
/* Verify that all rows (0..12) and columns (0..14) have converged to zero syndrome.
* Hamming_15_11_decode never returns false because all 15 non-zero 4-bit syndromes
* map to a bit flip, so without a post-pass consistency check a noisy burst can
* mis-correct data bits in Pass 2 Columns while still reporting 0 errors. */
for (i = 0; i < 13; i++)
{
for (j = 0; j < 15; j++)
{
LineUncorrected[j] = DataMatrix[i][j];
}
if (Hamming_15_11_decode(LineUncorrected, LineCorrected, 1) == false)
{
HammingIrrecoverableErrorNb++;
}
else
{
for (j = 0; j < 15; j++)
{
if (LineUncorrected[j] != DataMatrix[i][j])
{
HammingIrrecoverableErrorNb++;
break;
}
}
}
}
for (i = 0; i < 15; i++)
{
for (j = 0; j < 13; j++)
{
ColumnUncorrected[j] = DataMatrix[j][i];
}
if (Hamming_13_9_decode(ColumnUncorrected, ColumnCorrected, 1) == false)
{
HammingIrrecoverableErrorNb++;
}
else
{
for (j = 0; j < 13; j++)
{
if (ColumnUncorrected[j] != DataMatrix[j][i])
{
HammingIrrecoverableErrorNb++;
break;
}
}
} }
} }
#if BPTC_196x96_DEBUG #if BPTC_196x96_DEBUG
@@ -430,12 +483,33 @@ uint32_t BPTC_196x96_Extract_Data(uint8_t InputDeInteleavedData[196],
DMRDataExtracted[k++] = DataMatrix[i][j]; DMRDataExtracted[k++] = DataMatrix[i][j];
} }
uint32_t total_corr = row_corr_p1 + col_corr_p1 + row_corr_p2 + col_corr_p2;
uint32_t p2_corr = row_corr_p2 + col_corr_p2;
/* In DMR BPTC(196,96), R(0) and R(1) must be 0. Also reject R(2)==1 when the
* received R(2) bit was 0 or the matrix required heavy multi-pass corrections,
* because is_ras==1 bypasses downstream CRC checks when no RAS key is loaded. */
if (DataMatrix[0][2] != 0 || DataMatrix[0][1] != 0)
{
HammingIrrecoverableErrorNb++;
}
else if (DataMatrix[0][0] == 1 && ((InputDeInteleavedData[1] & 1) == 0 || total_corr > 8 || p2_corr > 2))
{
HammingIrrecoverableErrorNb++;
}
if (HammingIrrecoverableErrorNb == 0) if (HammingIrrecoverableErrorNb == 0)
{ {
R[0] = DataMatrix[0][2]; /* R(0) */ R[0] = DataMatrix[0][2]; /* R(0) */
R[1] = DataMatrix[0][1]; /* R(1) */ R[1] = DataMatrix[0][1]; /* R(1) */
R[2] = DataMatrix[0][0]; /* R(2) */ R[2] = DataMatrix[0][0]; /* R(2) */
} }
else
{
R[0] = 0;
R[1] = 0;
R[2] = 0;
}
if (R[0] == 0 && R[1] == 0 && R[2] == 1) if (R[0] == 0 && R[1] == 0 && R[2] == 1)
*is_ras = 1; *is_ras = 1;
@@ -466,7 +540,7 @@ uint32_t BPTC_128x77_Extract_Data(uint8_t InputDataMatrix[8][16], uint8_t DMRDat
uint32_t ParityCheckErrorNb = 0; uint32_t ParityCheckErrorNb = 0;
uint32_t NbOfOne; uint32_t NbOfOne;
uint8_t row_bad[7]; uint8_t row_bad[8];
uint8_t col_bad[16]; uint8_t col_bad[16];
#if BPTC_128x77_DEBUG #if BPTC_128x77_DEBUG
@@ -479,9 +553,9 @@ uint32_t BPTC_128x77_Extract_Data(uint8_t InputDataMatrix[8][16], uint8_t DMRDat
DataMatrix[i][j] = (InputDataMatrix[i][j] & 1); DataMatrix[i][j] = (InputDataMatrix[i][j] & 1);
} }
/* ---------- Pass 1: Hamming (16,11,4) on rows 0..6 ---------- */ /* ---------- Pass 1: Hamming (16,11,4) on rows 0..7 ---------- */
memset(row_bad, 0, sizeof(row_bad)); memset(row_bad, 0, sizeof(row_bad));
for (i = 0; i < 7; i++) for (i = 0; i < 8; i++)
{ {
for (j = 0; j < 16; j++) for (j = 0; j < 16; j++)
LineUncorrected[j] = DataMatrix[i][j]; LineUncorrected[j] = DataMatrix[i][j];
@@ -496,13 +570,11 @@ uint32_t BPTC_128x77_Extract_Data(uint8_t InputDataMatrix[8][16], uint8_t DMRDat
fprintf(stderr, "%u", LineUncorrected[j] & 1); fprintf(stderr, "%u", LineUncorrected[j] & 1);
fprintf(stderr, "\n"); fprintf(stderr, "\n");
#endif #endif
for (j = 0; j < 11; j++)
DataMatrix[i][j] = LineUncorrected[j];
} }
else else
{ {
for (j = 0; j < 11; j++) for (j = 0; j < 16; j++)
DataMatrix[i][j] = LineCorrected[j]; DataMatrix[i][j] = LineUncorrected[j];
} }
} }
#if BPTC_128x77_DEBUG #if BPTC_128x77_DEBUG
@@ -537,12 +609,14 @@ uint32_t BPTC_128x77_Extract_Data(uint8_t InputDataMatrix[8][16], uint8_t DMRDat
(unsigned)ParityCheckErrorNb); (unsigned)ParityCheckErrorNb);
#endif #endif
/* ---------- Parity-guided single-bit repair ---------- */ /* ---------- Parity-guided bit repair ---------- */
{ {
uint32_t n_bad_rows = 0, n_bad_cols = 0; uint32_t n_bad_rows = 0, n_bad_cols = 0;
uint32_t br = 0, bc = 0; uint32_t br = 0, bc = 0;
for (i = 0; i < 7; i++) UNUSED(bc);
for (i = 0; i < 8; i++)
if (row_bad[i]) { n_bad_rows++; br = i; } if (row_bad[i]) { n_bad_rows++; br = i; }
for (i = 0; i < 16; i++) for (i = 0; i < 16; i++)
if (col_bad[i]) { n_bad_cols++; bc = i; } if (col_bad[i]) { n_bad_cols++; bc = i; }
@@ -558,29 +632,35 @@ uint32_t BPTC_128x77_Extract_Data(uint8_t InputDataMatrix[8][16], uint8_t DMRDat
fprintf(stderr, "\n"); fprintf(stderr, "\n");
#endif #endif
if (n_bad_rows == 1 && n_bad_cols == 1 && bc < 11) if (n_bad_rows == 1 && (n_bad_cols == 1 || n_bad_cols == 2))
{ {
DataMatrix[br][bc] ^= 1; for (i = 0; i < 16; i++)
row_bad[br] = 0; {
if (col_bad[i])
{
DataMatrix[br][i] ^= 1;
#if BPTC_128x77_DEBUG #if BPTC_128x77_DEBUG
fprintf(stderr, fprintf(stderr,
" BPTC128 parity-guided FLIP at row=%u col=%u -> %u\n", " BPTC128 parity-guided FLIP at row=%u col=%u -> %u\n",
(unsigned)br, (unsigned)bc, (unsigned)DataMatrix[br][bc]); (unsigned)br, (unsigned)i, (unsigned)DataMatrix[br][i]);
#endif #endif
}
}
row_bad[br] = 0;
} }
#if BPTC_128x77_DEBUG #if BPTC_128x77_DEBUG
else if (n_bad_rows || n_bad_cols) else if (n_bad_rows || n_bad_cols)
{ {
fprintf(stderr, fprintf(stderr,
" BPTC128 no single-intersection flip " " BPTC128 no repair flip "
"(need exactly 1 bad row and 1 data col)\n"); "(need 1 bad row and 1 or 2 bad cols)\n");
} }
#endif #endif
} }
/* ---------- Pass 2: Hamming (16,11,4) again ---------- */ /* ---------- Pass 2: Hamming (16,11,4) again ---------- */
HammingIrrecoverableErrorNb = 0; HammingIrrecoverableErrorNb = 0;
for (i = 0; i < 7; i++) for (i = 0; i < 8; i++)
{ {
for (j = 0; j < 16; j++) for (j = 0; j < 16; j++)
LineUncorrected[j] = DataMatrix[i][j]; LineUncorrected[j] = DataMatrix[i][j];
@@ -594,13 +674,11 @@ uint32_t BPTC_128x77_Extract_Data(uint8_t InputDataMatrix[8][16], uint8_t DMRDat
fprintf(stderr, "%u", LineUncorrected[j] & 1); fprintf(stderr, "%u", LineUncorrected[j] & 1);
fprintf(stderr, "\n"); fprintf(stderr, "\n");
#endif #endif
for (j = 0; j < 11; j++)
DataMatrix[i][j] = LineUncorrected[j];
} }
else else
{ {
for (j = 0; j < 11; j++) for (j = 0; j < 16; j++)
DataMatrix[i][j] = LineCorrected[j]; DataMatrix[i][j] = LineUncorrected[j];
} }
} }
#if BPTC_128x77_DEBUG #if BPTC_128x77_DEBUG
@@ -696,22 +774,45 @@ uint32_t BPTC_16x2_Extract_Data(uint8_t InputInterleavedData[32], uint8_t DMRDat
DMRDataExtracted[i] = DataMatrix[i] & 1; DMRDataExtracted[i] = DataMatrix[i] & 1;
} }
/* Prepare the line to be corrected */ /* Prepare the first row (bits 0..15) to be corrected */
for(i = 0; i < 16; i++) for(i = 0; i < 16; i++)
{ {
LineUncorrected[i] = DataMatrix[i] & 1; LineUncorrected[i] = DataMatrix[i] & 1;
} }
/* Apply Hamming (16,11,4) code correction */ /* Apply Hamming (16,11,4) code correction to row 0 */
if(Hamming_16_11_4_decode(LineUncorrected, LineCorrected, 1) == false) if(Hamming_16_11_4_decode(LineUncorrected, LineCorrected, 1) == false)
{ {
HammingIrrecoverableErrorNb++; HammingIrrecoverableErrorNb++;
} }
else
/* Copy the corrected content to the output buffer */
for(i = 0; i < 11; i++)
{ {
DMRDataExtracted[i] = LineCorrected[i] & 1; /* Copy all 16 corrected bits (including parity bits 11..15) */
for(i = 0; i < 16; i++)
{
DMRDataExtracted[i] = LineUncorrected[i] & 1;
}
}
/* Prepare the second row (bits 16..31) to be corrected;
* 1^16 is a codeword of Hamming(16,11,4), so both even and odd parity rows are valid codewords */
for(i = 0; i < 16; i++)
{
LineUncorrected[i] = DataMatrix[i + 16] & 1;
}
/* Apply Hamming (16,11,4) code correction to row 1 */
if(Hamming_16_11_4_decode(LineUncorrected, LineCorrected, 1) == false)
{
HammingIrrecoverableErrorNb++;
}
else
{
/* Copy all 16 corrected bits (including parity bits 11..15) */
for(i = 0; i < 16; i++)
{
DMRDataExtracted[i + 16] = LineUncorrected[i] & 1;
}
} }
/* Check Parity bits */ /* Check Parity bits */

View File

@@ -60,6 +60,10 @@ void dmr_data_burst_handler(dsd_opts * opts, dsd_state * state, uint8_t info[196
uint8_t bptc_res_bits[3]; uint8_t bptc_res_bits[3];
memset (bptc_res_bits, 0, sizeof(bptc_res_bits)); memset (bptc_res_bits, 0, sizeof(bptc_res_bits));
uint8_t crc_original_validity = 0; uint8_t crc_original_validity = 0;
static uint8_t ras_confirm_count = 0;
static uint8_t prev_dmr_is_ras = 0;
if (prev_dmr_is_ras == 1 && state->dmr_is_ras == 0)
ras_confirm_count = 0;
uint32_t crcmask = 0; uint32_t crcmask = 0;
uint8_t crclen = 0; uint8_t crclen = 0;
@@ -305,13 +309,26 @@ void dmr_data_burst_handler(dsd_opts * opts, dsd_state * state, uint8_t info[196
{ {
if (is_ras) if (is_ras)
{ {
CRCComputed = ras_mac_calculator(state, BPTCDmrDataByte, 9, 1); uint8_t tmp_bytes[12];
if (CRCComputed == CRCExtracted) uint32_t std_crc = 0;
memcpy (tmp_bytes, BPTCDmrDataByte, sizeof(tmp_bytes));
if (ComputeAndCorrectFullLinkControlCrc(tmp_bytes, &std_crc, crcmask) && std_crc == CRCExtracted)
{
memcpy (BPTCDmrDataByte, tmp_bytes, sizeof(tmp_bytes));
is_ras = 0;
CRCComputed = std_crc;
CRCCorrect = 1; CRCCorrect = 1;
}
else
{
CRCComputed = ras_mac_calculator(state, BPTCDmrDataByte, 9, 1);
if (CRCComputed == CRCExtracted)
CRCCorrect = 1;
#ifdef DEBUG_RAS #ifdef DEBUG_RAS
fprintf (stderr, " EXT: %06X; MAC: %06X;", CRCExtracted, CRCComputed); fprintf (stderr, " EXT: %06X; MAC: %06X;", CRCExtracted, CRCComputed);
#endif #endif
}
} }
else CRCCorrect = ComputeAndCorrectFullLinkControlCrc(BPTCDmrDataByte, &CRCComputed, crcmask); else CRCCorrect = ComputeAndCorrectFullLinkControlCrc(BPTCDmrDataByte, &CRCComputed, crcmask);
@@ -354,18 +371,28 @@ void dmr_data_burst_handler(dsd_opts * opts, dsd_state * state, uint8_t info[196
//run CCITT on other data forms //run CCITT on other data forms
else else
{ {
if (is_ras == 1) uint32_t std_crc = ComputeCrcCCITT(BPTCDmrDataBit);
if (std_crc == CRCExtracted)
{
is_ras = 0;
CRCComputed = std_crc;
CRCCorrect = 1;
}
else if (is_ras == 1)
{ {
CRCComputed = ras_mac_calculator(state, BPTCDmrDataByte, 10, 0); CRCComputed = ras_mac_calculator(state, BPTCDmrDataByte, 10, 0);
if (CRCComputed == CRCExtracted) CRCCorrect = 1;
else CRCCorrect = 0;
#ifdef DEBUG_RAS #ifdef DEBUG_RAS
fprintf (stderr, " EXT: %04X; MAC: %04X;", CRCExtracted, CRCComputed); fprintf (stderr, " EXT: %04X; MAC: %04X;", CRCExtracted, CRCComputed);
#endif #endif
} }
else CRCComputed = ComputeCrcCCITT(BPTCDmrDataBit); else
{
if (CRCComputed == CRCExtracted) CRCCorrect = 1; CRCComputed = std_crc;
else CRCCorrect = 0; CRCCorrect = 0;
}
} }
//if this is a RAS system, set the CRC to okay if irrecoverable errors are okay //if this is a RAS system, set the CRC to okay if irrecoverable errors are okay
@@ -473,9 +500,11 @@ void dmr_data_burst_handler(dsd_opts * opts, dsd_state * state, uint8_t info[196
/* Compute the 5 bit CRC */ /* Compute the 5 bit CRC */
CRCComputed = ComputeCrc5Bit(LC_DataBit); CRCComputed = ComputeCrc5Bit(LC_DataBit);
//read ahead first two bytes, look for 1X10 or 2X10 pattern //read ahead first two bytes, look for 1X10 or 2X10 pattern (with PF/R bits 0)
uint16_t ras_test = (uint16_t)(ConvertBitIntoBytes(&LC_DataBit[0], 16) & 0x30FF); uint16_t ras_test = (uint16_t)(ConvertBitIntoBytes(&LC_DataBit[0], 16) & 0x30FF);
if ((IrrecoverableErrors == 0) && (ras_test == 0x2010 || ras_test == 0x1010)) if ((IrrecoverableErrors == 0) &&
(LC_DataBit[0] == 0) && (LC_DataBit[1] == 0) &&
(ras_test == 0x2010 || ras_test == 0x1010))
{ {
is_ras = 1; is_ras = 1;
if (state->ras_effective_key != 0) if (state->ras_effective_key != 0)
@@ -702,9 +731,28 @@ void dmr_data_burst_handler(dsd_opts * opts, dsd_state * state, uint8_t info[196
fprintf (stderr, "%s", KNRM); fprintf (stderr, "%s", KNRM);
} }
//might flicker the terminal on partially enabled systems, may need to find a better placement //require a key-verified RAS burst or 2 RAS bursts to latch [RAS]; clear on valid non-PI non-RAS BPTC burst
if (IrrecoverableErrors == 0 && (is_bptc || is_emb) && databurst != 0x05 && databurst != 0x07 && databurst != 0x09) if (IrrecoverableErrors == 0 && is_ras == 1 && (is_bptc || is_emb) && databurst != 0x05 && databurst != 0x07 && databurst != 0x09)
state->dmr_is_ras = is_ras; {
if (state->ras_effective_key != 0 && CRCCorrect == 1)
{
ras_confirm_count = 2;
state->dmr_is_ras = 1;
}
else if ((is_bptc || is_emb) && databurst != 0x00)
{
if (ras_confirm_count < 2)
ras_confirm_count++;
if (ras_confirm_count >= 2)
state->dmr_is_ras = 1;
}
}
else if (IrrecoverableErrors == 0 && is_ras == 0 && is_bptc && CRCCorrect == 1 && databurst != 0x00 && databurst != 0x05 && databurst != 0x07 && databurst != 0x09)
{
ras_confirm_count = 0;
state->dmr_is_ras = 0;
}
prev_dmr_is_ras = state->dmr_is_ras;
if (IrrecoverableErrors == 0 && CRCCorrect == 0 && is_ras == 0 && databurst != 0x09 && databurst != 0x05) if (IrrecoverableErrors == 0 && CRCCorrect == 0 && is_ras == 0 && databurst != 0x09 && databurst != 0x05)
{ {