Add functions for extended RACH coding

Add support for extended RACH (11 bit) according 3GPP TS 45.003 §5.3.2:

* convolutional code with puncturing
* encoding/decoding routines
* corresponding tests

Change-Id: I85a34a82d5cd39a594ee89d91a2338226066ab5d
Related: OS#1548

9 files changed, 30850 insertions, 21 deletions

diff --git a/TODO-RELEASE b/TODO-RELEASE
index 99865c68..a5def797 100644
--- a/TODO-RELEASE
+++ b/TODO-RELEASE
@@ -8,3 +8,4 @@
 # If any interfaces have been removed or changed since the last public release: c:r:0.
 #library	what			description / commit summary line
 core		msgb_queue_free()	add inline func to msgb.h
+coding		gsm0503_rach_ext-encode()	add func to gsm0503_coding.h
diff --git a/include/osmocom/coding/gsm0503_coding.h b/include/osmocom/coding/gsm0503_coding.h
index a2d4115b..86610bac 100644
--- a/include/osmocom/coding/gsm0503_coding.h
+++ b/include/osmocom/coding/gsm0503_coding.h
@@ -5,6 +5,8 @@
 #pragma once
 
 #include <stdint.h>
+
+#include <osmocom/core/defs.h>
 #include <osmocom/core/bits.h>
 
 /*! \addtogroup coding
@@ -63,8 +65,11 @@ int gsm0503_tch_ahs_decode(uint8_t *tch_data, const sbit_t *bursts, int odd,
 	int codec_mode_req, uint8_t *codec, int codecs, uint8_t *ft,
 	uint8_t *cmr, int *n_errors, int *n_bits_total);
 
-int gsm0503_rach_encode(ubit_t *burst, const uint8_t *ra, uint8_t bsic);
+int gsm0503_rach_ext_encode(ubit_t *burst, uint16_t ra, uint8_t bsic, bool is_11bit);
+int gsm0503_rach_encode(ubit_t *burst, const uint8_t *ra, uint8_t bsic) OSMO_DEPRECATED("Use gsm0503_rach_ext_encode() instead");
+
 int gsm0503_rach_decode(uint8_t *ra, const sbit_t *burst, uint8_t bsic);
+int gsm0503_rach_ext_decode(uint16_t *ra, const sbit_t *burst, uint8_t bsic);
 
 int gsm0503_sch_encode(ubit_t *burst, const uint8_t *sb_info);
 int gsm0503_sch_decode(uint8_t *sb_info, const sbit_t *burst);
diff --git a/src/coding/gsm0503_coding.c b/src/coding/gsm0503_coding.c
index cacc6121..f3b319ad 100644
--- a/src/coding/gsm0503_coding.c
+++ b/src/coding/gsm0503_coding.c
@@ -2824,13 +2824,47 @@ invalid_length:
  * b(0) = MSB of PLMN colour code
  * b(5) = LSB of BS colour code
  */
-static int rach_apply_bsic(ubit_t *d, uint8_t bsic)
+static inline void rach_apply_bsic(ubit_t *d, uint8_t bsic, uint8_t start)
 {
 	int i;
 
 	/* Apply it */
 	for (i = 0; i < 6; i++)
-		d[8 + i] ^= ((bsic >> (5 - i)) & 1);
+		d[start + i] ^= ((bsic >> (5 - i)) & 1);
+}
+
+static inline int16_t rach_decode(const sbit_t *burst, uint8_t bsic, bool is_11bit)
+{
+	ubit_t conv[17];
+	uint8_t ra[2] = { 0 }, nbits = is_11bit ? 11 : 8;
+	int rv;
+
+	osmo_conv_decode(is_11bit ? &gsm0503_rach_ext : &gsm0503_rach, burst, conv);
+
+	rach_apply_bsic(conv, bsic, nbits);
+
+	rv = osmo_crc8gen_check_bits(&gsm0503_rach_crc6, conv, nbits, conv + nbits);
+	if (rv)
+		return -1;
+
+	osmo_ubit2pbit_ext(ra, 0, conv, 0, nbits, 1);
+
+	return is_11bit ? osmo_load16le(ra) : ra[0];
+}
+
+/*! Decode the Extended (11-bit) RACH according to 3GPP TS 45.003
+ *  \param[out] ra output buffer for RACH data
+ *  \param[in] burst Input burst data
+ *  \param[in] bsic BSIC used in this cell
+ *  \returns 0 on success; negative on error (e.g. CRC error) */
+int gsm0503_rach_ext_decode(uint16_t *ra, const sbit_t *burst, uint8_t bsic)
+{
+	int16_t r = rach_decode(burst, bsic, true);
+
+	if (r < 0)
+		return r;
+
+	*ra = r;
 
 	return 0;
 }
@@ -2842,18 +2876,12 @@ static int rach_apply_bsic(ubit_t *d, uint8_t bsic)
  *  \returns 0 on success; negative on error (e.g. CRC error) */
 int gsm0503_rach_decode(uint8_t *ra, const sbit_t *burst, uint8_t bsic)
 {
-	ubit_t conv[14];
-	int rv;
-
-	osmo_conv_decode(&gsm0503_rach, burst, conv);
+	int16_t r = rach_decode(burst, bsic, false);
 
-	rach_apply_bsic(conv, bsic);
-
-	rv = osmo_crc8gen_check_bits(&gsm0503_rach_crc6, conv, 8, conv + 8);
-	if (rv)
-		return -1;
+	if (r < 0)
+		return r;
 
-	osmo_ubit2pbit_ext(ra, 0, conv, 0, 8, 1);
+	*ra = r;
 
 	return 0;
 }
@@ -2865,15 +2893,33 @@ int gsm0503_rach_decode(uint8_t *ra, const sbit_t *burst, uint8_t bsic)
  *  \returns 0 on success; negative on error */
 int gsm0503_rach_encode(ubit_t *burst, const uint8_t *ra, uint8_t bsic)
 {
-	ubit_t conv[14];
+	return gsm0503_rach_ext_encode(burst, *ra, bsic, false);
+}
+
+/*! Encode the Extended (11-bit) or regular (8-bit) RACH according to 3GPP TS 45.003
+ *  \param[out] burst Caller-allocated output burst buffer
+ *  \param[in] ra11 Input RACH data
+ *  \param[in] bsic BSIC used in this cell
+ *  \param[in] is_11bit whether given RA is 11 bit or not
+ *  \returns 0 on success; negative on error */
+int gsm0503_rach_ext_encode(ubit_t *burst, uint16_t ra11, uint8_t bsic, bool is_11bit)
+{
+	ubit_t conv[17];
+	uint8_t ra[2] = { 0 }, nbits = 8;
+
+	if (is_11bit) {
+		osmo_store16le(ra11, ra);
+		nbits = 11;
+	} else
+		ra[0] = (uint8_t)ra11;
 
-	osmo_pbit2ubit_ext(conv, 0, ra, 0, 8, 1);
+	osmo_pbit2ubit_ext(conv, 0, ra, 0, nbits, 1);
 
-	osmo_crc8gen_set_bits(&gsm0503_rach_crc6, conv, 8, conv + 8);
+	osmo_crc8gen_set_bits(&gsm0503_rach_crc6, conv, nbits, conv + nbits);
 
-	rach_apply_bsic(conv, bsic);
+	rach_apply_bsic(conv, bsic, nbits);
 
-	osmo_conv_encode(&gsm0503_rach, conv, burst);
+	osmo_conv_encode(is_11bit ? &gsm0503_rach_ext : &gsm0503_rach, conv, burst);
 
 	return 0;
 }
diff --git a/src/coding/libosmocoding.map b/src/coding/libosmocoding.map
index dbb53dec..95953cf2 100644
--- a/src/coding/libosmocoding.map
+++ b/src/coding/libosmocoding.map
@@ -108,6 +108,8 @@ gsm0503_tch_afs_encode;
 gsm0503_tch_afs_decode;
 gsm0503_tch_ahs_encode;
 gsm0503_tch_ahs_decode;
+gsm0503_rach_ext_encode;
+gsm0503_rach_ext_decode;
 gsm0503_rach_encode;
 gsm0503_rach_decode;
 gsm0503_sch_encode;
diff --git a/src/gsm/libosmogsm.map b/src/gsm/libosmogsm.map
index a72db524..6e6638a9 100644
--- a/src/gsm/libosmogsm.map
+++ b/src/gsm/libosmogsm.map
@@ -97,6 +97,7 @@ gsm0502_calc_paging_group;
 
 gsm0503_xcch;
 gsm0503_rach;
+gsm0503_rach_ext;
 gsm0503_sch;
 gsm0503_cs2;
 gsm0503_cs3;
diff --git a/tests/coding/coding_test.c b/tests/coding/coding_test.c
index b77410fd..511dbb7b 100644
--- a/tests/coding/coding_test.c
+++ b/tests/coding/coding_test.c
@@ -110,7 +110,7 @@ static void test_rach(uint8_t bsic, uint8_t ra)
 
 	/* Encode L2 message */
 	printf("Encoding: %02x\n", ra);
-	gsm0503_rach_encode(bursts_u, &ra, bsic);
+	gsm0503_rach_ext_encode(bursts_u, ra, bsic, false);
 
 	/* Prepare soft-bits */
 	osmo_ubit2sbit(bursts_s, bursts_u, 36);
@@ -126,7 +126,38 @@ static void test_rach(uint8_t bsic, uint8_t ra)
 	gsm0503_rach_decode(&result, bursts_s, bsic);
 	printf("Decoded: %02x\n", result);
 
-	OSMO_ASSERT(ra == result);
+	if (ra != result)
+		printf("FAIL [RACH]: encoded %u != %u decoded\n", ra, result);
+
+	printf("\n");
+}
+
+static void test_rach_ext(uint8_t bsic, uint16_t ra)
+{
+	uint16_t result = 3000; /* Max ext. RA is 2^11 = 2048 */
+	ubit_t bursts_u[36];
+	sbit_t bursts_s[36];
+
+	/* Encode L2 message */
+	printf("Encoding: %02x\n", ra);
+	gsm0503_rach_ext_encode(bursts_u, ra, bsic, true);
+
+	/* Prepare soft-bits */
+	osmo_ubit2sbit(bursts_s, bursts_u, 36);
+
+	printf("U-Bits: %s\n", osmo_ubit_dump(bursts_u, 36));
+
+	printf("S-Bits: %s\n", osmo_hexdump((uint8_t *)bursts_s, 36));
+
+	/* Destroy some bits */
+	memset(bursts_s + 9, 0, 8);
+
+	/* Decode, correcting errors */
+	gsm0503_rach_ext_decode(&result, bursts_s, bsic);
+	printf("Decoded: %02x\n", result);
+
+	if (ra != result)
+		printf("FAIL [RACH ext]: encoded %u != %u decoded\n", ra, result);
 
 	printf("\n");
 }
@@ -332,6 +363,12 @@ int main(int argc, char **argv)
 		test_rach(0x1a, i);
 	}
 
+	for (i = 0; i < 2048; i++) {
+		test_rach_ext(0x3f, i);
+		test_rach_ext(0x00, i);
+		test_rach_ext(0x1a, i);
+	}
+
 	for (i = 0; i < len_l2; i++)
 		test_sch(test_l2[i]);
 
diff --git a/tests/coding/coding_test.ok b/tests/coding/coding_test.ok
index 619f038b..8813af20 100644
--- a/tests/coding/coding_test.ok
+++ b/tests/coding/coding_test.ok
@@ -3880,6 +3880,30726 @@ U-Bits: 111010011010101001001101010001111111
 S-Bits: 81 81 81 7f 81 7f 7f 81 81 7f 81 7f 81 7f 81 7f 7f 81 7f 7f 81 81 7f 81 7f 81 7f 7f 7f 81 81 81 81 81 81 81 
 Decoded: ff
 
+Encoding: 00
+U-Bits: 000000000000000000000000000000000000
+S-Bits: 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 
+Decoded: 00
+
+Encoding: 00
+U-Bits: 000000000000000000011101001101001001
+S-Bits: 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 81 81 81 7f 81 7f 7f 81 81 7f 81 7f 7f 81 7f 7f 81 
+Decoded: 00
+
+Encoding: 00
+U-Bits: 000000000000000000011010000101110111
+S-Bits: 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 81 81 7f 81 7f 7f 7f 7f 81 7f 81 81 81 7f 81 81 81 
+Decoded: 00
+
+Encoding: 01
+U-Bits: 110111100000000000011101001100100010
+S-Bits: 81 81 7f 81 81 81 81 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 81 81 81 7f 81 7f 7f 81 81 7f 7f 81 7f 7f 7f 81 7f 
+Decoded: 01
+
+Encoding: 01
+U-Bits: 110111100000000000000000000001101011
+S-Bits: 81 81 7f 81 81 81 81 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 81 81 7f 81 7f 81 81 
+Decoded: 01
+
+Encoding: 01
+U-Bits: 110111100000000000000111001001010101
+S-Bits: 81 81 7f 81 81 81 81 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 81 81 81 7f 7f 81 7f 7f 81 7f 81 7f 81 7f 81 
+Decoded: 01
+
+Encoding: 02
+U-Bits: 010001111000000000000111010011001001
+S-Bits: 7f 81 7f 7f 7f 81 81 81 81 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 81 81 81 7f 81 7f 7f 81 81 7f 7f 81 7f 7f 81 
+Decoded: 02
+
+Encoding: 02
+U-Bits: 010001111000000000011010011110000000
+S-Bits: 7f 81 7f 7f 7f 81 81 81 81 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 81 81 7f 81 7f 7f 81 81 81 81 7f 7f 7f 7f 7f 7f 7f 
+Decoded: 02
+
+Encoding: 02
+U-Bits: 010001111000000000011101010110111110
+S-Bits: 7f 81 7f 7f 7f 81 81 81 81 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 81 81 81 7f 81 7f 81 7f 81 81 7f 81 81 81 81 81 7f 
+Decoded: 02
+
+Encoding: 03
+U-Bits: 100110011000000000011010011111101011
+S-Bits: 81 7f 7f 81 81 7f 7f 81 81 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 81 81 7f 81 7f 7f 81 81 81 81 81 81 7f 81 7f 81 81 
+Decoded: 03
+
+Encoding: 03
+U-Bits: 100110011000000000000111010010100010
+S-Bits: 81 7f 7f 81 81 7f 7f 81 81 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 81 81 81 7f 81 7f 7f 81 7f 81 7f 7f 7f 81 7f 
+Decoded: 03
+
+Encoding: 03
+U-Bits: 100110011000000000000000011010011100
+S-Bits: 81 7f 7f 81 81 7f 7f 81 81 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 81 81 7f 81 7f 7f 81 81 81 7f 7f 
+Decoded: 03
+
+Encoding: 04
+U-Bits: 001010011110000000011101010000011000
+S-Bits: 7f 7f 81 7f 81 7f 7f 81 81 81 81 7f 7f 7f 7f 7f 7f 7f 7f 81 81 81 7f 81 7f 81 7f 7f 7f 7f 7f 81 81 7f 7f 7f 
+Decoded: 04
+
+Encoding: 04
+U-Bits: 001010011110000000000000011101010001
+S-Bits: 7f 7f 81 7f 81 7f 7f 81 81 81 81 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 81 81 81 7f 81 7f 81 7f 7f 7f 81 
+Decoded: 04
+
+Encoding: 04
+U-Bits: 001010011110000000000111010101101111
+S-Bits: 7f 7f 81 7f 81 7f 7f 81 81 81 81 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 81 81 81 7f 81 7f 81 7f 81 81 7f 81 81 81 81 
+Decoded: 04
+
+Encoding: 05
+U-Bits: 111101111110000000000000011100111010
+S-Bits: 81 81 81 81 7f 81 81 81 81 81 81 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 81 81 81 7f 7f 81 81 81 7f 81 7f 
+Decoded: 05
+
+Encoding: 05
+U-Bits: 111101111110000000011101010001110011
+S-Bits: 81 81 81 81 7f 81 81 81 81 81 81 7f 7f 7f 7f 7f 7f 7f 7f 81 81 81 7f 81 7f 81 7f 7f 7f 81 81 81 7f 7f 81 81 
+Decoded: 05
+
+Encoding: 05
+U-Bits: 111101111110000000011010011001001101
+S-Bits: 81 81 81 81 7f 81 81 81 81 81 81 7f 7f 7f 7f 7f 7f 7f 7f 81 81 7f 81 7f 7f 81 81 7f 7f 81 7f 7f 81 81 7f 81 
+Decoded: 05
+
+Encoding: 06
+U-Bits: 011011100110000000011010000011010001
+S-Bits: 7f 81 81 7f 81 81 81 7f 7f 81 81 7f 7f 7f 7f 7f 7f 7f 7f 81 81 7f 81 7f 7f 7f 7f 7f 81 81 7f 81 7f 7f 7f 81 
+Decoded: 06
+
+Encoding: 06
+U-Bits: 011011100110000000000111001110011000
+S-Bits: 7f 81 81 7f 81 81 81 7f 7f 81 81 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 81 81 81 7f 7f 81 81 81 7f 7f 81 81 7f 7f 7f 
+Decoded: 06
+
+Encoding: 06
+U-Bits: 011011100110000000000000000110100110
+S-Bits: 7f 81 81 7f 81 81 81 7f 7f 81 81 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 81 81 7f 81 7f 7f 81 81 7f 
+Decoded: 06
+
+Encoding: 07
+U-Bits: 101100000110000000000111001111110011
+S-Bits: 81 7f 81 81 7f 7f 7f 7f 7f 81 81 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 81 81 81 7f 7f 81 81 81 81 81 81 7f 7f 81 81 
+Decoded: 07
+
+Encoding: 07
+U-Bits: 101100000110000000011010000010111010
+S-Bits: 81 7f 81 81 7f 7f 7f 7f 7f 81 81 7f 7f 7f 7f 7f 7f 7f 7f 81 81 7f 81 7f 7f 7f 7f 7f 81 7f 81 81 81 7f 81 7f 
+Decoded: 07
+
+Encoding: 07
+U-Bits: 101100000110000000011101001010000100
+S-Bits: 81 7f 81 81 7f 7f 7f 7f 7f 81 81 7f 7f 7f 7f 7f 7f 7f 7f 81 81 81 7f 81 7f 7f 81 7f 81 7f 7f 7f 7f 81 7f 7f 
+Decoded: 07
+
+Encoding: 08
+U-Bits: 000110100111100000000111010100000100
+S-Bits: 7f 7f 7f 81 81 7f 81 7f 7f 81 81 81 81 7f 7f 7f 7f 7f 7f 7f 7f 81 81 81 7f 81 7f 81 7f 7f 7f 7f 7f 81 7f 7f 
+Decoded: 08
+
+Encoding: 08
+U-Bits: 000110100111100000011010011001001101
+S-Bits: 7f 7f 7f 81 81 7f 81 7f 7f 81 81 81 81 7f 7f 7f 7f 7f 7f 81 81 7f 81 7f 7f 81 81 7f 7f 81 7f 7f 81 81 7f 81 
+Decoded: 08
+
+Encoding: 08
+U-Bits: 000110100111100000011101010001110011
+S-Bits: 7f 7f 7f 81 81 7f 81 7f 7f 81 81 81 81 7f 7f 7f 7f 7f 7f 81 81 81 7f 81 7f 81 7f 7f 7f 81 81 81 7f 7f 81 81 
+Decoded: 08
+
+Encoding: 09
+U-Bits: 110001000111100000011010011000100110
+S-Bits: 81 81 7f 7f 7f 81 7f 7f 7f 81 81 81 81 7f 7f 7f 7f 7f 7f 81 81 7f 81 7f 7f 81 81 7f 7f 7f 81 7f 7f 81 81 7f 
+Decoded: 09
+
+Encoding: 09
+U-Bits: 110001000111100000000111010101101111
+S-Bits: 81 81 7f 7f 7f 81 7f 7f 7f 81 81 81 81 7f 7f 7f 7f 7f 7f 7f 7f 81 81 81 7f 81 7f 81 7f 81 81 7f 81 81 81 81 
+Decoded: 09
+
+Encoding: 09
+U-Bits: 110001000111100000000000011101010001
+S-Bits: 81 81 7f 7f 7f 81 7f 7f 7f 81 81 81 81 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 81 81 81 7f 81 7f 81 7f 7f 7f 81 
+Decoded: 09
+
+Encoding: 0a
+U-Bits: 010111011111100000000000000111001101
+S-Bits: 7f 81 7f 81 81 81 7f 81 81 81 81 81 81 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 81 81 81 7f 7f 81 81 7f 81 
+Decoded: 0a
+
+Encoding: 0a
+U-Bits: 010111011111100000011101001010000100
+S-Bits: 7f 81 7f 81 81 81 7f 81 81 81 81 81 81 7f 7f 7f 7f 7f 7f 81 81 81 7f 81 7f 7f 81 7f 81 7f 7f 7f 7f 81 7f 7f 
+Decoded: 0a
+
+Encoding: 0a
+U-Bits: 010111011111100000011010000010111010
+S-Bits: 7f 81 7f 81 81 81 7f 81 81 81 81 81 81 7f 7f 7f 7f 7f 7f 81 81 7f 81 7f 7f 7f 7f 7f 81 7f 81 81 81 7f 81 7f 
+Decoded: 0a
+
+Encoding: 0b
+U-Bits: 100000111111100000011101001011101111
+S-Bits: 81 7f 7f 7f 7f 7f 81 81 81 81 81 81 81 7f 7f 7f 7f 7f 7f 81 81 81 7f 81 7f 7f 81 7f 81 81 81 7f 81 81 81 81 
+Decoded: 0b
+
+Encoding: 0b
+U-Bits: 100000111111100000000000000110100110
+S-Bits: 81 7f 7f 7f 7f 7f 81 81 81 81 81 81 81 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 81 81 7f 81 7f 7f 81 81 7f 
+Decoded: 0b
+
+Encoding: 0b
+U-Bits: 100000111111100000000111001110011000
+S-Bits: 81 7f 7f 7f 7f 7f 81 81 81 81 81 81 81 7f 7f 7f 7f 7f 7f 7f 7f 81 81 81 7f 7f 81 81 81 7f 7f 81 81 7f 7f 7f 
+Decoded: 0b
+
+Encoding: 0c
+U-Bits: 001100111001100000011010000100011100
+S-Bits: 7f 7f 81 81 7f 7f 81 81 81 7f 7f 81 81 7f 7f 7f 7f 7f 7f 81 81 7f 81 7f 7f 7f 7f 81 7f 7f 7f 81 81 81 7f 7f 
+Decoded: 0c
+
+Encoding: 0c
+U-Bits: 001100111001100000000111001001010101
+S-Bits: 7f 7f 81 81 7f 7f 81 81 81 7f 7f 81 81 7f 7f 7f 7f 7f 7f 7f 7f 81 81 81 7f 7f 81 7f 7f 81 7f 81 7f 81 7f 81 
+Decoded: 0c
+
+Encoding: 0c
+U-Bits: 001100111001100000000000000001101011
+S-Bits: 7f 7f 81 81 7f 7f 81 81 81 7f 7f 81 81 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 7f 81 81 7f 81 7f 81 81 
+Decoded: 0c
+
+Encoding: 0d
+U-Bits: 111011011001100000000111001000111110
+S-Bits: 81 81 81 7f 81 81 7f 81 81 7f 7f 81 81 7f 7f 7f 7f 7f 7f 7f 7f 81 81 81 7f 7f 81 7f 7f 7f 81 81 81 81 81 7f 
+Decoded: 0d
+
+Encoding: 0d
+U-Bits: 111011011001100000011010000101110111
+S-Bits: 81 81 81 7f 81 81 7f 81 81 7f 7f 81 81 7f 7f 7f 7f 7f 7f 81 81 7f 81 7f 7f 7f 7f 81 7f 81 81 81 7f 81 81 81 
+Decoded: 0d
+
+Encoding: 0d
+U-Bits: 111011011001100000011101001101001001
+S-Bits: 81 81 81 7f 81 81 7f 81 81 7f 7f 81 81 7f 7f 7f 7f 7f 7f 81 81 81 7f 81 7f 7f 81 81 7f 81 7f 7f 81 7f 7f 81 
+Decoded: 0d
+
+Encoding: 0e
+U-Bits: 011101000001100000011101010111010101
+S-Bits: 7f 81 81 81 7f 81 7f 7f 7f 7f 7f 81 81 7f 7f 7f 7f 7f 7f 81 81 81 7f 81 7f 81 7f 81 81 81 7f 81 7f 81 7f 81 
+Decoded: 0e
+
+Encoding: 0e
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+Encoding: 2a
+U-Bits: 010111000101111110011101010111010101
+S-Bits: 7f 81 7f 81 81 81 7f 7f 7f 81 7f 81 81 81 81 81 81 7f 7f 81 81 81 7f 81 7f 81 7f 81 81 81 7f 81 7f 81 7f 81 
+Decoded: 2a
+
+Encoding: 2a
+U-Bits: 010111000101111110011010011111101011
+S-Bits: 7f 81 7f 81 81 81 7f 7f 7f 81 7f 81 81 81 81 81 81 7f 7f 81 81 7f 81 7f 7f 81 81 81 81 81 81 7f 81 7f 81 81 
+Decoded: 2a
+
+Encoding: 2b
+U-Bits: 100000100101111110011101010110111110
+S-Bits: 81 7f 7f 7f 7f 7f 81 7f 7f 81 7f 81 81 81 81 81 81 7f 7f 81 81 81 7f 81 7f 81 7f 81 81 7f 81 81 81 81 81 7f 
+Decoded: 2b
+
+Encoding: 2b
+U-Bits: 100000100101111110000000011011110111
+S-Bits: 81 7f 7f 7f 7f 7f 81 7f 7f 81 7f 81 81 81 81 81 81 7f 7f 7f 7f 7f 7f 7f 7f 81 81 7f 81 81 81 81 7f 81 81 81 
+Decoded: 2b
+
+Encoding: 2b
+U-Bits: 100000100101111110000111010011001001
+S-Bits: 81 7f 7f 7f 7f 7f 81 7f 7f 81 7f 81 81 81 81 81 81 7f 7f 7f 7f 81 81 81 7f 81 7f 7f 81 81 7f 7f 81 7f 7f 81 
+Decoded: 2b
+
+Encoding: 2c
+U-Bits: 001100100011111110011010011001001101
+S-Bits: 7f 7f 81 81 7f 7f 81 7f 7f 7f 81 81 81 81 81 81 81 7f 7f 81 81 7f 81 7f 7f 81 81 7f 7f 81 7f 7f 81 81 7f 81 
+Decoded: 2c
+
+Encoding: 2c
+U-Bits: 001100100011111110000111010100000100
+S-Bits: 7f 7f 81 81 7f 7f 81 7f 7f 7f 81 81 81 81 81 81 81 7f 7f 7f 7f 81 81 81 7f 81 7f 81 7f 7f 7f 7f 7f 81 7f 7f 
+Decoded: 2c
+
+Encoding: 2c
+U-Bits: 001100100011111110000000011100111010
+S-Bits: 7f 7f 81 81 7f 7f 81 7f 7f 7f 81 81 81 81 81 81 81 7f 7f 7f 7f 7f 7f 7f 7f 81 81 81 7f 7f 81 81 81 7f 81 7f 
+Decoded: 2c
+
+Encoding: 2d
+U-Bits: 111011000011111110000111010101101111
+S-Bits: 81 81 81 7f 81 81 7f 7f 7f 7f 81 81 81 81 81 81 81 7f 7f 7f 7f 81 81 81 7f 81 7f 81 7f 81 81 7f 81 81 81 81 
+Decoded: 2d
+
+Encoding: 2d
+U-Bits: 111011000011111110011010011000100110
+S-Bits: 81 81 81