2015-06-19 08:27:05 +00:00
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RS41-SG
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RS41-SGP (mit Preambel)
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2015-06-19 13:11:04 +00:00
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Modulation: GFSK, 4800 baud
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2015-06-19 08:27:05 +00:00
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Pro Sekunde 1 Frame
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4800 bit/s, jedoch nur ca 534ms pro sek.
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little endian, 8bit->1byte
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FrameLen (Header+Daten): 320 byte -> 2560/4800=0.5333
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64 byte xor-Maske (data whitening/scrambling)
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0x00..0x07, 8byte: Header
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10 B6 CA 11 22 96 12 F8
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0x3B..0x3C, 2byte: Frame Nummer
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0x3D..0x44, 8byte: Sonde ID
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Mask[0x3B..0x44]=0xAEBF7B4CC196833E51B1
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0x52, 1byte: Zaehler 0x00..0x32 (51 Frames)
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0x53..0x62, 16byte: Calibration/Config/Info
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Mask[0x52..0x62]=0xC2EA795D6DA15469470CDCE85CF1F77682
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GPS-Week/-TOW
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0x95..0x96, 2byte: Full GPS week (seit So 6.1.1980)
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2015-07-20 09:24:17 +00:00
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0x97..0x9A, 4byte: TOW in Millisekunden seit Sonntag 00 UTC (+ 16 Schaltsekunden) (+17s ab 1.7.2015)
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2015-06-19 08:27:05 +00:00
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Mask[0x95..0x9A]=0x5D6DA1546947
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Position: ECEF-Koordinaten
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0x114..0x117, 4byte: X-Koord.
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0x118..0x11B, 4byte: Y-Koord.
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0x11C..0x11F, 4byte: Z-Koord.
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Mask[0x114..0x11F]=0x795D6DA15469470CDCE85CF1
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2015-12-12 18:48:41 +00:00
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0x120..0x125, 6byte: ECEF-Velocities/cm (3x signed 16bit-int)
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2015-06-19 08:27:05 +00:00
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2015-07-20 09:24:17 +00:00
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Zur Umrechnung ecef2elli() kommt noch eine Differenz Geoid-Ellipsoid hinzu.
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GPS Chip: u-blox UBX-G6010-ST
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2015-06-19 08:27:05 +00:00
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0x52, 0x53..0x62 16byte:
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frame 0x00: e8 08 80 0c 03 00 00 0e 00 00 00 00 00 4b 34 37 : freq 400500 kHz (Payerne)
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a1 f1 00 19 03 00 00 0e 00 00 00 00 00 4b 34 36 : freq 401000 kHz (Payerne)
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b0 78 00 32 03 00 00 0e 00 00 00 00 00 4b 31 38 : freq 402000 kHz (Zagreb)
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63 92 00 4b 03 00 00 0e 00 00 00 00 00 4b 33 37 : freq 403000 kHz (Zagreb)
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ae 18 00 64 03 00 00 0f 00 00 00 00 00 4c 31 31 : freq 404000 kHz
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d5 80 80 66 03 00 00 0e 00 00 00 00 00 4b 34 36 : freq 404100 kHz
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dc e3 80 75 03 00 00 0e 00 00 00 00 00 4a 34 30 : freq 404700 kHz (Budapest)
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c3 b0 00 0f 03 00 00 0e 00 00 00 00 00 4b 32 34 : freq 400600 kHz (Poprad)
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41 ab 00 91 03 00 00 0f 00 00 00 00 00 4c 31 30 : freq 405800 kHz (Lindenberg)
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^^0x56: k1
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^^0x55: k0 freq = 400000 + (k0/2^8 + k1) * 2^2 * 10
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0x80 = 00000001 -> 1/2^1
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0x40 = 00000010 -> 1/2^2
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2015-11-07 21:28:21 +00:00
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0xC0 = 00000011 -> 3/4
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2015-06-19 08:27:05 +00:00
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Bsp.: k0,k1: 0x80 0x75 -> (117+1/2)*40 = 4700 -> 404700
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frame 0x02: 06 0a 87 32 00 00 00 ff ff 00 00 00/01 00 ..
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^^0x5E: burst kill?
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0x5A/5B: kill timmer?
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Ende-0x00/Anfang-0x01: Sonde-Id
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0x00: 3e 09 00 32 03 00 00 0e 00 00 00 00 00 4b 31 39 : fq 402000
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0x01: 33 30 32 39 33 25 4e 00 00 2c 01 12 05 b4 3c a4
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-> 4b 31 39 33 30 32 39 33 : K1930293
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0x00: f7 d7 00 32 03 00 00 0e 00 00 00 00 00 4b 31 39 : fq 402000
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0x01: 33 30 32 36 30 25 4e 00 00 2c 01 12 05 b4 3c a4
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-> 4b 31 39 33 30 32 36 30 : K1930260
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0x00: 41 ab 00 91 03 00 00 0f 00 00 00 00 00 4c 31 30 : fq 405800
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0x01: 34 30 30 31 30 f2 4e 00 00 58 02 12 05 b4 3c a4
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-> 4c 31 30 34 30 30 31 30 : L1040010
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frame 0x21: ff ff ff c6 ff ff ff c6 52 53 34 31 2d 53 47 00 : RS41-SG
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ee 19 79 44 9a 39 79 44 52 53 34 31 2d 53 47 50 : RS41-SGP
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2015-06-19 13:11:04 +00:00
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Data whitening/scrambling:
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2015-06-19 08:27:05 +00:00
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Block shiften und gegen sich selbst XOR-en.
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Wenn man die richtige Blocklaenge gefunden hat, erhaelt man enc_i ^ enc_j = dec_i ^ dec_j.
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Wenn in einem Klartext dec_j viele Nullen stehen, erhaelt man im anderen Block den Klartext.
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Somit erhaelt man auch die XOR-Maske fuer diesen Teil.
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2015-06-19 13:13:47 +00:00
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Frame 320=5x64 byte:
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2015-06-19 08:27:05 +00:00
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10B6CA11229612F804A1EAAC92622978C044887A4ACE6BA0A35822FC5F447F349D9BA3603B69B89197656C6875B40A2624E5AE26788CCDFC7717131EA9307DF8
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A5B30C688252089833055902F944C6262652EE0F476CF4BBEB7B9DD6E25ED8993611D7626BE38846D57E1965F74ADD635DB1BC5410AD393D708208AC957D4E9A
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65813E51B14908983205590EF944C62621E7179667556AC1FAB340130BF5A9E8017C0C71D39B55206864E7655AEF2E9ED043B4358BD7AD58595A3A51E27522CE
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A36BC0BFBBF10BAC17FA790EF9442483DEFD0EB867CA545E45B0511F758E5CCC7C518E3DF3665C76A77A092FF5388691C65E60B60B5A9C34786E3BAEBF7B4CC1
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96833E51B14908983205590EF944C6266D2FB9FF2F84E9B8F032260B90B403EAC7756786F09BAA2E82894215E4102E61D0BCB4B606AAF423786E3BAEBF7BA006
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block1 ^ block4:
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>>> hex(0x10B6CA11229612F804A1EAAC92622978C044887A4ACE6BA0A35822FC5F447F349D9BA3603B69B89197656C6875B40A2624E5AE26788CCDFC7717131EA9307DF8
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^0xA36BC0BFBBF10BAC17FA790EF9442483DEFD0EB867CA545E45B0511F758E5CCC7C518E3DF3665C76A77A092FF5388691C65E60B60B5A9C34786E3BAEBF7B4CC1)
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'0xb3dd0aae99671954135b93a26b260dfb1eb986c22d043ffee6e873e32aca23f8e1ca2d5dc80fe4e7301f6547808c8cb7e2bbce9073d651c80f7928b0164b3139L'
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^^^^^^^^^^
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block2 ^ block5:
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>>> hex(0xA5B30C688252089833055902F944C6262652EE0F476CF4BBEB7B9DD6E25ED8993611D7626BE38846D57E1965F74ADD635DB1BC5410AD393D708208AC957D4E9A
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^0x96833E51B14908983205590EF944C6266D2FB9FF2F84E9B8F032260B90B403EAC7756786F09BAA2E82894215E4102E61D0BCB4B606AAF423786E3BAEBF7BA006)
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'0x33303239331b00000100000c000000004b7d57f068e81d031b49bbdd72eadb73f164b0e49b78226857f75b70135af3028d0d08e21607cd1e08ec33022a06ee9cL'
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^^^^^^^^^^
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Wenn im Klartext des einen Blocks viele Nullen stehen, erhaelt man durch XOR-en den Klartext des anderen:
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...b0164b3139 3330323933...
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FrameNr , SondeId : 0x16b0 , 4b31393330323933 (K1930293)
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[ 5808] (K1930293) Mo 2014-07-07 12:36:12 (W 1800) lat: 46.04934 lon: 16.13034 h: 32347.21
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2015-06-19 13:11:04 +00:00
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Der XOR-Text mit den Nullen ist dann die scrambling-Maske:
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Maske[0xFB..0x104]=0xAEBF7B4CC196833E51B1=Mask[0x3B..0x44]
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2015-06-19 08:27:05 +00:00
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2016-01-19 12:24:35 +00:00
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Maske
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LFSR: ab i=8 (mod 64):
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m[16+i] = m[i] ^ m[i+2] ^ m[i+4] ^ m[i+6]
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________________3205590EF944C6262160C2EA795D6DA15469470CDCE85CF1
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F776827F0799A22C937C3063F5102E61D0BCB4B606AAF423786E3BAEBF7B4CC1
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96833E51B1490898
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Error Correction Code
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CRC16 / Reed-Solomon RS(255,231)
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2016-01-19 12:32:03 +00:00
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(aehnlich wie RS92)
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2016-01-19 12:24:35 +00:00
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HEADER 8
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RS-PARITY 48 = 2*24
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DATA 264-462 (max 2*231=462)
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DATA hat zu Beginn z.B. 0F oder F0,
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dann Bloecke der Form IDLEN|DAT|CRC16:
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IDLEN 2 (ID+LEN)
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DAT LEN
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CRC16 2 (poly=0x(1)1021, init=0xFFFF)
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Reed-Solomon:
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RS(255,231)
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GF(2^8)=GF(2)[X]/(f): f=X^8+X^4+X^3+X^2+1 = 0x11D
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Generator von GF(2^8)*: alpha=0x02 (primitive Einheitswurzel)
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Generatorpolynom fuer RS-Code:
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(X-alpha^0)...(X-alpha^23) =
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X^24 + 0x7A X^23 + 0x76 X^22 + 0xA9 X^21 + 0x46 X^20 + 0xB2 X^19 + 0xED X^18 + 0xD8 X^17 + 0x66 X^16 + 0x73 X^15 + 0x96 X^14 + 0xe5 X^13 + 0x49 X^12
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+ 0x82 X^11 + 0x48 X^10 + 0x3D X^9 + 0x2B X^8 + 0xCE X^7 + 0x01 X^6 + 0xED X^5 + 0xF7 X^4 + 0x7F X^3 + 0xD9 X^2 + 0x90 X + 0x75
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"interleaved" RS(255,231)
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255-231=24 parity bytes, kann 12 Bytes je Codewort reparieren.
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Die 2 Codewoerter setzen sich zusammen aus den DATA-Bytes an den geraden bzw. ungeraden Positionen und ersten bzw. zweiten RS-PARITY-Teil.
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2 Beispiele, Frame1 (320 byte) und Frame2 (518 byte):
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1) 8635f44093df1a602c87e0fa0521e8943d9cef4c7a67393f6d39fb546461f2111b6447ab79a746c80350cda5344157f8c0c12234f46902220f792816174b313933303239331a00000300000a00002f0007322ce53e31991abf12dada3eb68468c16755d51c7a2a15310216060245f302000d08a31607821e08bb210219060243f302000000000000000000000000000000220d7c1e0807d03cdc071fd81ddb19d70a8d0eb602b60cb518d40692ff00ff00ff001c277d59b8d83301ff0f881f0f38f4fe18b283038735ff000000003eb8ff4947201e6e3aff55415f13fc6e005440440cf100009e9f7406f85800832b631719d70010bebc172a8b00000000000000000000000000000000000000000000a48b7b15366181193ef05d07e1245b1be0f721f801f60804107b0b76110000000000000000000000000000000000ecc7
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2) 8635f44093df1a608f9b1025bf8ec9e28ad68413c31788307e9881c5cb2f37f754fa09b711c5c39977ed8fbf22377b3e5e1cee59fc644b19f0792896134b343032303234341c00000100000c00007a0007320f00000000008920bac20000000000000092697a2ae9030226fd015de502363208522a075f330874040228fd015de502000000000000000000000000000000e7917c1e4d0750f1921703fb01f8068d1fd811f70bd604d50afa17f913d90c8b20f9a16a7d5921103501ff440000006c1f00cd977e059ab7009566fd191d1affd82fbf143fb8ff5277180991faff9ca1d10d441b01927bf211dd190190999f0553a1ff9120b10c3847ff06eeee0e571301a2c0891c000000cddd1a0882d10011167b153c154217941930005fc50b1eb9fde107d2050902115a537ea6ed343030313030303120313037393020202033312e37203036373520303334392030373030203132383636203630303520313339333120363031342031343038322035383830203738313420383032372031303039203930392039353631353632203935303839323220343238383339313633382032393335383636203539343238203335323439203636393920333738332034363837203637303120363930312037393939049a762d000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000f35a
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CRC:
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1)
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8635f44093df1a60 (HDR)
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2c87e0fa0521e8943d9cef4c7a67393f6d39fb546461f2111b6447ab79a746c80350cda5344157f8c0c12234f4690222 (2xRS)
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0f
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7928 (L=0x28=40)
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16174b313933303239331a00000300000a00002f0007322ce53e31991abf12dada3eb68468c16755 d51c (CRC-OK)
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7a2a (L=0x2a=42)
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15310216060245f302000d08a31607821e08bb210219060243f302000000000000000000000000000000 220d (CRC-OK)
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7c1e (L=0x1e=30)
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0807d03cdc071fd81ddb19d70a8d0eb602b60cb518d40692ff00ff00ff00 1c27 (CRC-OK)
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7d59 (L=0x59=89)
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b8d83301ff0f881f0f38f4fe18b283038735ff000000003eb8ff4947201e6e3aff55415f13fc6e005440440cf100009e9f7406f85800832b631719d70010bebc172a8b00000000000000000000000000000000000000000000 a48b (CRC-OK)
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7b15 (L=0x15=21)
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366181193ef05d07e1245b1be0f721f801f6080410 7b0b (CRC-OK)
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7611 (L=0x11=17)
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0000000000000000000000000000000000 ecc7 (CRC-OK)
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2)
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8635f44093df1a60 (HDR)
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8f9b1025bf8ec9e28ad68413c31788307e9881c5cb2f37f754fa09b711c5c39977ed8fbf22377b3e5e1cee59fc644b19 (2xRS)
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f0
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7928 (L=0x28=40)
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96134b343032303234341c00000100000c00007a0007320f00000000008920bac200000000000000 9269 (CRC-OK)
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7a2a (L=0x2a=42)
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e9030226fd015de502363208522a075f330874040228fd015de502000000000000000000000000000000 e791 (CRC-OK)
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7c1e (L=0x1e=30)
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4d0750f1921703fb01f8068d1fd811f70bd604d50afa17f913d90c8b20f9 a16a (CRC-OK)
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7d59 (L=0x59=89)
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21103501ff440000006c1f00cd977e059ab7009566fd191d1affd82fbf143fb8ff5277180991faff9ca1d10d441b01927bf211dd190190999f0553a1ff9120b10c3847ff06eeee0e571301a2c0891c000000cddd1a0882d100 1116 (CRC-OK)
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7b15 (L=0x15=21)
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3c154217941930005fc50b1eb9fde107d205090211 5a53 (CRC-OK)
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7ea6 (L=0xa6=166)
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ed343030313030303120313037393020202033312e37203036373520303334392030373030203132383636203630303520313339333120363031342031343038322035383830203738313420383032372031303039203930392039353631353632203935303839323220343238383339313633382032393335383636203539343238203335323439203636393920333738332034363837203637303120363930312037393939 049a (CRC-OK)
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762d (L=0x2d=45)
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000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 f35a (CRC-OK)
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Reed-Solomon:
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Fehler feststellen ist einfach, reparieren ist aufwendig.
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Decoder:
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http://www.ka9q.net/code/fec/
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https://en.wikiversity.org/wiki/Reed%E2%80%93Solomon_codes_for_coders
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Codewort generieren bzw. parity bytes checken z.B. durch Polynomdivision (CRC).
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>>> gen=rs_generator_poly(24)
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>>> print ' '.join([hex(x) for x in gen])
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0x1 0x7a 0x76 0xa9 0x46 0xb2 0xed 0xd8 0x66 0x73 0x96 0xe5 0x49 0x82 0x48 0x3d 0x2b 0xce 0x1 0xed 0xf7 0x7f 0xd9 0x90 0x75
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1)
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8635f44093df1a60
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2c87e0fa0521e8943d9cef4c7a67393f6d39fb546461f2111b6447ab79a746c80350cda5344157f8c0c12234f4690222
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0f792816174b313933303239331a00000300000a00002f0007322ce53e31991abf12dada3eb68468c16755d51c7a2a15310216060245f302000d08a31607821e08bb210219060243f302000000000000000000000000000000220d7c1e0807d03cdc071fd81ddb19d70a8d0eb602b60cb518d40692ff00ff00ff001c277d59b8d83301ff0f881f0f38f4fe18b283038735ff000000003eb8ff4947201e6e3aff55415f13fc6e005440440cf100009e9f7406f85800832b631719d70010bebc172a8b00000000000000000000000000000000000000000000a48b7b15366181193ef05d07e1245b1be0f721f801f60804107b0b76110000000000000000000000000000000000ecc7
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>>> str='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'.decode('hex')
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>>> len(str)
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264
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>>> msg1=str[262::-2]
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>>> msg2=str[263::-2]
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>>> code1=rs_encode_msg(msg1, 24)
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>>> code2=rs_encode_msg(msg2, 24)
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>>> print ''.join('%02x'%x for x in code1[-24:])
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11f2616454fb396d3f39677a4cef9c3d94e82105fae0872c
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>>> print ''.join('%02x'%x for x in code2[-24:])
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220269f43422c1c0f8574134a5cd5003c846a779ab47641b
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2)
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8635f44093df1a60
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8f9b1025bf8ec9e28ad68413c31788307e9881c5cb2f37f754fa09b711c5c39977ed8fbf22377b3e5e1cee59fc644b19
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>>> str='f0792896134b343032303234341c00000100000c00007a0007320f00000000008920bac20000000000000092697a2ae9030226fd015de502363208522a075f330874040228fd015de502000000000000000000000000000000e7917c1e4d0750f1921703fb01f8068d1fd811f70bd604d50afa17f913d90c8b20f9a16a7d5921103501ff440000006c1f00cd977e059ab7009566fd191d1affd82fbf143fb8ff5277180991faff9ca1d10d441b01927bf211dd190190999f0553a1ff9120b10c3847ff06eeee0e571301a2c0891c000000cddd1a0882d10011167b153c154217941930005fc50b1eb9fde107d2050902115a537ea6ed343030313030303120313037393020202033312e37203036373520303334392030373030203132383636203630303520313339333120363031342031343038322035383830203738313420383032372031303039203930392039353631353632203935303839323220343238383339313633382032393335383636203539343238203335323439203636393920333738332034363837203637303120363930312037393939049a762d000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000f35a'.decode('hex')
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>>> len(str)
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462
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>>> msg1=str[460::-2]
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>>> msg2=str[461::-2]
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>>> code1=rs_encode_msg(msg1, 24)
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>>> code2=rs_encode_msg(msg2, 24)
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>>> print ''.join('%02x'%x for x in code1)
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>>> print ''.join('%02x'%x for x in code2)
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>>> print ''.join('%02x'%x for x in code1[-24:])
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f7372fcbc581987e308817c31384d68ae2c98ebf25109b8f
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>>> print ''.join('%02x'%x for x in code2[-24:])
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194b64bc59ee1c5e3e7b3722bf8fed7799c3c511b749fa54
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