kopia lustrzana https://github.com/rs1729/RS
515 wiersze
46 KiB
Plaintext
515 wiersze
46 KiB
Plaintext
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In der Regel enthalten die einzelnen frames Checksummen oder CRC-Werte.
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Einige Radiosonden senden frames mit Codewoertern, die eine Fehlerkorrektur ermoeglichen.
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Graw
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====
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Hammingcode (N, N-R) = (2^m - 1, N-m), d.h. R=mt mit t=1,
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korrigiert t=1 Fehler pro Codewort der Laenge N,
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die Codewoerter haben den (min.) Abstand d=3
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(bei 2 Fehlern wird zum Nachbarcodewort falsch dekodiert).
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Fuer die Sonden DFM-06/09 ist m=3, d.h. Hamming(7,4),
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jedoch mit einem Paritaetsbit zu (8,4) erweitert.
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Der erweiterte Hammingcode (8,4) kann zudem 2 Fehler
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als nicht-korrigierbar erkennen (wird nicht falsch decodiert).
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Zu einem Wort mit 2 Fehlern gibt es 4 Codewoerter mit Abstand 2.
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Von diesen kann das Codewort, das am besten passt, ausgewaehlt
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werden (soft decision). Allerdings steigt die Wahrscheinlichkeit,
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dass neben 2 Fehlern auch Woerter mit 3 Fehlern vorkommen, wobei
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diese dann falsch decodiert werden.
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Meisei
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======
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BCH(63,51)-Code (m=6, t=2) mit Generatorpolynom
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(x^6+x+1)(x^6+x^4+x^2+x+1)=x^12+x^10+x^8+x^5+x^4+x^3+1.
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gekuerzt auf (46,34), die letzten 12 bit sind die BCH-Kontrollbits.
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Das Generatorpolynom kann man finden, wenn man geeignete Codewoerter addiert (linearer Code),
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um das kleinste Codewort ungleich 0 zu finden, z.B.:
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0000000000000000 1 0000000000000000 1 000010111011
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+
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0000000000000000 1 0000000000000010 0 010001011111
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=
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0000000000000000 0 0000000000000010 1 010011100100
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->
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101010011100100 = (x^12+x^10+x^8+x^5+x^4+x^3+1)x^2
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Die 34 Nachrichtenbit sind aufgeteilt in 16+1+16+1, d.h. nach einem 16 bit Block kommt ein Paritaetsbit,
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dass 1 ist, wenn die Anzahl 1en in den 16 bit davor gerade ist und sonst 0.
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Pro Codewort koennen t=2 Fehler korrigiert werden.
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Ist die Anzahl Fehler #E groesser t, dann ist fuer t < #E <= 2t die Wahrscheinlichkeit,
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dass Fehler falsch erkannt/decodiert werden, etwa 1/t!, somit fuer t=2 garnicht gering.
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Da hier gekuerzte Codewoerter und 2 zusaetzliche Paritaetsbits verwendet werden, sollte
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man bei decodierten Codewoertern pruefen, ob die Paritaetsbits stimmen und ob bei der
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Decodierung Werte im Null-padding veraendert wurden.
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Um nur die BCH-Codewoerter zu pruefen, kann man Polynomdivision durchfuehren (CRC):
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1)
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0000000000000000 1 0000000000000000 1 000010111011 : 0000 0000 0BB
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-> 0000000000000000100000000000000001000010111011
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./crc_polymod --bch 0000000000000000100000000000000001000010111011
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100000000000000001000010111011
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1010100111001
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1010011100100001000010111011
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1010100111001
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111011101001000010111011
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1010100111001
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10001110101100010111011
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1010100111001
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100111011110010111011
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1010100111001
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1101000010110111011
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1010100111001
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111100101111111011
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1010100111001
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10110110011011011
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1010100111001
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11111101001011
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1010100111001
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1010100111001
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1010100111001
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0
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2)
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0000000000000000 1 1010111100100010 1 000110000001 : 0000 AF22 181
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-> 0000000000000000110101111001000101000110000001
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./crc_polymod --bch 0000000000000000110101111001000101000110000001
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110101111001000101000110000001
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1010100111001
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11111100101100101000110000001
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1010100111001
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1010101011110101000110000001
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1010100111001
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1100111101000110000001
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1010100111001
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110011010001110000001
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1010100111001
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11001001101010000001
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1010100111001
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1100000011000000001
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1010100111001
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110100100001000001
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1010100111001
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11110111101100001
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1010100111001
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1011110011110001
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1010100111001
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1010100111001
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1010100111001
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0
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Decoder:
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bch_ecc.c
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Vaisala
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=======
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http://www.vaisala.com/Vaisala%20Documents/Vaisala%20News%20Articles/VN164/VN164_State-of-the-Art_Radiosonde_Telemetry.pdf
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CRC16: (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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Es koennen t=12 Fehler pro Codewort korrigiert werden.
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Fehler der Anzahl t < #E <= 2t werden zuverlaessig erkannt.
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Decoder:
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bch_ecc.c
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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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RS92
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----
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HEADER 6
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DATA 210
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RS-PARITY 24
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2a2a2a2a2a10 (header)
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6510 (L=2*0x10=32)
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e81820204b34393533393334006100083d3d07b342bb3e9809d3bc3f754c963b ebfb
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690c (L=2*0x0c=24)
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ca2b0fd9670f00670f8c0f11a458111e8810da410d30430d dc84
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673d (L=2*0x3d=122)
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b01c852167ab07298b3cb05a536e0fffcf4faf7f4f3fff8fcfffffffff7fe5918aef20e8110175879900d0e0e900061f8c048aa393009edea1fe2557dc0019549f04b5160d00ae998b00e12a4200370b8608cacc1900b3e08905bd60040126da9303e1d4b4006d04a00573469700d6a98b00699f120195828f04 6ed7
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6805 (L=2*0x05=10)
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03030000000000000000 b27d
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ff02 (L=2*0x02=4)
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02000200
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f0be2a40a7cd69b9ed0668ec12182e8560ea6dd0733612a1 (Reed-Solomon parity)
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ecc-rs_vaisala.c:
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1)
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./ecc-rs_vaisala 2a2a2a2a2a106510e81820204b34393533393334006100083d3d07b342bb3e9809d3bc3f754c963bebfb690cca2b0fd9670f00670f8c0f11a458111e8810da410d30430ddc84673db01c852167ab07298b3cb05a536e0fffcf4faf7f4f3fff8fcfffffffff7fe5918aef20e8110175879900d0e0e900061f8c048aa393009edea1fe2557dc0019549f04b5160d00ae998b00e12a4200370b8608cacc1900b3e08905bd60040126da9303e1d4b4006d04a00573469700d6a98b00699f120195828f046ed7680503030000000000000000b27dff0202000200f0be2a40a7cd69b9ed0668ec12182e8560ea6dd0733612a1
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RS92
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codeword
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errors: 0
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frame:
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2a2a2a2a2a106510e81820204b34393533393334006100083d3d07b342bb3e9809d3bc3f754c963bebfb690cca2b0fd9670f00670f8c0f11a458111e8810da410d30430ddc84673db01c852167ab07298b3cb05a536e0fffcf4faf7f4f3fff8fcfffffffff7fe5918aef20e8110175879900d0e0e900061f8c048aa393009edea1fe2557dc0019549f04b5160d00ae998b00e12a4200370b8608cacc1900b3e08905bd60040126da9303e1d4b4006d04a00573469700d6a98b00699f120195828f046ed7680503030000000000000000b27dff0202000200f0be2a40a7cd69b9ed0668ec12182e8560ea6dd0733612a1
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2a)
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./rs92gps -r rs92.wav > rs92raw.txt
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cat rs92raw.txt | ./ecc-rs_vaisala > rs92raw_ecc.txt
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./rs92gps --rawin1 -a almanac.txt rs92raw_ecc.txt
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2b)
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cat rs92raw.txt | ./ecc-rs_vaisala | ./rs92gps --rawin1 -a almanac.txt
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2c)
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./rs92gps -r rs92.wav | ./ecc-rs_vaisala | ./rs92gps --rawin1 -a almanac.txt
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3)
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./rs92ecc -b --ecc -e rinex.txt rs92.wav
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./rs92ecc -b --ecc --crc -e rinex.txt rs92.wav
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./rs92ecc -b --ecc -r rs92.wav
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RS41
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----
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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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"interleaved"
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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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RS(255,231) RS(255,231) L=40 CRC L=42 CRC L=30 CRC L=89 CRC L=21 CRC L=17 CRC
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8635f44093df1a60 2c87e0fa0521e8943d9cef4c7a67393f6d39fb546461f2111b6447ab79a746c80350cda5344157f8c0c12234f4690222 0f 7928 16174b313933303239331a00000300000a00002f0007322ce53e31991abf12dada3eb68468c16755 d51c 7a2a 15310216060245f302000d08a31607821e08bb210219060243f302000000000000000000000000000000 220d 7c1e 0807d03cdc071fd81ddb19d70a8d0eb602b60cb518d40692ff00ff00ff00 1c27 7d59 b8d83301ff0f881f0f38f4fe18b283038735ff000000003eb8ff4947201e6e3aff55415f13fc6e005440440cf100009e9f7406f85800832b631719d70010bebc172a8b00000000000000000000000000000000000000000000 a48b 7b15 366181193ef05d07e1245b1be0f721f801f6080410 7b0b 7611 0000000000000000000000000000000000 ecc7
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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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./ecc-rs_vaisala 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RS41
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codeword1
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errors: 0
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codeword2
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errors: 0
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frame:
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2)
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./ecc-rs_vaisala 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RS41
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codeword1
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errors: 1
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pos: 136
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codeword2
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errors: 2
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pos: 106 176
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frame:
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3)
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./rs41ecc -b --ecc rs41.wav
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./rs41ecc -b --ecc --crc rs41.wav
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./rs41ecc -b --ecc -r rs41.wav
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CRC16
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-----
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./crc_polymod --crc 0000000000000000000000000000000000 ecc7
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C7EC
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11111111111111110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001100011111101100
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10001000000100001
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0
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./crc_polymod --crc 0000000000000000000000000000000000
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C7EC
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1100011111101100
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10001000000100001
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|
1100011111101100
|
|
Rest:
|
|
1100011111101100 = 0xC7EC
|
|
|