Transcription of 5章 誤り訂正技術の応用 - ieice-hbkb.org
1 4 1 5 . 4 - 1 . 5 . [2009 2 ].. FEC: Forward Error Correction . ARQ: Automatic Repeat Request .. BCH Golay RS . LAN LDPC: Low density parity check .. 3 .. Concatenated code . RS .. FEC .. ARQ FEC. ARQ ARQ 5 1 .. 2010 1/(9). 4 1 5 . 5 1 . PAN LAN MAN . WiFi WiMAX . BCH CC-RS CC-RS CC CC BCH. CC TC8 PSK-RS CC LDPC CC-RS CC. CC-RS LDPC CTC CTC. CTC BTC LDPC . LDPC HARQ. HARQ. CC - CTC . RS BTC . TC8 PSK 8 PSK HARQ ARQ. CC- RS RS . 2010 2/(9). 4 1 5 . 4 - 1 - 5 . 5-1 . [2009 2 ].. 2 3 .. OFDM .. 2010 3/(9). 4 1 5 . 4 - 1 - 5 . 5-2 . [2009 2 ]. 5-2-1 . (1) CRC Cyclic Redundancy check . k m n (n k m).. r k/n n k . t (n, k) (n, k, t) . CRC Cyclic Redundancy check .. 5 1 . EX-OR: Exclusive OR . LAN . ARQ .. I(X )X n-k C(X ) . I(X )X n-k c(X ). c(X ).. + + + +. g1 g2 gm 1 .. + EX-OR 1 EX-O R . 5 1 . (2) BCH . BCH Bose-Chaudhuri-Hocquenghem 1,2) 3 . 1 .. n 2m 1 k ( 2m 1 mt) t . BCH .. t 1 . SEC Single Error Correction 2 DEC Double Error 2010 4/(9).
2 4 1 5 . Correction t 1 . t 1 1 2 . SEC-DED Double Error Detection 2 3 DEC-TED Triple Error Detection . BCH . 127,112,2 DEC-TED .. (3) . RS: Reed-Solomon 3) BCH BCH . 1 0 2 m 2m . 1 m n . k n 2m 1 k 2m 1 (dmin 1) = n dmin 1 . (dmin 1)/2 . 204, 188 .. 188 51 0 239 . 255, 239 51 204.. 204, 188 188 16 . 8 . RS .. (4) LDPC . LDPC Low density parity check 4) 1960 Gallager . LDPC. LDPC H .. H m n . k n m r k/n (n m)/n . LDPC LAN WiMAX . LTE . 5-2-2 . (1) - . 5 2 . r 1/2 K 3 . 5 3 Dmin 5 . K 7 Dmin 10 Ns 2B(K-1) . B Dmin . r 1/2 K 7 Ns 64 r 3/4 K 3 . Ns 64 . 2010 5/(9). 4 1 5 . 0. 1 .. (X1,X2 ). (0,0). 00. (1,1).. (1,1). 10.. + X1 (0,0). (1,0). 01. I (0,1). (0,1). + X2 11. (1,0). 5 2 5 3 .. 5).. 1960 Viterbi .. r 1/2 . 2/3, 3/4, 7/8 .. LSI . 5 4 . ACS . LSI.. OFDM LAN .. (2) . 6) 1993 Berrou .. 1 2 . 2010 6/(9). 4 1 5 . 2 . 1 2 7-4 . 7-4-2 3 .. 3 WiMAX . 00 . 00 00 .. ACS . 10 .. ACS . 00 . X1.
3 I. X2. ACS . 01 . ACS . 11 .. 5 4 . 5-2-3 Concatenated Code . 7).. Forney. Jr 2 . Inner Code 2k RS. Outer Code .. 2010 7/(9). 4 1 5 . 4 - 1 - 5 . 5-3 . [2009 2 ].. 8 PSK 8) 8 3 .. r 2/3 . 8 PSK 1 2 . 4 PSK 8 PSK . 3dB .. 2010 8/(9). 4 1 5 . 4 - 1 - 5 . 5-4 ARQ Automatic Repeat Request: . [2009 2 ]. ARQ CRC .. ARQ . Stop-and-wait SAW ACK .. N NACK . Go-back-N GBN .. NACK . Selective-Repeat SR .. ARQ . ARQ FEC ARQ . ARQ I 2 3 . NAK . II . 1 ARQ NAK FEC. 1 . ARQ .. 1) Hocquenghem, Codes corecteurs d'erreurs, Chiffres, , , 1959. 2) Bose, Chaudhuri, On a class of error correcting binary group codes, Inform. Control, , , March. 1960. 3) Reed, G. Solomon, Polynomial codes over certain finite fields, Journal Soc. Ind. Appl. Math., , , June. 1960. 4) Gallager, Low- density parity - check codes, MIT Press, Cambridge, 1963. 5) Viterbi, Error bounds for convolutional codes and an asymptotically optimum decoding algorithm, IEEE.
4 Trans. Inform. Theory, , , , April. 1967. 6) Berrou, , , Near Shannon limit error-correcting coding and decoding, Proceeding IEEE ICC, , May. 1993. 7) Forney Jr., Concatenated codes, MIT Press, Cambridge, 1966. 8) G. Ungerboeck, Channel coding with multilevel/phase signals, IEEE Trans. Inform. Theory, , , , Jan. 1982. 2010 9/(9).
