id sid tid token lemma pos jd472v2639f 1 1 in in ADP jd472v2639f 1 2 1948 1948 NUM jd472v2639f 1 3 , , PUNCT jd472v2639f 1 4 claude claude NOUN jd472v2639f 1 5 shannon shannon PROPN jd472v2639f 1 6 provided provide VERB jd472v2639f 1 7 a a DET jd472v2639f 1 8 sound sound ADJ jd472v2639f 1 9 mathematical mathematical ADJ jd472v2639f 1 10 foundation foundation NOUN jd472v2639f 1 11 for for ADP jd472v2639f 1 12 communication communication NOUN jd472v2639f 1 13 , , PUNCT jd472v2639f 1 14 and and CCONJ jd472v2639f 1 15 proved prove VERB jd472v2639f 1 16 the the DET jd472v2639f 1 17 existence existence NOUN jd472v2639f 1 18 of of ADP jd472v2639f 1 19 good good ADJ jd472v2639f 1 20 codes code NOUN jd472v2639f 1 21 . . PUNCT jd472v2639f 2 1 low low ADJ jd472v2639f 2 2 - - PUNCT jd472v2639f 2 3 density density NOUN jd472v2639f 2 4 parity parity NOUN jd472v2639f 2 5 - - PUNCT jd472v2639f 2 6 check check NOUN jd472v2639f 2 7 ( ( PUNCT jd472v2639f 2 8 ldpc ldpc NOUN jd472v2639f 2 9 ) ) PUNCT jd472v2639f 2 10 codes code NOUN jd472v2639f 2 11 are be AUX jd472v2639f 2 12 a a DET jd472v2639f 2 13 family family NOUN jd472v2639f 2 14 of of ADP jd472v2639f 2 15 error error NOUN jd472v2639f 2 16 - - PUNCT jd472v2639f 2 17 correcting correct VERB jd472v2639f 2 18 codes code NOUN jd472v2639f 2 19 that that PRON jd472v2639f 2 20 achieve achieve VERB jd472v2639f 2 21 reliable reliable ADJ jd472v2639f 2 22 performance performance NOUN jd472v2639f 2 23 ( ( PUNCT jd472v2639f 2 24 i.e. i.e. X jd472v2639f 2 25 , , PUNCT jd472v2639f 2 26 arbitrarily arbitrarily ADV jd472v2639f 2 27 low low ADJ jd472v2639f 2 28 probability probability NOUN jd472v2639f 2 29 of of ADP jd472v2639f 2 30 decoding decode VERB jd472v2639f 2 31 error error NOUN jd472v2639f 2 32 ) ) PUNCT jd472v2639f 2 33 near near ADP jd472v2639f 2 34 the the DET jd472v2639f 2 35 shannon shannon ADJ jd472v2639f 2 36 - - PUNCT jd472v2639f 2 37 limit limit NOUN jd472v2639f 2 38 when when SCONJ jd472v2639f 2 39 decoded decode VERB jd472v2639f 2 40 iteratively iteratively ADV jd472v2639f 2 41 via via ADP jd472v2639f 2 42 very very ADV jd472v2639f 2 43 efficient efficient ADJ jd472v2639f 2 44 graph graph NOUN jd472v2639f 2 45 - - PUNCT jd472v2639f 2 46 based base VERB jd472v2639f 2 47 message message NOUN jd472v2639f 2 48 - - PUNCT jd472v2639f 2 49 passing pass VERB jd472v2639f 2 50 decoders decoder NOUN jd472v2639f 2 51 , , PUNCT jd472v2639f 2 52 the the DET jd472v2639f 2 53 complexity complexity NOUN jd472v2639f 2 54 of of ADP jd472v2639f 2 55 which which PRON jd472v2639f 2 56 grows grow VERB jd472v2639f 2 57 only only ADV jd472v2639f 2 58 linearly linearly ADV jd472v2639f 2 59 in in ADP jd472v2639f 2 60 the the DET jd472v2639f 2 61 block block NOUN jd472v2639f 2 62 - - PUNCT jd472v2639f 2 63 length length NOUN jd472v2639f 2 64 . . PUNCT jd472v2639f 3 1 despite despite SCONJ jd472v2639f 3 2 their their PRON jd472v2639f 3 3 tremendous tremendous ADJ jd472v2639f 3 4 success success NOUN jd472v2639f 3 5 , , PUNCT jd472v2639f 3 6 ldpc ldpc NOUN jd472v2639f 3 7 codes code NOUN jd472v2639f 3 8 lack lack VERB jd472v2639f 3 9 a a DET jd472v2639f 3 10 strong strong ADJ jd472v2639f 3 11 theoretical theoretical ADJ jd472v2639f 3 12 foundation foundation NOUN jd472v2639f 3 13 and and CCONJ jd472v2639f 3 14 few few ADJ jd472v2639f 3 15 explicit explicit ADJ jd472v2639f 3 16 constructions construction NOUN jd472v2639f 3 17 of of ADP jd472v2639f 3 18 them they PRON jd472v2639f 3 19 are be AUX jd472v2639f 3 20 known know VERB jd472v2639f 3 21 that that PRON jd472v2639f 3 22 outperform outperform VERB jd472v2639f 3 23 their their PRON jd472v2639f 3 24 random random ADJ jd472v2639f 3 25 counterparts counterpart NOUN jd472v2639f 3 26 . . PUNCT jd472v2639f 4 1 the the DET jd472v2639f 4 2 first first ADJ jd472v2639f 4 3 part part NOUN jd472v2639f 4 4 of of ADP jd472v2639f 4 5 this this DET jd472v2639f 4 6 thesis thesis NOUN jd472v2639f 4 7 investigates investigate VERB jd472v2639f 4 8 how how SCONJ jd472v2639f 4 9 the the DET jd472v2639f 4 10 structure structure NOUN jd472v2639f 4 11 of of ADP jd472v2639f 4 12 a a DET jd472v2639f 4 13 graph graph NOUN jd472v2639f 4 14 representing represent VERB jd472v2639f 4 15 an an DET jd472v2639f 4 16 ldpc ldpc PROPN jd472v2639f 4 17 code code NOUN jd472v2639f 4 18 affects affect VERB jd472v2639f 4 19 the the DET jd472v2639f 4 20 decoding decoding ADJ jd472v2639f 4 21 performance performance NOUN jd472v2639f 4 22 . . PUNCT jd472v2639f 5 1 in in ADP jd472v2639f 5 2 particular particular ADJ jd472v2639f 5 3 , , PUNCT jd472v2639f 5 4 lower low ADJ jd472v2639f 5 5 bounds bound NOUN jd472v2639f 5 6 on on ADP jd472v2639f 5 7 the the DET jd472v2639f 5 8 minimum minimum ADJ jd472v2639f 5 9 pseudocodeword pseudocodeword PROPN jd472v2639f 5 10 weight weight NOUN jd472v2639f 5 11 , , PUNCT jd472v2639f 5 12 a a DET jd472v2639f 5 13 key key ADJ jd472v2639f 5 14 parameter parameter NOUN jd472v2639f 5 15 in in ADP jd472v2639f 5 16 predicting predict VERB jd472v2639f 5 17 iterative iterative ADJ jd472v2639f 5 18 decoding decoding ADJ jd472v2639f 5 19 performance performance NOUN jd472v2639f 5 20 , , PUNCT jd472v2639f 5 21 are be AUX jd472v2639f 5 22 obtained obtain VERB jd472v2639f 5 23 which which PRON jd472v2639f 5 24 link link VERB jd472v2639f 5 25 the the DET jd472v2639f 5 26 performance performance NOUN jd472v2639f 5 27 of of ADP jd472v2639f 5 28 the the DET jd472v2639f 5 29 code code NOUN jd472v2639f 5 30 to to ADP jd472v2639f 5 31 the the DET jd472v2639f 5 32 structural structural ADJ jd472v2639f 5 33 properties property NOUN jd472v2639f 5 34 of of ADP jd472v2639f 5 35 its its PRON jd472v2639f 5 36 graph graph NOUN jd472v2639f 5 37 . . PUNCT jd472v2639f 6 1 one one NUM jd472v2639f 6 2 bound bind VERB jd472v2639f 6 3 is be AUX jd472v2639f 6 4 a a DET jd472v2639f 6 5 tree tree NOUN jd472v2639f 6 6 bound bind VERB jd472v2639f 6 7 and and CCONJ jd472v2639f 6 8 is be AUX jd472v2639f 6 9 extended extend VERB jd472v2639f 6 10 to to ADP jd472v2639f 6 11 generalized generalized ADJ jd472v2639f 6 12 and and CCONJ jd472v2639f 6 13 p p PROPN jd472v2639f 6 14 - - PUNCT jd472v2639f 6 15 ary ary PROPN jd472v2639f 6 16 ldpc ldpc PROPN jd472v2639f 6 17 codes code NOUN jd472v2639f 6 18 . . PUNCT jd472v2639f 7 1 to to ADP jd472v2639f 7 2 this this DET jd472v2639f 7 3 end end NOUN jd472v2639f 7 4 , , PUNCT jd472v2639f 7 5 a a DET jd472v2639f 7 6 suitable suitable ADJ jd472v2639f 7 7 definition definition NOUN jd472v2639f 7 8 of of ADP jd472v2639f 7 9 pseudocodeword pseudocodeword PROPN jd472v2639f 7 10 weight weight NOUN jd472v2639f 7 11 is be AUX jd472v2639f 7 12 derived derive VERB jd472v2639f 7 13 for for ADP jd472v2639f 7 14 the the DET jd472v2639f 7 15 p p PROPN jd472v2639f 7 16 - - PUNCT jd472v2639f 7 17 ary ary PROPN jd472v2639f 7 18 symmetric symmetric ADJ jd472v2639f 7 19 channel channel PROPN jd472v2639f 7 20 . . PUNCT jd472v2639f 8 1 moreover moreover ADV jd472v2639f 8 2 , , PUNCT jd472v2639f 8 3 the the DET jd472v2639f 8 4 relationship relationship NOUN jd472v2639f 8 5 between between ADP jd472v2639f 8 6 pseudocodeword pseudocodeword PROPN jd472v2639f 8 7 weight weight NOUN jd472v2639f 8 8 distributions distribution NOUN jd472v2639f 8 9 and and CCONJ jd472v2639f 8 10 different different ADJ jd472v2639f 8 11 graph graph NOUN jd472v2639f 8 12 representations representation NOUN jd472v2639f 8 13 is be AUX jd472v2639f 8 14 examined examine VERB jd472v2639f 8 15 . . PUNCT jd472v2639f 9 1 bounds bound NOUN jd472v2639f 9 2 on on ADP jd472v2639f 9 3 the the DET jd472v2639f 9 4 minimum minimum ADJ jd472v2639f 9 5 pseudocodeword pseudocodeword PROPN jd472v2639f 9 6 weight weight NOUN jd472v2639f 9 7 are be AUX jd472v2639f 9 8 also also ADV jd472v2639f 9 9 presented present VERB jd472v2639f 9 10 for for ADP jd472v2639f 9 11 several several ADJ jd472v2639f 9 12 classes class NOUN jd472v2639f 9 13 of of ADP jd472v2639f 9 14 expander expander NOUN jd472v2639f 9 15 codes code NOUN jd472v2639f 9 16 based base VERB jd472v2639f 9 17 on on ADP jd472v2639f 9 18 the the DET jd472v2639f 9 19 eigenvalues eigenvalue NOUN jd472v2639f 9 20 of of ADP jd472v2639f 9 21 the the DET jd472v2639f 9 22 adjacency adjacency ADJ jd472v2639f 9 23 matrix matrix NOUN jd472v2639f 9 24 of of ADP jd472v2639f 9 25 the the DET jd472v2639f 9 26 tanner tanner NOUN jd472v2639f 9 27 graph graph NOUN jd472v2639f 9 28 . . PUNCT jd472v2639f 10 1 the the DET jd472v2639f 10 2 second second ADJ jd472v2639f 10 3 part part NOUN jd472v2639f 10 4 of of ADP jd472v2639f 10 5 this this DET jd472v2639f 10 6 thesis thesis NOUN jd472v2639f 10 7 constructs construct VERB jd472v2639f 10 8 ldpc ldpc NOUN jd472v2639f 10 9 codes code NOUN jd472v2639f 10 10 having have VERB jd472v2639f 10 11 desirable desirable ADJ jd472v2639f 10 12 properties property NOUN jd472v2639f 10 13 . . PUNCT jd472v2639f 11 1 the the DET jd472v2639f 11 2 first first ADJ jd472v2639f 11 3 construction construction NOUN jd472v2639f 11 4 is be AUX jd472v2639f 11 5 combinatorial combinatorial ADJ jd472v2639f 11 6 and and CCONJ jd472v2639f 11 7 uses use VERB jd472v2639f 11 8 permutations permutation NOUN jd472v2639f 11 9 and and CCONJ jd472v2639f 11 10 mutually mutually ADV jd472v2639f 11 11 orthogonal orthogonal ADJ jd472v2639f 11 12 latin latin PROPN jd472v2639f 11 13 squares square NOUN jd472v2639f 11 14 . . PUNCT jd472v2639f 12 1 one one NUM jd472v2639f 12 2 type type NOUN jd472v2639f 12 3 results result NOUN jd472v2639f 12 4 in in ADP jd472v2639f 12 5 the the DET jd472v2639f 12 6 well well ADV jd472v2639f 12 7 - - PUNCT jd472v2639f 12 8 known know VERB jd472v2639f 12 9 projective projective NOUN jd472v2639f 12 10 - - PUNCT jd472v2639f 12 11 geometrybased geometrybase VERB jd472v2639f 12 12 ldpc ldpc PROPN jd472v2639f 12 13 codes code NOUN jd472v2639f 12 14 . . PUNCT jd472v2639f 13 1 another another DET jd472v2639f 13 2 type type NOUN jd472v2639f 13 3 yields yield VERB jd472v2639f 13 4 a a DET jd472v2639f 13 5 new new ADJ jd472v2639f 13 6 family family NOUN jd472v2639f 13 7 of of ADP jd472v2639f 13 8 codes code NOUN jd472v2639f 13 9 having have VERB jd472v2639f 13 10 comparable comparable ADJ jd472v2639f 13 11 parameters parameter NOUN jd472v2639f 13 12 and and CCONJ jd472v2639f 13 13 pseudocodeword pseudocodeword PROPN jd472v2639f 13 14 weights weight NOUN jd472v2639f 13 15 suitable suitable ADJ jd472v2639f 13 16 for for ADP jd472v2639f 13 17 iterative iterative ADJ jd472v2639f 13 18 decoding decoding NOUN jd472v2639f 13 19 . . PUNCT jd472v2639f 14 1 the the DET jd472v2639f 14 2 resulting result VERB jd472v2639f 14 3 performance performance NOUN jd472v2639f 14 4 of of ADP jd472v2639f 14 5 these these DET jd472v2639f 14 6 codes code NOUN jd472v2639f 14 7 is be AUX jd472v2639f 14 8 superior superior ADJ jd472v2639f 14 9 in in ADP jd472v2639f 14 10 comparison comparison NOUN jd472v2639f 14 11 with with ADP jd472v2639f 14 12 that that PRON jd472v2639f 14 13 of of ADP jd472v2639f 14 14 comparable comparable ADJ jd472v2639f 14 15 random random ADJ jd472v2639f 14 16 ldpc ldpc PROPN jd472v2639f 14 17 codes code NOUN jd472v2639f 14 18 , , PUNCT jd472v2639f 14 19 a a DET jd472v2639f 14 20 feature feature NOUN jd472v2639f 14 21 attributed attribute VERB jd472v2639f 14 22 to to ADP jd472v2639f 14 23 the the DET jd472v2639f 14 24 lack lack NOUN jd472v2639f 14 25 of of ADP jd472v2639f 14 26 low low ADJ jd472v2639f 14 27 - - PUNCT jd472v2639f 14 28 weight weight NOUN jd472v2639f 14 29 bad bad ADJ jd472v2639f 14 30 pseudocodewords pseudocodeword NOUN jd472v2639f 14 31 . . PUNCT jd472v2639f 15 1 for for ADP jd472v2639f 15 2 the the DET jd472v2639f 15 3 second second ADJ jd472v2639f 15 4 construction construction NOUN jd472v2639f 15 5 , , PUNCT jd472v2639f 15 6 unbalanced unbalanced ADJ jd472v2639f 15 7 expander expander NOUN jd472v2639f 15 8 graphs graph NOUN jd472v2639f 15 9 are be AUX jd472v2639f 15 10 obtained obtain VERB jd472v2639f 15 11 by by ADP jd472v2639f 15 12 modifying modify VERB jd472v2639f 15 13 the the DET jd472v2639f 15 14 original original ADJ jd472v2639f 15 15 zig zig NOUN jd472v2639f 15 16 - - PUNCT jd472v2639f 15 17 zag zag NOUN jd472v2639f 15 18 graph graph NOUN jd472v2639f 15 19 product product NOUN jd472v2639f 15 20 to to PART jd472v2639f 15 21 take take VERB jd472v2639f 15 22 bi bi ADJ jd472v2639f 15 23 - - ADJ jd472v2639f 15 24 regular regular ADJ jd472v2639f 15 25 expander expander NOUN jd472v2639f 15 26 graphs graph NOUN jd472v2639f 15 27 as as ADP jd472v2639f 15 28 components component NOUN jd472v2639f 15 29 , , PUNCT jd472v2639f 15 30 with with ADP jd472v2639f 15 31 suitable suitable ADJ jd472v2639f 15 32 constraints constraint NOUN jd472v2639f 15 33 on on ADP jd472v2639f 15 34 the the DET jd472v2639f 15 35 degrees degree NOUN jd472v2639f 15 36 . . PUNCT jd472v2639f 16 1 graphs graph NOUN jd472v2639f 16 2 resulting result VERB jd472v2639f 16 3 from from ADP jd472v2639f 16 4 the the DET jd472v2639f 16 5 zig zig NOUN jd472v2639f 16 6 - - PUNCT jd472v2639f 16 7 zag zag NOUN jd472v2639f 16 8 and and CCONJ jd472v2639f 16 9 replacement replacement NOUN jd472v2639f 16 10 product product NOUN jd472v2639f 16 11 graphs graph NOUN jd472v2639f 16 12 are be AUX jd472v2639f 16 13 then then ADV jd472v2639f 16 14 used use VERB jd472v2639f 16 15 in in ADP jd472v2639f 16 16 the the DET jd472v2639f 16 17 design design NOUN jd472v2639f 16 18 of of ADP jd472v2639f 16 19 generalized generalize VERB jd472v2639f 16 20 ldpc ldpc NOUN jd472v2639f 16 21 codes code NOUN jd472v2639f 16 22 having have VERB jd472v2639f 16 23 compact compact ADJ jd472v2639f 16 24 representation representation NOUN jd472v2639f 16 25 and and CCONJ jd472v2639f 16 26 pseudocodeword pseudocodeword PROPN jd472v2639f 16 27 weights weight NOUN jd472v2639f 16 28 lower lower ADV jd472v2639f 16 29 - - PUNCT jd472v2639f 16 30 bounded bound VERB jd472v2639f 16 31 by by ADP jd472v2639f 16 32 the the DET jd472v2639f 16 33 eigenvalue eigenvalue NOUN jd472v2639f 16 34 bounds bound NOUN jd472v2639f 16 35 . . PUNCT