LDPC koodide paarsuskontrolli maatriksite optimiseerimine
Date
2014
Authors
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Abstract
Madala tihedusega paarsuskontroll (LDPC) on laialdaselt kasutusel kommunikatsioonis
tänu oma suurepärasele praktilisele võimekusele. LDPC koodi vigade tõenäosust iteratiivse
dekodeerimise puhul binaarsel kustutuskanalil määrab klass kombinatoorseid objekte, nimega
peatamise rühm. Väikese suurusega peatamise rühmad on dekodeerija vigade põhjuseks.
Peatamise liiasust määratletakse kui minimaalset ridade arvu paarsuskontrolli koodi
maatriksis, mille puhul pole selles väikesi peatuse rühmi.
Han, Siegel ja Vardy kasutavad üld binaarse lineaarkoodi ülemise piiri peatamiste liiasuse
tuletamiseks tõenäosuslikku analüüsi. Need piirid on teadaolevalt parimad paljude koodi
perekondade puhul. Selles töös me parendame Hani, Siegeli ja Vardy tulemusi modifitseerides
selleks nende analüüsi. Meie lähenemine erineb sellepoolest, et me valime mõistlikult esimese
ja teise rea paarsuskontrolli maatriksis ja siis läheme edasi tõenäosusliku analüüsiga.
Numbrilised väärtused kinnitavad seda, et piirid mis on määratletud selles töös on paremad
Hani, Siegeli ja Vardy omadest kahe koodi puhul: laiendatud Golay koodis ja kvadraatses jääk
koodis pikkusega 48.
Low-density parity-check (LDPC) codes are widely used in communications due to their excellent practical performance. Error probability of LDPC code under iterative decoding on the binary erasure channel is determined by a class of combinatorial objects, called stopping sets. Stopping sets of small size are the reason for the decoder failures. Stopping redundancy is defined as the minimum number of rows in a parity-check matrix of the code, such that there are no small stopping sets in it. Han, Siegel and Vardy derive upper bounds on the stopping redundancy of general binary linear codes by using probabilistic analysis. For many families of codes, these bounds are the best currently known. In this work, we improve on the results of Han, Siegel and Vardy by modifying their analysis. Our approach is different in that we judiciously select the first and the second rows in the parity-check matrix, and then proceed with the probabilistic analysis. Numerical experiments confirm that the bounds obtained in this thesis are superior to those of Han, Siegel and Vardy for two codes: the extended Golay code and the quadratic residue code of length 48.
Low-density parity-check (LDPC) codes are widely used in communications due to their excellent practical performance. Error probability of LDPC code under iterative decoding on the binary erasure channel is determined by a class of combinatorial objects, called stopping sets. Stopping sets of small size are the reason for the decoder failures. Stopping redundancy is defined as the minimum number of rows in a parity-check matrix of the code, such that there are no small stopping sets in it. Han, Siegel and Vardy derive upper bounds on the stopping redundancy of general binary linear codes by using probabilistic analysis. For many families of codes, these bounds are the best currently known. In this work, we improve on the results of Han, Siegel and Vardy by modifying their analysis. Our approach is different in that we judiciously select the first and the second rows in the parity-check matrix, and then proceed with the probabilistic analysis. Numerical experiments confirm that the bounds obtained in this thesis are superior to those of Han, Siegel and Vardy for two codes: the extended Golay code and the quadratic residue code of length 48.