Single-Scan Min-Sum Algorithms for Fast Decoding of LDPC Codes
Many implementations for decoding LDPC codes are based on the (normalized/offset) min-sum algorithm due to its satisfactory performance and simplicity in operations. Usually, each iteration of the min-sum algorithm contains two scans, the horizontal scan a
EachrowHi(1≤i≤M)ofHintroducesoneparitycheckconstraintoninputdatax=(x1,x2,...,xn),i.e.,
HixT=0mod2.
SothereareMconstraintsonxintotal.
LetN(m)bethesetofvariablenodesthatareincludedinthem-thparitycheckconstraint.LetM(n)bethesetofchecknodeswhichcontainthevariablenoden.N(m)\ndenotesthesetofvariablenodesexcludingnodenthatareincludedinthem-thparitycheckconstraint.M(n)\mstandsforthesetofchecknodesexcludingthechecknodemwhichcontainthevariablenoden.Thesymbol‘\’denotesthesetminus.ForanadditivewhiteGaussiannoisechannelandabinarymodulation,letynbethereceiveddatabitatpositionn,
yn=( 1)xn+ξn,
whereξnisthechannelnoise.TheinitialLog-likelihoodratio
(0)
(LLR)fortheinputdatabitn,denotedasZn,is
(0)Zn≡ln
p(xn=0/yn)
