文件名称:limitedrandomnessltcodes
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LTcodesareasymptoticallyoptimalratelesserasurecodeswithhighlyeffi cientencod-
inganddecodingalgorithms.Intheoriginalanalysisofthesecodes,itwasassumedthat
foreachencodingsymbol,theneighborsusedtogeneratethatencodingsymbolarechosen
uniformlyatrandom.
PracticalimplementationsofLTcodescannotaff ordthisamountofrandomness,be-
causeallrandombitsmustbecommunicatedtothedecodingparty.Instead,theyuse
alinearcongruentialgeneratortoreducetherandomnessusedperencodingsymboltoa
seedconsistingoftworandomnumbers.Weshowthatsuch limitedrandomness LTcodes
performalmostaswellasthefullyrandomversion.ThusevenlimitedrandomnessLT
codesareasymptoticallyoptimal.-LTcodesareasymptoticallyoptimalratelesserasurecodeswithhighlyefficientencod-inganddecodingalgorithms.Intheoriginalanalysisofthesecodes, itwasassumedthat foreachencodingsymbol, theneighborsusedtogeneratethatencodingsymbolarechosen uniformlyatrandom. PracticalimplementationsofLTcodescannotaffordthisamountofrandomness, be-causeallrandombitsmustbecommunicatedtothedecodingparty.Instead, theyuse alinearcongruentialgeneratortoreducetherandomnessusedperencodingsymboltoa seedconsistingoftworandomnumbers.Weshowthatsuch limitedrandomness LTcodes performalmostaswellasthefullyrandomversion.ThusevenlimitedrandomnessLT codesareasymptoticallyoptimal.
inganddecodingalgorithms.Intheoriginalanalysisofthesecodes,itwasassumedthat
foreachencodingsymbol,theneighborsusedtogeneratethatencodingsymbolarechosen
uniformlyatrandom.
PracticalimplementationsofLTcodescannotaff ordthisamountofrandomness,be-
causeallrandombitsmustbecommunicatedtothedecodingparty.Instead,theyuse
alinearcongruentialgeneratortoreducetherandomnessusedperencodingsymboltoa
seedconsistingoftworandomnumbers.Weshowthatsuch limitedrandomness LTcodes
performalmostaswellasthefullyrandomversion.ThusevenlimitedrandomnessLT
codesareasymptoticallyoptimal.-LTcodesareasymptoticallyoptimalratelesserasurecodeswithhighlyefficientencod-inganddecodingalgorithms.Intheoriginalanalysisofthesecodes, itwasassumedthat foreachencodingsymbol, theneighborsusedtogeneratethatencodingsymbolarechosen uniformlyatrandom. PracticalimplementationsofLTcodescannotaffordthisamountofrandomness, be-causeallrandombitsmustbecommunicatedtothedecodingparty.Instead, theyuse alinearcongruentialgeneratortoreducetherandomnessusedperencodingsymboltoa seedconsistingoftworandomnumbers.Weshowthatsuch limitedrandomness LTcodes performalmostaswellasthefullyrandomversion.ThusevenlimitedrandomnessLT codesareasymptoticallyoptimal.
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limitedrandomnessltcodes.pdf