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AnnexA

（informative）

InformativepartofMPEG-4Audiover.2CDtext

A.1.Finegrainscalabilitytool:

BSAC（Bit-SlicedArithmeticCoding）

A.1.1Introduction

IntheBSACencodertheinputstothenoiselesscodingmodulearethesetof1024quantizedspectralcoefficientsandthescalefactorofthescalefactorband.Sincethenoiselesscodingisdoneinsidethequantizerinnerloop,itispartofaniterativeprocessthatconvergeswhenthetotalbitcount（ofwhichthenoiselesscodingisthevastmajority）iswithinsomeintervalsurroundingtheallocatedbitcount.Thissectionwilldescribetheencodingprocessforasinglecalltothenoiselesscodingmodule.

Noiselesscodingisdoneviathefollowingsteps:

∙BitSlicingofthequantizedspectralcoefficient

∙PreliminaryArithmeticcodingofthesetofqunatizedspectumwithinacodingbandusingthearithemticmodel

∙PreliminaryArithmeticcodingofthescalefactors,stereoinfomation,artihmeticmodelinfomation.

∙ArithmeticModeldeterminationtoachievelowestbitcount

A.1.2BitSlicingofthequantizedspectralcoefficients

AsafirststepIofBSACencodingprocess,asequenceoftheabsolutevaluesofquantizedspectralcoefficientsismappedintoabit-slicedsequence.Andinordertomaximizethematchofthestatisticsofthebit-slicedsequencestothatofthearithmeticmodel,4-tuplesareformedfromthebit-slicedsequenceoftheabsolutevaluesofquantizedspectralcoeffientsasshowninthefollowingFigure.

MSB

LSB

B0,m

B0,m-1

...

B0,0

0thquantizedspectraldata

B1,m

B1,m-1

...

B1,0

B2,m

B2,m-1

...

B2,0

...

...

...

...

Bk,m

Bk,m-1

...

Bk,0

kthquantizedspectraldata

where,allocated_bitis（m+1）bitandBk,mindicatesthebinaryvalueofthemthbitofkthquantizedspectralcoefficients

tuple0,m

...

tuplek/4,m

B0,m

B1,m

B2,m

B3,m

...

Bk-3,m

Bk-2,m

Bk-1,m

Bk,m

tuple0,m-1

tuplek/4,m-1

B0,m-1

B1,m-1

B2,m-1

B3,m-1

...

Bk-3,m-1

Bk-2,m-1

Bk-1,m-1

Bk,m-1

...

...

...

tuple0,0

...

tuplek/4,0

B0,0

B1,0

B2,0

B3,0

...

Bk-3,0

Bk-2,0

Bk-1,0

Bk,0

Forexample,considerasequenceoftheabsolutevalues,x[n]asfollows:

x[0]=9,x[1]=0,x[2]=7andx[3]=11...

Iftheallocated_bitis5,54-tuplesareformedfromaquantizedsequenceasshownasfollows:

MSB

LSB

x[0]:

09

0

1

0

0

1

x[1]:

00

0

0

0

0

0

x[2]:

07

0

0

1

1

1

x[3]:

11

0

1

0

1

1

1011（LeastSignificanttuple）

0011（3rdSignificanttuple）

0010（2ndSignificanttuple）

1001（1stSignificanttuple）

0000（MostSignificanttuple）

The4-tupleconsistsofsuccessivenon-overlapping4slicedbits.The4-tupleofthebit-slicedbitsareconverttothevectordependingupontheflags,sign_is_coded[].Theflag,sign_is_codedrepresentswhetherthesignbitofquantizedspectralcoeffiencienthasbeenencoded

（1）ornot（0）previously.Theyareinitializedto0.AndtheyareupdatedalongwithcodingthevectorsfromMSBtoLSB.Theyareunchangedwhenbitvalueiszeroandaresetto1whenbitvalueisnon-zero.Theprocessformakingthe4-dimensionalvectorfrom4tupleoftheslicedbitsisshownasfollows:

sign_is_coded[]=representswhetherthesignofthespectrumhasbeen

coded

（1）ornot（0）previously.

snf=thesignificanceofthevectortobedecoded.

vec=thevectortobeencodedwhichismadeupofthe

slicedbitsofthequantizedspectrum

sample[]=quantizedspectralcoeffients

start_i=startfrequencelineofthevector.

vec=0

for（i=0;i<4;i++）{

if（sign_is_coded[start_i+i]==1）{

bit_value=abs（sample[start_i+i]）&（1<<（snf-1））

vec<<=1;

if（bit_value）

vec|=0x01

}

}

for（i=0;i<4;i++）{

if（sign_is_coded[start_i+i]==0）{

bit_value=abs（sample[start_i+i]）&（1<<（snf-1））

vec<<=1;

if（bit_value）

vec|=0x01

}

}

A.1.3Arithmeticmodeldeterminations

Arithmeticmodelisusedforencodingthebit-sliceddataofeachcodingband.ThecodedspectrumusesoneArithmeticmodelpercodingband.Thenoiselesscodingsegmentsthesetof1024quantizedspectralcoefficientsintocodingbands,suchthatasingleArithmeticmodelisusedtocodeeachcodingband（themethodofArithmeticcodingisexplainedinalatersection）.Forreasonsofcodingefficiency,thequantizedspectralcoefficientsaredividedintocodingbandswhichcontain32quantizedspectralcoefficientsforthenoiselesscoding.CodingbandsarethebasicunitsusedforthenoiselesscodingforBSAC.

Arithmeticmodelindexisdeterminedamongthepossiblearithmeticmodels,suchthatthenumberofbitsneededtorepresentthefullsetofthebit-sliceddataofquantizedspectralcoefficientswithineachcodingbandisminimized.ThepossilbearithmeticmodelshavethenumberoftheallocatedbitlargerthanorequaltothatofthebitneededtorepresentthePCMdataofquantizedspectralcoefficientswithinacodingband.

codingbandsoftencontainonlycoefficientswhosevalueiszero.Forexample,iftheaudioinputisbandlimitedto20kHzorlower,thenthehighestcoefficientsarezero.SuchcodingbandsarecodedwithArithmeticmodelzero,wheretheallocatedbitis0andallcoefficientsarezero.

Inordertotransmitthearithmeticmodelinformationusedinencodingprocess,theindexofarithmeticmodeliscodedandincludedinthesyntaxofbsac_model_info（）.Thearithmeticmodelindexforencodingthebit-sliceddatawithineachcodingbandistransmittedstartingfromthelowestfrequencycodingbandandprogressingtothehighestfrequencycodingband.Forallarithmeticmodelindexesthedifferencetotheoffsetvalueisarithmetic-codedusingthearithmeticmodelArModel_model.Afterthemodelindexisencoded,thedecodingofthebit-sliceddatashallbestarted.

A.1.4Groupingandinterleaving

Ifthewindowsequenceiseightshortwindowsthenthesetof1024coefficientsisactuallyamatrixof8by128frequencycoefficientsrepresentingthetime-frequencyevolutionofthesignaloverthedurationoftheeightshortwindows.Althoughthesectioningmechanismisflexibleenoughtoefficientlyrepresentthe8zerosections,groupingandinterleavingprovideforgreatercodingefficiency.Asexplainedearlier,thecoefficientsassociatedwithcontiguousshortwindowscanbegroupedsuchthattheysharescalefactorsamongstallscalefactorbandswithinthegroup.Inaddition,thecoefficientswithinagroupareinterleavedbyinterchangingtheorderofscalefactorbandsandwindows.Tobespecific,assumethatbeforeinterleavingthesetof1024coefficientscareindexedas

c[g][w][k/4][k%4]

where

gistheindexongroups

wistheindexonwindowswithinagroup

kistheindexoncoefficientswithinawindow

andtheright-mostindexvariesmostrapidly.

Afterinterleavingthecoefficientsareindexedas

c[g][k/4][w][k%4]

Thishastheadvantageofcombiningallzerosectionsduetoband-limitingwithineachgroup.

A.1.5Scalefactors

Thecodedspectrumusesonequantizerperscalefactorband.Thestepsizesofeachofthesequantizersisspecifiedasasetofscalefactorsandamaximumscalefactorwhichnormalizesthesescalefactors.Inordertoincreasecompression,scalefactorsassociatedwithscalefactorbandsthathaveonlyzero-valuedcoefficientsareignoredinthecodingprocessandthereforedonothavetobetransmitted.Boththemaximumscalefactorandscalefactorsarequantizedin1.5dBsteps.

TheBSACscalablecodingschemeincludesthenoiselesscodinginordertofurtherreducetheredundancyofthescalefactors.

Themaximumscalefactoriscodedasan8bitunsignedinteger.Thefirstscalefactorassociatedwiththequantizedspectrumisdifferentiallycodedrelativetothemaximumscalefactorandthearithmeticcodedusingthedifferentialscalefactorarithmeticmodel.TheremainingscalefactorsaredifferentiallycodedrelativetothepreviouslyencodedscalefactorandthenArithmeticcodedusingthedifferentialscalefactormodel.

Thedynamicrangeofthemaximumscalefactorissufficienttorepresentfull-scalevaluesfroma24-bitPCMaudiosource.

A.1.6Arithmeticcoding

Arithmeticcodingisusedtorepresent4-tuplesofthebit-valueswhichareslicedfromquantizedcoefficients,withoneof32Arithmeticmodels.Inordertofurtherreducetheredundancyofbit-sliceddata,thevectorisformedwhichconsistsofsuccessivenon-overlapping4-tuplesoftheMSBdatastartingfromthelowest-frequencycoefficientandprogressingtothehighest-frequencycoefficient.

Four-dimensionalvectorofbit-slicedsequencearearithmeticcodedandtransmitted.Forthecaseofmultiplewindowsperblock,theconcatenatedandpossiblygroupedandinterleavedsetofspectralcoefficientsistreatedasasinglesetofcoefficientsthatprogressfromlowtohigh.Thissetofspectralcoefficientsmayneedtobede-interleavedaftertheyaredecoded.Thespectralinformationforallscalefactorbandsequaltoorgreaterthanmax_sfbissettozero.

AfterallMSBdataareencodedfromthelowestfrequencylinetothehighest,thesameencodingprocessisrepeateduntilLSBdataisencoded.

Four-dimensionalvectoristhebasicunitinencoding/decodingthebit-sliceddata.Thearithmeticmodelforencodingthevectorisdeterminedwiththearithmeticmodelindex,thesignificanceoftheslicedbitandthenumberofthenon-zerosampleas.And,thenextvectorsareencoded.Thenumberofthenon-zer