Lossless Compression of Digital Audio

Transcript

1 Lossless Compression of Digital Audio Mat Hans, Ronald W. Schafer* Client and Media Systems Laboratory HP Laboratories Palo Alto HPL November, audio cooling, lossless compression, Internet audio The first part of this paper surveys and classifies the best performing currently available lossless compression algorithms for stereo-cd-quality digital audio signals sampled at 44.1 khz and quantized to 16 bits. This study finds that these algorithms appear to have reached a limit in compression that is very modest compared to what can be achieved with lossy audio coding technology. With this limit as a target, we designed a computationally efficient algorithm for lossless audio compression (which we call AudioPaK). This new lossless compression algorithm uses only a small number of integer arithmetic operations and performs as well, or better than most state-of-the-art lossless compression algorithms. The main operations of the algorithm are prediction with integer coefficients and Golomb-Rice coding. The second part of the paper presents the complete architecture of AudioPaK including suggestions on parallelizing parts of the algorithm using the MMX instruction set. Internal Accession Date Only Center for Signal & Image Processing at the School of Electrical and Computer Engineering, Georgia Institute of the Technology, Atlanta, Georgia. Copyright Hewlett-Packard Company 1999

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20 $R AsR I >xh RYBbR j$j $P stk si%sts BP Y yyi } I${B B% st 3yi } I${B yt Y {sr BP Y _Y$j$}R sjb $Y8 YBb % Y {B8} RR$Bt s$b bsr }ZAj$RY I $t >dh wp s8 R$9 bsr R B d(1; Rs8}j RD PB {B8} RR$Bt BP sjj ( q s{,r BP >H qb sjjbb s js$% {B8}s $RBt b$y Y BY {BI R b sjrb {B8} RR I sjj ( q s{,r ZR$t VZI$B_s qsaj E RZ88s $9 R RZjR BP Y$R {B8}s $RBt qy $sj${$9 I tz8a R b }ZAj$RY I $t >dh sti Y BY tz8a } R tr Y } PB 8st{ BP VZI$B_s Bt Y t$ 7+V ]* qy RZjR _Y$j$}R 7YB t!7jz$ry VZI$B_s nnd 1nn nde 1MM qsaj E ]B8} RR$Bt s$b PB {B8}j ]* >H $t qsaj E 8ZR A $t } I b$y {s 7$t{ b b tb saj B {B8}s Y _Y$j$}R {B8} RR$Bt sjb $Y8 Bt Y $ti$%$izsj hj R BP BZ R R b {sttb I sb Y {Bt{jZR$Bt Ys Y$R sjb $Y8 b$jj } PB 8 Zt$PB 8jk A Yst sjj Y BY sjb $Y8R qy 7+V ]* {Bts$tR 8stk R$8}j RBZtIR RZ{Y sr }Z Bt R R$tj $tr Z8 tr sti R$j t{ by${y 8$Y A 8B sr$jk {B8} RR I Ak RB8 sjb $Y8R sti tb BY R!Y RZjR $t >dh RYBb Y _Y$j$}R sjb $Y8 } PB 8$t R$8$js jk B!7JZ$RY Bt $ti$%$izsj hj R Ys b Zts%s$jsAj PB BZ RZIk qy R s j$ $ti$%$izsj {B8}s $RBtR RYBb I R$t$h{stjk jbb {B8} RR$Bt s$br Yst Y nnd }B I PB Y t$ 7+V I$R, dn ]Bt{jZR$Bt BP BZ RZIk yt {Bt{jZR$Bt BZ RZIk BP {Z tjk s%s$jsaj jbrrj RR szi$b {BI R RZ RR Ys Y {Z t {YtBjBk YsR s{y I s j$8$ $t bys {st A s{y$ % I PB jbrrj RR {B8} RR$Bt BP szi$b 1(

21 3Z Y 8B $t R}$ BP s b$i st BP s}} Bs{Y R sti {B8}j -$$ R Y I$& t sjb $Y8R } PB 8 R$8$js jk Bt Y Rs8 szi$b R$tsjR b$y t sjjk j RR Yst Bt A$ } Rs8}j I$& t{ $t {B8} RR I A$ s qy PB s {BI {B8} RR$t s Y$R j$8$ b$y Y j sr tz8a BP s $Y8 ${ B} T s$btr bbzji I ht Y A R {YtBjBk PB jbrrj RR szi$b {B8} RR$Bt qys $R Y I R$t BP s jbrrj RR szi$b {BI RYBZjI tbb PB{ZR Bt IZ{$t sjb $Y8 {B8}j -$k G$YY$R $t 8$tI b I R$t I s R$8}j jbrrj RR szi$b {BI by${y b {sjj I VZI$B_s qy$r {BI ZR R Btjk s P b $t s $Y8 ${ B} s$btr Bt ABY Y {BI sti Y I {BI R$I qy 8s$t B} s$btr s } I${$Bt b$y $t {B ^{$ tr sti pbjb8a {BI$t by${y s IBt Bt s P s8 AsR$R VR RZ88s $9 I $t qsaj R ; x sti E BZ sjb $Y8 } PB 8R sr b jj B % t A Yst 8BR Rs TBPTY Ts jbrrj RR {BI R V {B8}j I R{ $}$Bt BP VZI$B_s $R $% t $t Y t - R {$Bt 1 VZI$B_s U s jbb {B8}j -$k jbrrj RR {BI VZI$B_s $R b jj RZ$ I PB yt t str8$rr$bt A {szr BP $R jbb $tr Z{$Bt {B8}j -$k sti BBI {B8} RR$Bt } PB 8st{ qy sjb $Y8 $R {Bt% t$ tjk I R{ $A I $t 8R BP Y Rs8 R Z{Z w3$z dd Ys bsr ZR I B I$R{ZRR sjj Y BY jbrrj RR {B8} RR$Bt sjb $Y8R VZI$B_s I$& R P B8 Y BY sjb $Y8R $t YBb Y IZtIst{k 8B%sj sti {BI$t s $8}j 8 t I qy I s$jr BP Y sjb $Y8 s I$R{ZRR I A jbb ytpb 8s$Bt Bt Y R Z{Z BP Y {B8} RR I A$ R s8 $R $% t $t V}} ti$- V 1d

22 1d 3 s8$t VR $t Y {sr BP sjj Y BY jbrrj RR szi$b {BI R $t BZ RZIk VZI$B_s I$%$I R Y $t}z szi$b R$tsj $tb $ti } ti t P s8 R qy j ty BP s P s8 $R s {BI }s s8 sti 8sk A R s {BI$t $8 YBb % Y s BBI } s{${sj srbtr PB ZR$t P s8 R$9 R Ys s s 8Zj$}j BP d1 Y tz8a BP Rs8}j R {s $ I Ak st Ve7\e = P s8 ; qsaj RYBbR Y RZjR PB P s8 j tyr st$t P B8 d1 B ;E(M $t 8Zj$}j R BP d1 qy$r Iss RYBbR Ys Y {B8} RR$Bt s$br s tb % k R tr$$% B Y P s8 j ty sti RZ RR Ys s BBI j ty PB ;;d,<9 de A$ szi$b Rs8}j I R s8r $R ddx1 Rs8}j R q s{, d1 xe ddx1 1n(; ;E(M q s{, (; dnm dn dn dnm dne q s{, 1( n(1 nd; nd nd nd q s{, 1 1x( 1; 1;E 1;1 1n q s{, ;M 1;M 1xx 1xE 1xE 1xE q s{, EE 1;1 1; 1; 1;E 1;1 qsaj ]B8} RR$Bt s$br PB Y j P {Ystt j BP -} $8 tsj szi$b hj R ZR$t VZI$B_s b$y I$& t P s8 R$9 R w$t tz8a BP Rs8}j RD 11 yt st]ystt j * {B js$bt Z{Y BP Y s $Y8 ${ $t Y sjb $Y8R I R{ $A I $t 7 {$Bt d $R $t Y {B8}Zs$Bt BP Y } I${$Bt B R$tsj RB Y$R s s $R s } $8 s PB R$8}j$h{s$Bt qy PB Y $t st{ystt j I {B js$bt B} s$bt ZR R s % k R$8}j 3yi sis}$% } I${$Bt 8 YBI ; qy Ve7\e = $R s RstIs I $t {Btt {$Bt I$$sj $t Ps{ RsAj$RY I Ak Y VZI$B et$t $t 7B{$ k wve7d sti Y ez B} st BsI{sR$t =t$bt we =D y $R s R $sj str8$rr$bt PB 8s PB j$t s jk } R t I I$$sj szi$b Iss by${y } 8$R str8$rr$bt BP bbt{ystt j I$$sj szi$b $tpb 8s$Bt $t{jzi$t ABY szi$b sti tbt szi$b Iss P B8 Bt } BP RR$Btsj szi$b I %${ B stby 11

23 ZR$t Btjk $t {B ^{$ tr qy$r s}} B-$8s$Bt bsr h R } B}BR I $t 7YB t >1dH sti b$jj A I$R{ZRR I $t I s$j Y qy } I${$Bt 8 YBI ZR R Y PBjjBb$t PBZ R$8}j 3yi } I${B R s{y BP by${y YsR Btjk $t {B ^{$ tru T?(>zH ) ( z? d>zh )?>z dh?1>zh ) 1?>z dh?>z 1H Z?n>zH ) n?>z dh n?>z 1H L?>z nh qy R } I${B R s 3yi } I${B R R$t{ Y k $t%bj% j$t s {B8A$ts$BtR BP }sr Rs8}j R <Bb % Y k sjrb Ys% st $t R$t $t } s$bt $t 8R BP Y YTB I }BjktB8$sjR Ys Y k I ht i {sjj Ys s w ddtb I }BjktB8$sj {st A PBZtI Ys }srr R Y BZY Y } %$BZR Iss }B$tR?>zdH,?>z1H, 3 3 3,?>z H qy$r }BjktB8$sj {st A %sjzs I s Y zy Rs8}j $8 B BAs$t Y } I${ I %sjz?>zh qy R }BjktB8$sjR sti Y } I${ I %sjz R Ys Y k } BIZ{ s $jjzr s I $t 3$Z E PB s k}${sj R BP } %$BZR Rs8}j R Vt $t R$t } B} k BP Y R }BjktB8$sj s}} B-$8s$BtR $R Ys Y RZj$t R$IZsj R$tsjR à >zh )?>zh? >zh {st A ^{$ tjk {B8}Z I $t Y PBjjBb$t {Z R$% 8stt U T à (>zh )?>zh z à d>zh ) à (>zh à (>z dh Ã1>zH ) Ãd>zH Ãd>z dh Z à n>zh ) à 1>zH à 1>z dh qy$r } 8$R Y t$ R BP } I${$Bt B R$tsjR B A {B8}Z I b$ybz stk 8Zj$}j${s$BtR x x G RYBb $t V}} ti$- Ys Y$R sjb $Y8 {st A }s sjj j$9 I B s, si%sts BP yt j:r 7y* s {Y$ {Z 1n

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25 3B s{y P s8 Y PBZ } I${$Bt R$IZsjR à (>zh, à d>zh, à 1>zH,à n>zh s {B8}Z I s % k Rs8}j $t Y P s8 sti Y sarbjz %sjz R BP Y R R$IZsjR s s% s I wrz88 ID B% Y {B8}j P s8 qy R$IZsj b$y Y R8sjj R RZ8 BP 8st$ZI R B% sjj Rs8}j R $t Y P s8 $R Y t I ht I sr Y A R s}} B-$8s$Bt PB Ys P s8 sti Ys } I${B $R ZR I PB Ys P s8 qy $tpb 8s$Bt Bt by${y } I${B bsr ZR I {st A {BI I b$y bb A$R BP $tpb 8s$Bt sti Ys A {B8 R }s BP Y B% Y si $tpb 8s$Bt PB Y P s8 qsaj M RZ88s $9 R YBb 8stk $8 R s{y } I${B bsr ZR I $t {BI$t Y -} $8 tsj szi$b s{,r q s{, à ( à d à 1 à n qbsj P s8 R q s{, (; M( ;;M xe; nd1 d;en; q s{, 1( E1d ne; dn(( (d 1ME q s{, 1 nn; n(( EEE 1n1 dxn1 q s{, ;M 1MM 1x1 nn d1e 1d;; q s{, EE n(d n( ;( E;d dn qsaj M WZ8A BP $8 R s{y R$IZsj $R {YBR t IZ $t {BI$t BP s j P {Ystt j P s8 VR R t $t qsaj M Y $R tb R Bt } P t{ PB stk BP Y } I${B R $ Y $R st si%sts $t %s k$t Y } I${B P B8 P s8 TBTP s8 B j$y $R RY I Bt Y R } I${B R Ak {BtR$I $t Y $ P JZ t{k R}BtR R y $R sr$jk RYBbt Ys Y FT strpb 8 RkR 8 PZt{$Bt BP Y YTB I } I${B $R \ wfd )wd F d D, sti Y 8st$ZI BP Y P JZ t{k R}BtR BP Y YTB I } I${B $R /\ wã ix D/ ) /1 R$twxb1D/, w;d 1x

26 by x $R Y Rs8}j$t s 3$Z RYBbR }jbr BP w;d PB Y PBZ } I${B R ZR I $t VZI$B_s wqy P JZ t{k s-$r $t Y$R }jb $R tb 8sj$9 I RB Ys YsjP Y Rs8}j$t s $R s tb 8sj$9 I P JZ t{k dd WB Ys A {szr BP Y YTB I 9 B s F ) d Y } I${B R 10 Integer Coefficient Predictor Frequency Responses magnitude p=3 p= normalized frequency = ωt/π 3$Z 3 JZ t{k R}BtR R BP 3yi } I${B R ZR I Ak VZI$B_s PB $t st{ystt j I {B js$bt p=1 p=0 PB )d, 1, n sjj Ys% s Y$Y P JZ t{k ABBR Ys $t{ sr R b$y $t{ sr$t 7} {$h{sjjk Y s$t s P JZ t{k 11(x,<9 $R ( 1( ;( sti E( I qyzr Y {YB${ BP } I${B {st sjrb A YBZY BP $t 8R BP R j {$t Y $Y s8bzt BP Y$Y P JZ t{k ABBR B 4s t Y B% sjj R} { Z8 BP Y } I${$Bt B qy YTB I }Bj s F ) d bbzji A } BAj 8s${ $t 8stk s}}j${s$btr BP j$t s } I${$% 8BI j$t A {szr Y {B R}BtI$t {BtR Z{$Bt RkR 8 BP 3$Z ; bbzji A ZtRsAj <Bb % $t Y jbrrj RR {sr $P b Rs Y {BtR Z{$Bt RkR 8 b$y -s{ Rs8}j R P B8 Y } %$BZR P s8 Y s tb JZst$9s$Bt B R B s{{z8zjs sti Y {BtR Z{$Bt $R -s{ qy JZ R$Bt tsz sjjk s $R R sr B YBb 8Z{Y } PB 8st{ $R Rs{ $h{ I Ak ZR$t R$8}j } I${B R qy %sjzs$btr $t 7 {$Bt d BP Y 7YB t sjb $Y8 RZ R Ys R$8}j$h{s$Bt BP Y } I${$Bt B} s$bt Ak ZR$t jbbtb I } I${B R b$y $t {B ^{$ tr IB R tb 1E

27 I si } PB 8st{ s}} {$sajk yti I sr qsaj x RYBbR Y $R j$j I$& t{ $t } T PB 8st{ A b t Y R$8}j $t } I${B R sti Y B}$8Z8 d(ytb I j$t s } I${B sti $t Ps{ $t RB8 {sr R Y Y$YTB I } I${B } PB 8R Rj$Yjk bb R 1n yt T{Ystt j I {B js$bt VZI$B_s {st s, si%sts BP $t T{Ystt j I } ti t{$ R } R t $t R B {Ystt j szi$b R s8r qy$r $R IBt by t Y {BI $R R $t R B 8BI yt Y$R 8BI $t sii$$bt B s}} B-$8s$t Y $Y R B {Ystt j Rs8}j R b {B8}Z Y }BjktB8$sj s}} B-$8s$Bt BP Y I$& t{ A b t Y j P sti $Y {Ystt j sjbt b$y Y srrb{$s I R$IZsjR qy R8sjj R %sjz s8bt Y M RZ8R BP sarbjz R$IZsjR w; P B8 Y $Y {Ystt j sti ; P B8 Y I$& t{ D I ht R Y A R s}} B-$8s$Bt qsaj } R tr Y R$8s I h RTB I t B}k I ( PB Y j P B {Ystt j Y $Y B {Ystt j $t IZsj 8BI sti Y $Y B {Ystt j $t R B 8BI E qy R 8 srz R q s{, N P B {Ystt j i$y B {Ystt j *Zsj 8BI 7 B 8BI q s{, (; d1d( d11 d1( q s{, 1( E(n Ed Ed q s{, 1 xm x1 x1 q s{, ;M dm de de q s{, EE M1 ( M qsaj 3$ RTB I t B}k I ( $t A$R } Rs8}j PB j P sti $Y B {Ystt jr wã>zhd RYBb % k j$j $8} B% 8 t $t {B8} RR$Bt by t Y $t T{Ystt j I {B js$bt $R Rb${Y I Bt qy$r $R tb RZ } $R$t R$t{ Y $t T{Ystt j I {B js$bt B} s$bt IB R tb s, $tb E qy IZsj {Ystt j 8BI {B8} RR R Y j P sti $Y {Ystt jr R }s s jk 1

28 s{{bzt $8 I jskr sti BY I$& t{ R Ys s {B88Bt A b t {Ystt jr BP s R B R$tsj {szr b R, s {BI b$y 8$t$8Z8 sjb $Y8 {B8}j -$k Y$R RZ RR ZR$t VZI$B_s $t IZsj 8BI 1; et B}k {BI$t 7$j t P s8 R {st sr$jk A I { I b$y R$IZsjR à ( >zh,ã d >zh sti ^{$ tjk t B}k {BI I b$y st R{s} {BI yp Y R$j t P s8 $R 8sI BP sjj ( %sjz Rs8}j R Y t Y RZ8 BP /à ( >zh/ $R 9 B sti $P Y R$j t P s8 $R 8sI BP %sjz R BY Yst ( wtd B d sr RB8 $8 R PBZtID Y t Y RZ8 BP /à d >zh/ $R 9 B w {sjj Ys à d >zh )?>zh?>z dhd GY t Y P s8 $R tb BP {BtRst %sjz b ZR pbjb8a {BI$t sjbt b$y s 8s}}$t B B I Y $t tz8a R qy$r {BI $R ZR I $t Y t b F_epTN7 jbrrj RR $8s {B8} RR$Bt R{Y 8 >d;h V A $ P I R{ $}$Bt BP Y$R {BI PBjjBbR pbjb8a ]BI$tU pbjb8a {BI R s I ht I B A B}$8sj PB -}Bt t$sjjk I {sk$t } BAsA$j$k I$R $AZ$BtR BP }BR$$% $t R >MH p$% t s Zt$JZ }s s8 E Y pbjb8a {BI I$%$I R s }BR$$% $t z $tb bb }s RU s A$ts k } R ts$bt BP wz 8BI ED sti s Zts k } R ts$bt BP w! z EÅ D >d(h yp E )1 > Y t Y {BI bb I PB z {BtR$RR BP Y > j sr R$t$h{st A$R BP z PBjjBb I Ak Y tz8a PB 8 I Ak Y 8s$t$t 8BR R$t$h{st A$R BP z $t Zts k } R ts$bt sti s RB} A$ qy j ty BP Y$R {BI bb I $R > LdL! z 1 > Å {szr Y R$IZsjR à 7 >zh s tb sjj }BR$$% s 8s}}$t -w D $R IBt B B I Y 1M

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30 G 8 srz I Y 8s-$8Z8 {B8} RR$Bt s$b }BRR$Aj ZR$t {Bt - 8BI j$t PB VZT I$B_s qy$r 8s-$8Z8 bsr PBZtI Ak ZR$t Y A R t B}k {BI$t }s s8 PB % k R$IZsj Rs8}j Ã>zH qy$r 8 str R $t Y }s s8 > PB s{y R$IZsj Ã>zH B $% Y R8sjj R {BI bb I j ty =R$t BZ -} $8 tsj szi$b hj R b PBZtI s 8s-$8Z8 {B8T } RR$Bt s$b $8} B% 8 t st$t P B8 E B d(0 yt B I B s{y$ % Y$R sy R8sjj $8} B% 8 t $ bbzji A t { RRs k B $tp Y {Bt - P B8 Y R$tsj Iss s s {B8}ZsT $Btsj {BR Ys $R tb `ZR$h I Ak Y Rs%$tR $t A$ s 1x V $Y8 ${ {B8}j -$k qy tz8a BP $t sii$$btr sti 8Zj$}j${s$BtR } R {BtI Ys VZI$B_s JZ$ R $t IZsj 8BI PB s ;;d,<9 R B de A$ szi$b R s8 $R RZ88s $9 I $t qsaj d( ]BI * {BI (M!_7 P B8 (nx B (M!_7 qsaj d( V $Y8 ${ {B8}j -$k PB VZI$B_s $t IZsj 8BI!_7 RstIR PB 8$jj$Bt B} s$btr } R {BtI WB Ys Y!_7 PB Y I {BI I } tir Bt Y } I${B ZR I 8BR P JZ tjk 1E $ s %s $sa$j$k {szr BP Y tbttrs$bts k tsz BP szi$b R$tsjR Y {B8} RR$Bt R{Y 8 YsR s %s $saj A$ s 3$Z M $jjzr s R Y$R %s $sa$j$k yt Y$R hz Y {B8} RR$Bt s$br B% P s8 R tz8a nxx( sti nx PB Y j P {Ystt j BP q s{, (; BP >dh s } R t I VjRB I }${ I s Y 8$t$8Z8 sti 8s-$8Z8 Rs8}j %sjz R $t s{y P s8 sjbt b$y Y 8 st sti %s $st{ %sjz B% s{y P s8 WB Y js$btry$} A b t Y %s $st{ wby${y sjrb I ht R Y n(

31 t kd sti Y {B8} RR$Bt s$b VR Y t k BP s P s8 $t{ sr R Y {B8} RR$Bt s$b I { sr R 1.8 Compression Ratio Per Frame x Minimum, Maximum Sample Values And Average Value Per frame x Variance Per Frame Frame Number 3$Z M zs $saj A$ s tsz BP {BI yt RB8 s}}j${s$btr $ 8sk A BP $t R B Ys% s R8BBY I } s, s $tr si BP s R Bt 4Z{Zs$Bt $t $trstst BZR Iss s V RBjZ$Bt B Y$R } BAj 8 bsr } B}BR I Ak ] s% t sj $t >xh byb RZ R I $tr $t AZ& R s ABY Y {BI sti Y I {BI R$I R n ]Bt{jZR$Bt NBRRj RR szi$b {B8} RR$Bt $R j$, jk B }jsk st $8}B st }s $t 8ZR${ I$R $AZ$Bt B% Y yt t *z* szi$b I$$sj szi$b s {Y$%$t sti 8$-$t {szr {B88Bt jbrrj RR {B8} RR$Bt Z$j$$ R RZ{Y sr _,$} IB s }BB `BA BP {B8} RR$t szi$b R s8r s I$& t {YtBjBk sis} I B Y R R$tsjR $R JZ$ I nd

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