LOSSLESS audio coding is used in such applications as

Transcription

1 INTL JOURNAL OF ELECTRONICS AND TELECOMMUNICATIONS, 2013, VOL. 59, NO. 1, PP Manuscipt eceived Januay 10, 2013; evised Mach, DOI: /eletel Novel Ideas fo Lossless Audio Coding Gzegoz Ulacha and Ryszad Stasiński Abstact Novel ideas fo lossless audio coding analyzed in the pape ae linked with fowad pedicto adaptation, and concen optimization of pedictos on the basis of zeo-ode entopy and MMAE citeions, and context sound coding. Diect use of the fome citeion is linked with exponential gowth of optimization pocedue, hence, a suboptimal algoithm having polynomial complexity is poposed. It is shown that on aveage the new types of pedictos ae bette than those obtained by MMSE technique, while two- and thee context systems ae on aveage bette than a single pedicto one. It also appeas that 7-bit PARCOR coefficients in the MPEG-4 ALS standad have insufficient pecision fo some pedicto length, and that fo vey long fames coding esults impove with the pedicto ank pactically in unlimited way. Keywods Lossless audio coding, context coding, LS pedictos, MMSE, MMAE, zeo-ode entopy. I. INTRODUCTION LOSSLESS audio coding is used in such applications as achiving of ecodings, distibution of highest quality music on disks, o by Intenet. It is also useful when ecoding sound mateial intended fo post-poduction (advetisements, adio o TV pogams, videogaphy, etc), namely, numeous lossy decompession-compession cycles gadually deteioate it. The most intensive peiod of eseach in this domain was linked with call fo poposals fo MPEG-4 Audio Lossless Coding (ALS) standad in yeas [1]. They ae also inteesting altenative lossless coding systems fom that time e.g. OptimFog [2], and Monkey s Audio [3]. Modeling stage of lossless audio coding algoithms is usually based on pedictos [4] [6], but thee exist systems based on DCT (MPEG-4 SLS [7]), o wavelet tansfoms. Pediction methods can be divided into those with fowad and backwad pedicto adaptation. Good esults ae obtained when cascading stages of pediction: two stage fowad adaptation technique can be found in [8], backwad adaptation using cascaded RLS and LMS pedictos is pesented in [9], in [1] the numbe of stages eaches five. Futhe impovement can be obtained by exploiting multichannel dependencies. The coding gain of steeo systems depends on sound chaacteistics and vaies fom 0.5% up to 5% [10]. In the pape fundamental popeties of fowad adaptation pediction systems ae analyzed. In section IV pefomance of non-mmse optimized pedictos is tested. In section V The wok has been suppoted by the Polish NCN gant n 4922/B/T02/2011/40. G. Ulacha is with the Depatment of Compute Science, West Pomeanian Univesity of Technology, Żołnieska 49, Szczecin, Poland ( gulacha@wi.ps.pl). R. Stasiński is with the Faculty of Electonics and Communications, Poznań Univesity of Technology, Polanka 3, Poznań, Poland ( stasins@et.put.poznan.pl). context coding is intoduced. Devoted to theoetical backgound sections II and III contain analyses of pedicto length impact, and its coefficient pecision on system pefomance. The conclusion is that indeed, thee is still a lot of oom fo impovement of sound lossless coding systems. II. THEORETICAL BACKGROUND In moden lossless coding techniques multimedia signal pocessing begins with data modeling intended fo minimization of mutual infomation between signal samples. If the mutual infomation is completely emoved, then the bit ate at the output of entopy codes may each the entopy limit [11]. Data modeling algoithms ae usually based on pedictos. A linea pedicto of ank estimates x n sample: ˆx n = b j x(j) (1) j=1 x(j) ae pevious sample values, b j ae pediction coefficients [11]. The estimate is used to calculate the pediction eo (ounded up in lossless coding): e n = x n ˆx n (2) Pobability distibution of the eo is usually close to Laplacian, which means that it can be effectively coded by easy to implement Golomb-Rice code [11]. It foms a pat of specially constucted fo coding of audio signals Gilbet- Mooe code, whee it is combined with aithmetic one [12]. Befoe pocessing a sound ecoding is usually divided into fames. Fame length may vay fom a few tens to seveal thousand samples. In MPEG-4 ALS the maximum fame length is bounded by the fee access equiement, namely, audio data set apat by 500 ms should be decoded independently. This implies samples fo a 48 khz signal. The equiement is impotant fo live tansmission, o when the sound mateial will undego post-poduction. Fo othe applications even longe fames can be established, and thee ae good easons fo that. Namely, fo avoiding illcondition solution of (4) it is impotant that the fame length N is much geate than pedicto ank. In fact, this is a geneal popety of paametic signal modeling methods, wheneve data sample count is esticted a poblem aises what is appopiate ank of a signal model. Note that highly efficient lossless audio coding methods ae based on lage signal models, e.g. total numbe of paametes in the method fom [1] is almost 400 (5 pedictos, the longest consisting of 300 coefficients, weights of pedicto outputs), and MPEG- 4 ALS allows pedicto anks up to Results of ou expeiments also indicate that long pedictos tend to be bette than shot ones, see Fig. 1. MPEG-4 ALS contains also fame

2 18 G. ULACHA, R. STASIŃSKI length optimization pocedue: fame may be halved, and coding esults compaed to those fo the full fame. If the appoach succeeds, one o both subfames can be halved, too, down to 1/32 pat of the initial lengths. Pediction coefficients can be fixed, but much bette esults ae obtained when pedictos ae optimized fo estimation of a paticula signal. Thee ae two majo classes of optimization pocedues, named fowad and backwad adaptation. In fowad adaptation appoach pedicto coefficients ae optimized afte collecting fame samples, othe optimized paametes ae fame length, pedicto ank, and possibly, numbe of bits fo coefficients coding. The appoach is asymmetic fom the complexity point of view, decoding is much simple. The tem backwad adaptation is used fo denoting adaptive pedictos (RLS, LMS). The latte techniques ae symmetic (simila complexities of code and decode), on the othe hand they do not equie side infomation accompanying coded data (mainly coefficient values). Both appoaches lead to poweful algoithms, cuently backwad adaptation methods seem to be somewhat moe efficient [1]. Pedicto coefficients ae usually optimized using minimum mean-squae eo citeion (MMSE), some altenative appoaches will be pesented in the next section. MMSE theoetical fomulation leads to two pactical appoaches to coefficient optimization: ecusive coections implied by the gadient of cost function, and least-squaes (LS) optimization. The most widely used algoithm fom the fist class is LMS used in backwad adaptation algoithms. LS ap-poach can be both ecusive (RLS), o non-ecusive, and hence, used both in backwad and fowad adaptation techniques. In non-ecusive case it consists in minimization of the sum of squaes of the absolute eo values, i.e. not mean but total squae eo is minimized: min b j e n 2 (3) n= Optimal fomulae fo calculating vecto B of pedicto coefficients ae: B = R 1 P, (4) whee R is the expeimental signal autocoelation matix: vecto P is: R(j,i) = P(j) = x(n i) x(n j), (5) n= x(n) x(n j), (6) n= samples x ae taken fom a fame of size N. To avoid matix invesion in (4) it is often assumed that matix R is Toeplitz (i.e. it is fully defined by one-dimensional autocoelation function), which allows the use of Levinson-Dubin algoithm fo solving (4). Its computational complexity is O( 2 ), in contast to O( 3 ) fo diect appoach. Anothe convenient solution is to use lattice implementation of the pedicto, defined by eflection, o PARCOR coefficients [11]. Its advantage consists in fact that the lattice pedicto implementation is usually moe obust to ounding eos than the diect one, Aveage bitate Aveage bitate a) b) Fig. 1. Aveage code bit ate (in bits pe sample) as a function of pedicto ank: a) fo up to 30, and b) fo fom 10 to 600. additionally, coefficient absolute values, if coectly computed, neve exceed 1. Then, they can be easily coded using shot bit epesentation, e.g. 7 bits in MPEG-4 ALS. Moeove, Golomb-Rice coding leads to eduction of this numbe to appoximately 4 bits pe coefficient [13]. III. OPTIMIZATION OF BASIC PREDICTOR PROPERTIES Consideations pesented in the pevious section pompted us to use vey long fames in ou expeiments. Moe pecisely, whole test ecodings wee pocessed, these wee 16 sequences fom the base [14]. Namely, ou expeiments aimed at intoduction of some novel ideas to lossless audio coding, hence, the poblem of appopiate model ank should not affect esults. Secondly, sequences fom [14] contain a athe homogenous sound mateial, in contast to e.g. adio pogam, in which music inteweaves with speech and logo signals, which fact suggests thei statistical homogeneity. Finally, the

3 NOVEL IDEAS FOR LOSSLESS AUDIO CODING 19 longe the fame the smalle contibution of side infomation to coded data, as the fomula on the coded data bit ate is: L = H(S)+ m h N, (7) whee m is the numbe of bits used fo coefficient epesentation, h is the numbe of contexts of the algoithm, in sections peceding section V: h = 1, and H(S) is the measued data zeo-ode entopy: H(S) = M p i logp i, (8) i=1 hee p i ae pobabilities of possible eo values, M is thei numbe. Unless stated othewise the numbe of bits was not optimized, and was set to m = 32, but because of vey lage N values this had minimal impact on expeiment esults. Occasional instability of Levinson-Dubin algoithm pompted us to analyze the poblem of sufficient numbe of bits fo coding of defining lattice stuctue eflection coefficients, signal pocessing esults wee compaed to those fo double pecision calculations. In expeiments LifeShattes fom [4] was excluded, as esults fo it wee clealy outlies. It appeaed that 7-bit coding was sufficient fo 13 fom 15 ecodings fo pedicto ank = 10, fo 7 ecodings when the ank was = 30, and only fo 2 fo = 100. The poblem was solved when numbes of bits wee inceased to 9, 11, o 15, espectively. Additionally, in the case of instability esults peceding instable iteation by 3 steps wee eplacing the cuent ones. Longe epesentations of coefficients means geate side infomation, nevetheless, the findings suggest that esults of MPEG-4 ALS can be impoved by optimization of coefficients epesentation length, especially fo long fames. Anothe question that has been investigated was if thee exists the globally optimal pedicto length, o equivalently, if thee exists a ank ange above which extending pedicto length is not pactical. The answe was negative, at least fo pedictos of ank up to = 600, see Fig. 1. This is in spite of excessive side infomation, as 32-bit epesentation of coefficients was assumed. Nevetheless, manifestation of the ule of diminishing etuns is clealy visible, linea decease of bit ate is obtained fo exponential incease of pedicto length. Moeove, when obseving esults fo individual sequences it appeas that fo half of them the optimal pedicto length is shote than = 600, the best esults fo individual ecodings in Table I ae in bold. In this situation a bette solution is to implement shote pedictos matched to local popeties of a signal, individual pedictos optimized fo collections of samples having simila popeties can be used. This can be done by defining clustes of fames [15], o by implementing context coding, initial esults showing advantages of the latte idea can be found in section V. IV. NON-MMSE OPTIMIZED PREDICTORS The MMSE optimization (3) leads to linea pedictos. A linea pedicto de-coelates a signal to which it is matched, autocoelation function of pediction eo is the same as Gain Fig. 2. Aveage gain in zeo-ode entopy when compaing iteative selective seach appoach with those based on MMSE. Aveage bitate Fig. 3. Aveage code bit ates (bits pe sample) fo pedictos optimized using citeia: MMSE (uppe cuve), MMAE (middle cuve), and iteative selective seach (lowe cuve). that of white noise, and white noise is a pefect example of memoy-less data souce. The idea woks, but only patially. Namely, the consecutive samples of pediction eo can be statistically independent only if a signal is fully descibed by second-ode statistics. This is often not tue. In this section we ae addessing the poblem of MMSE citeion sub-optimality by intoducing a technique based on diect minimization of bit ate geneated by a code. We will also povide some esults fo Minimum Mean Absolute Eo (MMAE) citeion. The seach fo the optimal signal model should be done by minimization of zeo-ode entopy of the model eo (8). Namely, this is the lowe bound fo bit ate geneated by an entopy code pocessing that eo [11]. Unfotunately, such model optimization can be done only by exhaustive seach of possible model paametes, hence, its complexity gows exponentially with the model ank and numbe of bits used fo its paametes epesentation.

4 20 G. ULACHA, R. STASIŃSKI Aveage bitate Fig. 4. Aveage code bit ates (bits pe sample) fo single pedicto (uppe cuve), and thee contexts appoach (lowe cuve), methods equie same amount of side infomation. We popose to educe dastically the seach space by the Iteative Selective Seach algoithm fo pedicto coefficients, which gave supisingly good esults fo lossless image coding in [16]. We stat with coefficient vecto B = [1, 0,..., 0], and test optimality of its sum with each vecto B = [ b 1, b 2,..., b ], whee only two b j ae non-zeo integes having opposite values: -1, and 1, is the pedicto ank. Note that they ae only ( 1) such vectos, which implies polynomial complexity of the method. The pocess is epeated a few times (in ou expeiments: 9). Then, in the next iteation B vectos ae divided by 2, added to optimal B fom the pevious iteation and the sum tested fo optimality. Fo iteation i: B(t+1) = B(t)+2 i B, (9) i = 0,1,2,...,m 3, whee m is the numbe of bits used fo coefficient epesentation, as iteations ae epeated, in geneal t i. We have found that m = 12 is sufficient, which is only one bit moe than fo MMSE optimized pedictos of ank = 30, see pevious section. Repetitions of iteations incease the maximum value of coefficients, hee by two bits. Note that diect implementation of pedictos is done. The aveaged diffeence in bit ate between the iteative selective seach and MMSE-optimized pedictos is shown in Fig. 2 fo pedictos anks up to 30. The esults have been obtained fo sequences fom the base [14], each was teated as a single fame. It can be seen that the diffeence is positive, i.e. on the aveage the new method is bette than the taditional appoach. In Fig. 3 the actual aveage bit ates fo the methods ae pesented, additionally, esults fo MMAE-optimized pedictos ae shown. Results fo the last appoach lay between those fo the peceding ones, similaly, its computational complexity is smalle than fo iteative selective seach, but geate than fo MMSE. This means that MMAE citeion is woth consideing when iteative selective seach is too complex fo an application. Table II shows that in fact iteative selective seach (ISS) is not always the best choice fo coding of ecodings fom [14] (numbes in bold point out bette esults fom the two appoaches). Then, optimum is eached fo a hybid appoach, when data is coded using both methods, and only the esults fo the bette one ae consideed, see the last column of Table II. V. CONTEXT CODING OF SOUND Context coding is widely used in image pocessing [16]. It consists in implementing independent pedictos fo disjoint sets of samples. The pedicto used fo estimating cuent signal sample is chosen on the basis of context, i.e. a popety of the sample neighbohood. The popety is usually associated with a value, o ange of values of some paamete. Context switching esults in missing data in sample sequences used fo calculating (4) and (5). It appeas that due to these gaps in data the Levinson-Dubin algoithm tends to be unstable. The most obvious emedy to ovecome this phenomenon is to compute pedicto coefficient diectly fom fomula (3), thus somewhat inceasing computational complexity of the appoach. Pecision of pedicto coefficients has not be optimized, 32 bits have been used fo thei epesentation. In the expeiments two o thee contexts have been defined. Fistly, aveaged diffeences of samples wee computed: S ave = 1 N 1 x(n) x(n 1) (10) n=2 Contexts wee computed fom the paamete: q = max{ x(n j) x(n j 1) } fo j = 1,2,...,9; (11) In the case of two contexts q was compaed to a theshold α S ave, α = 2.5. Indeed, the appoach esulted in impovement of bit ate: fo MMSE optimized single pedicto of ank = 20 and vey long fames (whole sequences fom [14]) the aveage bit ate was , while fo two context pedictos of ank = 10 (equiing the same amount of side infomation) it educed to Even bette esults wee obtained when the best fom a set of thesholds was applied, the set of theshold multiplies was α i = {0.5,1,1.5,2,2.5,3,3.5,4}. Then, the aveage bit ate educed to Context appoach can be combined with iteative selective seach, which esults even in slight eduction of the method complexity, namely, the numbe of vectos B is h ( 1), only (and not h ( h 1)), whee h is the numbe of contexts. Table III summaizes esults obtained fo context technique and both coefficient optimization algoithms fo pedicto anks = 4, 10, 30. On the aveage esults fo MMSE citeion ae infeio to those fo the iteative selective seach (ISS), howeve, this need not to be tue fo some paticula ecodings (bette esults ae in bold). Then, the table contains also bit ates fo the hybid appoach fo = 30, in which esults ae taken always fo the bette of the two methods, last column of Table III. Pomising esults fo two-context coding pompted us to incease the numbe of contexts to thee. In such a case

5 NOVEL IDEAS FOR LOSSLESS AUDIO CODING 21 two thesholds should be applied to q value (7), the optimal pai of S ave multiplies was {α 1 ;α 2 } = {1.5;4}. This time much longe pedicto anks have been implemented: = 200 fo thee contexts, and esults of thei pocessing wee com-paed to those fo two context pedictos of ank 300 (the same context theshold as in pevious expeiments), and one pedicto of ank 600 (note that all thee appoaches equie the same amount of side infomation). Obviously, such big ISS pedictos have not been tested, which is due to thei much lage computational complexity. Results fom this stage of expeiments ae epoted in Table IV, as can be seen, aveage bit ate fo thee-context appoach was only Futhe eduction of bit ate has been obtained when the pai of thesholds has been chosen fom the set obtained by multiplication of S ave by multiplies fom a set of pais: {α 1i ;α 2i } = {{0.5;4},{1;2.5},{1.5;4},{1.5;5.5}, {1.5;6}, {1.5;6.5}, {2;4}, {2;5}}, aveage bit ate dopped to As can be seen fom Table IV, esults fo thee contexts ae geneally bette than those fo two contexts, but diffeences ae not as big as between those fo two contexts and single pedicto. Finally, efficiency of thee-context appoach has been tested fo a wide ange of pedicto anks, Fig. 4. The esults have been compaed to those fo a single pedicto, its ank eached value = 600. Ranks of pedictos in thee-context method have been thee times smalle than fo the single pedicto, in this way the amount of side infomation fo both techniques was always the same. As peviously, the esults wee aveaged bit ates fo 16 ecodings fom [14], each teated as a single fame. Highe efficiency of context appoach is clealy demonstated. VI. CONCLUSIONS It has been shown in the pape that a evision of basic techniques used in lossless sound coding leads to impovements. Fistly, it is shown that MMSE citeion need not lead to the best pedictos, bette ones can be obtained on the basis of MMAE, o suboptimal implementation of code zeo-ode entopy minimization. Secondly, it appeas that the widely used in image coding context appoach woks also in the audio coding domain. Finally it is suggested to optimize pedicto coefficient pecision, as thei 7-bit epesentation in MPEG-4 ALS may be too shot. An inteesting obsevation is also the fact that fo vey long fames code bit ate deceases with incease of pedicto ank even fo its extemely lage values. The new poposals can be implemented in moe advanced lossless audio coding systems, like multistage one descibed in the pape [8]. Moeove, context coding is also well suited fo backwad adaptation systems, the fact is widely exploited in image coding techniques [16]. REFERENCES [1] H. Huang, P. Fänti, D. Huang, and S. Rahadja, Cascaded RLS-LMS pediction in MPEG-4 lossless audio coding, IEEE Tansactions on Audio, Speech and Language Pocessing, vol. 16, no. 3, pp , [2] [3] [4] C. D. Giucaneau, I. Tabus, and J. Astola, Adaptive context based sequential pediction fo lossless audio compession, Poceedings of IX Euopean Signal Pocessing Confeence EUSIPCO, vol. 4, pp , [5] T. Robinson, SHORTEN: Simple lossless and nea-lossless wavefom compession, Cambidge Univesity, Engineeing Depatment, Cambidge, UK, Tech. Rep. 156, 1994, pp [6] E. Ravelli, P. Gounay, and R. Lefebve, A Two-Stage MLP+NLMS Lossless code fo ste-eo audio, Poceedings of IEEE Intenational Confeence on Acoustics, Speech, and Signal Pocessing, vol. 5, pp , [7] R. Yu, S. Rahadja, C. C. Ko, and H. Huang, Impoving coding efficiency fo MPEG-4 Audio Scalable Lossless coding, Poceedings of IEEE Intenational Confeence on Acoustics, Speech, and Signal Pocessing, vol. 3, pp , [8] L. Xiao, L. Gang, L. Zhengguo, C. Thien King, and Y. Ai Ling, A novel pediction scheme fo lossless compession of audio wavefom, in Intenational Confeence on Multimedia and Expo, 2001, pp [9] R. Yu, C. Ko, S. Rahadja, and X. Lin, An RLS-LMS algoithm fo lossless audio coding, in Confeence Recod of the Thity-Seventh Asiloma Confeence onsignals, Systems and Computes, Pacific Gove, CA USA, June 2003, pp [10] T. Moiya, D. Yang, and T. Liebchen, Extended Linea Pediction Tools fo Lossless Audio Coding, Poceedings of IEEE Intenational Confeence on Acoustics, Speech, and Signal Pocessing, vol. 3, pp , [11] K. Sayood, Intoduction to Data Compession, 2nd ed. Mogan Kaufmann Publishes, [12] Y. A. Reznik, Coding of pediction esidual in MPEG-4 standad fo lossless audio cod-ing (MPEG-4 ALS), Poceedings of IEEE Intenational Confeence on Acoustics, Speech, and Signal Pocessing, vol. 3, pp , May 2004, Monteal, Quebec, Canada. [13] T. Liebchen and Y. A. Reznik, Impoved Fowad-Adaptive Pediction fo MPEG-4 Audio Lossless Coding, in 118th AES Convention, Bacelona, Spain, May 2005, pp [14] jdebock/lossless audio compession test.htm. [15] B. Aiazzi, S. Baonti, and L. Alpaone, Nea-lossless image compession by elaxation-labeled pediction, Signal Pocessing, vol. 82, no. 11, pp , [16] G. Ulacha and R. Stasinski, Paths to futue image lossless coding, in Poceedings of 54th Intenational Symposium ELMAR, 2012.

6 22 G. ULACHA, R. STASIŃSKI TABLE I BITRATES FOR CODING OF TEST RECORDINGS USING MMSE PREDICTORS OF LENGHT R Recodings \ ATain BeautySlept chanchan death expeiencia female speech FlooEssence ItCouldBeSweet Layla LifeShattes macabe male speech SinceAlways thea TomsDine velvet Mean TABLE II BITRATES FOR CODING OF TEST RECORDINGS BY LOSSLESS CODING ALGORITHMS BASED ON MMSE ANDD ZERO-ORDER ENTROPY CRITERIA Recodings = 4 MMSE = 4 ISS = 10 MMSE = 10 ISS = 30 MMSE = 30 ISS = 30 hybid ATain BeautySlept chanchan death expeiencia female speech FlooEssence ItCouldBeSweet Layla LifeShattes macabe male speech SinceAlways thea TomsDine velvet Mean

7 NOVEL IDEAS FOR LOSSLESS AUDIO CODING 23 TABLE III BITRATES FOR CODING OF TEST RECORDINGS BY CONTEXT LOSSLESS CODING ALGORITHMS DESCRIBED IN THE PAPER Recodings = 4 MMSE = 4 ISS = 10 MMSE = 10 ISS = 30 MMSE = 30 ISS = 30 hybid ATain BeautySlept chanchan death expeiencia female speech FlooEssence ItCouldBeSweet Layla LifeShattes macabe male speech SinceAlways thea TomsDine velvet Mean TABLE IV BITRATES FOR CODING OF TEST RECORDINGS BY CONTEXT LOSSLESS CODING ALGORITHMS DESCRIBED IN THE PAPER = 600 = 300 = 300 = 200 = 200 Recodings no context 2 contexts, 2 contexts, 3 contexts, 3 contexts, 1 theshold 1 of 8 thesholds 1 theshold pai 1 of 8 theshold pais ATain BeautySlept chanchan death expeiencia female speech FlooEssence ItCouldBeSweet Layla LifeShattes macabe male speech SinceAlways thea TomsDine velvet Mean