ROBUST ENCODING OF THE FS1016 LSF PARAMETERS : APPLICATION OF THE CHANNEL OPTIMIZED TRELLIS CODED VECTOR QUANTIZATION

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1 ROBUST ENCODING OF THE FS6 LSF PARAMETERS : APPLICATION OF THE CHANNEL OPTIMIZED TRELLIS CODED VECTOR QUANTIZATION BOUZID Merouane Speech Communcaton and Sgnal Processng Laboratory, Electroncs Faculty, Unversty of Scences and Technology Houar Boumedene (USTHB), P.O. Box 3, El-Ala, Bab-Ezzouar, Algers, 6, ALGERIA mbouzd@usthb.dz, mbouzd@yahoo.com ABSTRACT Speech coders operatng at low bt rates necesstate effcent encodng of the lnear predctve codng (LPC) coeffcents. Lne spectral Frequences (LSF) parameters are currently one of the most effcent choces of transmsson parameters for the LPC coeffcents. In ths paper, we present an optmzed trells coded vector quantzaton (OTCVQ) scheme desgned for robust encodng of the LSF parameters. The objectve of ths system, called ntally "LSF-OTCVQ Encoder", s to acheve a low bt-rate quantzaton of the FS6 LSF parameters. The effcency of the LSF-OTCVQ encoder (wth weghted dstance) was frst proved n the deal case of transmssons over noseless channel. After that we were nterested on the mprovement of ts robustness for real transmssons over nosy channel. To protect mplctly the transmsson parameters of the LSF-OTCVQ encoder ncorporated n the FS6, we used a jont source-channel codng carred out by the channel optmzed vector quantzaton (COVQ) method. In the case of transmssons over nosy channel, we wll show that the new encodng system, called "COVQ-LSF-OTCVQ Encoder", would be able to contrbute sgnfcantly to the mprovement of the FS6 performances by ensurng a good codng robustness of ts LSF spectral parameters. Keywords: source-channel codng, robust speech codng, LSF parameters. INTRODUCTION In speech codng systems, the short-term spectral nformaton of the speech sgnal s often modelled by the frequency response of an all-pole flter whose transfer functon s denoted by H(z) = /A(z) n whch A(z) = + a z + + a p z p []. In telephone band speech codng (3-34 Hz, f e = 8 KHz), the parameters of ths flter are derved from the nput sgnal through lnear predcton (LP) analyss of p = order. The parameters {a } =,,,, known as the Lnear Predctve Codng (LPC) coeffcents [], play a major role n the overall bandwdth and preservng the qualty of the encoded speech. Therefore, the challenge n the quantzaton of the LPC parameters s to acheve the transparent quantzaton qualty [], wth the mnmum bt-rate whle mantanng the memory and computatonal complexty at a low level. In practce, one doesn't quantfy drectly the LPC coeffcents because they have poor quantzaton propertes. Thus, other equvalent parametrc representatons have been formulated whch convert them nto much more sutable parameters to quantze. One of the most effcent representatons of the LPC coeffcents s the Lne Spectral Frequency (LSF) [3]. The LSF parameters (LSFs) whch are related to the zeros of polynomals derved from A(z) [] exhbt a number of nterestng propertes. These propertes [] make them a very attractve set of transmsson parameters for the LPC coeffcents. Explotng these propertes, varous codng schemes based on scalar and vector quantzaton were developed n the past for the effcent quantzaton of spectral LSF parameters. Several works showed that the vector quantzer (VQ) schemes, such as multstage VQ [4], Splt VQ [], can acheve at lower bt-rates the transparent quantzaton qualty of the LSFs compared wth those conceved based on scalar quantzer (SQ). In ths paper, we present an optmzed trells coded vector quantzaton (OTCVQ) scheme desgned for the effcent and robust codng of LSF parameters. The am of ths system, called at the begnnng "LSF-OTCVQ Encoder", s to acheve a low bt rate transparent quantzaton of LSFs by explotng the ntra-frame dependence between the closest pars of the LSF parameters. In the case of

2 deal transmssons over a noseless channel, we have already proved n [5] that the LSF-OTCVQ encoder (wth weghted dstance) could acheve good performances when appled to encode the LSF parameters of the US Federal Standard FS6. Indeed, we have showed that LSF-OTCVQ encoder of 7 bts/frame produces equvalent perceptual qualty to that obtaned when the LSF parameters are unquantzed. Subsequently, our nterest was drawn to the mprovement of the LSF-OTCVQ encoder robustness for real transmssons over nosy channel. In low bt rate speech codng doman, the essental objectve s to reduce the bt rates of speech coders whle mantanng a good qualty of transmsson. In general, durng the desgn of speech codng systems, the effects of transmsson noses are often neglected. A redundant channel codng [6] s conventonally used to ensure an "explct" protecton to senstve parameters of speech coders aganst channel errors. Accordng to the separate desgn approach, suggested by Shannon n hs classcal source/channel codng theorems [7], the channel encoder can be desgned separately from the source encoder by addng redundant bts (Error-detectng-correctng codes) to source data. Indeed, robust encodng systems could be desgned accordng to ths separaton approach but at the cost of an ncrease of the bt-rate/delay transmsson and the complexty of the codng/decodng. However, at low bt rate where the constrants n complexty and delay are very severe, ths channel codng s not especally recommended. The separaton desgn dsadvantages have motvated some researchers to nvestgate a jont soluton to the source and channel codng optmzaton problem so that they can reduce the complexty on both sdes, whle provdng performances close to the optmum. For these purposes, Jont Source-Channel Codng (JSCC) was ntroduced n whch the overall dstorton s mnmzed by smultaneously consderng the mpact of the transmsson errors and the dstorton due to source codng [8], [9], []. Most of these works have proved the effectveness of the JSCC to protect mplctly (.e., wthout redundancy) source data whle mantanng a constant bt rate and a reduced complexty. To mplctly protect the transmsson ndces of our LSF-OTCVQ encoder ncorporated n the FS6, we used a JSCC method carred out by the Channel Optmzed Vector Quantzaton (COVQ). We wll show frst how to adapt and apply successfully the COVQ technque for the robust desgn of a new encodng system (called "COVQ- LSF-OTCVQ encoder") n order to mplctly protect some of ts ndces. To fnsh, we wll generalze the study wth the complete protecton of all the ndces of the COVQ-LSF-OTCVQ encoder. An outlne of ths paper s as follows. In secton, we brefly revew the bascs of vector quantzaton. In secton 3, we descrbe the desgn steps of the OTCVQ encodng system. Examples of comparatve results of TCVQ/OTCVQ encoders are reported n ths secton. Next, we present the jont codng method by the COVQ technque. The performances of the COVQ system appled to encode memoryless source are presented at the end of the secton. The applcaton of the OTCVQ scheme for encodng the LSF parameters s descrbed n secton 5. Smulaton results, when usng two dfferent dstance measures (unweghted and weghted) n the desgn and the operaton of the LSF-OTCVQ encoder, are provded. In secton 6, we present the applcaton of the LSF- OTCVQ encoder to quantze the LSF parameters of the FS6 speech coder. After, a JSCC-COVQ method was used to mplctly protect the LSF- OTCVQ ndces for transmssons over nosy channel. Conclusons are gven n secton 7. VECTOR QUANTIZATION A k-dmensonal vector quantzer (VQ) of sze L s a mappng Q of k-dmensonal Eucldean space R k nto a fnte subset (codebook) Y = {y,, y L } composed of L codevectors []. The desgn prncple of a VQ conssts of parttonng the k- dmensonal space of source vectors nto L non overlappng cells {R,.., R L } and assocatng wth each cell R a unque codevector y. Codng a sequence of nput source vectors by a VQ conssts thus to assocate to each source vector x the bnary ndex {,, L } of a close codevector y whose dstance from the nput vector s mnmzed. In general, the vector quantzaton nvolves an rreversble loss of nformaton whch results n a qualty degradaton evaluated commonly by a dstorton measure. For a gven VQ, the average dstorton s defned by []: D k L = = x R d( x, y ) p ( x) dx, () where x) s the k-fold probablty densty functon of the source and d(x, y ) s the wdely used squared Eucldean dstance. The optmal desgn of a VQ s based on the prncple of searchng smultaneously the partton {R,.., R L } and the representng codevectors {y,.., y L } whch mnmzes the average dstorton D. To resolve ths problem, two man necessary condtons of optmalty need to be successvely satsfed durng the VQ desgn process []:. For a gven codebook Y = {y, y,..., y L }, the optmal partton satsfy :

3 R { x d( x, y ) d( x, y j } = : ), () It's the nearest neghbor optmalty condton.. Gven an encoder partton {R, =,..., L }, the optmal codevectors y are the centrods n each partton cell R (centrod condton) : y j = Cent R ) = E( X / X R ) (3) ( Varous algorthms for the desgn of VQ have been developed n the past. The most popular one s certanly the LBG algorthm []. Ths algorthm (LBG-VQ) s an teratve applcaton of the two optmalty condtons such as the partton and the codebook are teratvely updated. 3 OPTIMIZED ENCODING SYSTEM BASED ON THE TRELLIS CODED VECTOR QUANTIZATION The scalar trells coded quantzaton (TCQ) [3] and ts generalzed verson to vector case (TCVQ) [4], [5] mprove upon tradtonal trells encoders [6] by labellng the trells branches wth entre subsets rather than wth ndvdual reproducton levels. Ths approach, whch was motvated by Ungerboeck's formulaton of Trells Coded Modulaton (TCM) [7], uses a structured alphabet wth an extended set of quantzaton levels. In ths work, one was nterested partcularly on the TCVQ encoder whch structure s qute smlar to TCQ, wth an ncrease n complexty due to vector codebook searchng [4]. The desgn of a TCVQ encoder conssts of several nterrelated steps. These steps nclude selecton of trells, extended ntal codebook constructon, parttonng of the codebook's codevectors nto subcodebooks (subsets) and labellng the trells branches wth these subsets. Consder the desgn process of a k-dmensonal TCVQ encoder of rate R bts per sample (bps) used to encode a sequence of source vectors. The S-state trells used n TCVQ can be any one of Ungerboeck's ampltude modulaton trellses [7]. The extended ntal TCVQ codebook s generally desgned by the LBG algorthm. It contans kr+ codevectors (twce that of the VQ). However, durng the TCVQ encodng process, only a subset of sze kr of these codevectors may be used to represent a source vector at any nstance of tme. Accordng to Ungerboeck's set parttonng method, the codevectors are then parttoned nto four subsets D, D, D and D 3 each of sze kr. In our TCVQ encoders desgn, we used the heurstc algorthm descrbed n [5] to partton the extended TCVQ codebook. After that, the subsets are labelled on the trells branches accordng to Ungerboeck's rules of TCM [7]. These rules are meant to ensure that the dstorton between the orgnal and the reconstructed source sequences (under clear channel assumptons) s close to the mnmum. To encode the source vectors sequence, the wellknown Vterb algorthm [6] s used to fnd a legtmate optmal path through the trells, whch results n mnmum dstorton. The TCVQ encoder transmts to recepton a bt sequence specfyng the correspondng optmal path (sequence of subsets) n addton to a sequence of kr bts codewords necessary to specfy codevectors from the chosen subsets. At the TCVQ decoder sde, the bt sequence that specfes the selected optmal trells path s used as the nput to the convolutonal coder of the TCVQ system. The output of ths coder selects the proper subset D. The codewords of the second bnary sequence are used to select the correct codevectors from each subset. An example of a 4-states scalar TCQ encoder of rate R = bps used to encode a memoryless source, whch s unformly dstrbuted on the nterval [-A A], s llustrated on Fg.. x Input bt /D /D /D /D 3 /D /D /D 3 /D (a) D D D D 3 D D D D 3-7A/8-5A/8-3A/8 -A/8 A/8 3A/8 5A/8 7A/8 (b) (c) Fgure : TCQ encoder of rate R= bps : (a) Secton of labelled 4-states trells, (b) Output alphabet levels and partton, (c) TCQ convolutonal coder. Examples of smulaton results for encodng unty-varance memoryless Gaussan sources usng nteger and fractonal rates TVCQ encoders are respectvely gven n tables and. For dfferent rates, results are gven n terms of Sgnal to Nose Rato (SNR) n db, along wth the correspondng LBG-VQ performance and dstorton rate functon s s s y Output bts y

4 D(R). Notce that when the rate s fractonal, the dmenson k has to be such that kr becomes an nteger. Table : Performances of TCVQ encodng wth nteger rates for the Gaussan source. Rate bps Table : Performances of TCVQ encodng wth fractonal rates for the Gaussan source. Rate Dm. TCVQ Trellses Sze (State's Number) LBG- D(R) bps k VQ At the same encodng rate, these results show that the TCVQ outperforms the TCQ (k = ). Moreover, the TCVQ allows fractonal rates as shown by the smulaton results lsted n table. We can see also that, for a gven rate, the TCQ/TCVQ performances are hgher than those of the conventonal SQ/VQ. To more mprove the TCVQ performances, a tranng optmzaton procedure for the extended TCVQ codebook desgn was developed [5]. For a gven tranng source vectors, ths procedure updates the TCVQ codebook by replacng each codevector wth the average of all the source vectors mapped to ths codevector. Ths leads to an teratve desgn algorthm for the overall TCVQ encoder. Usng ths optmzaton varant, the algorthm wll be called OTCVQ (Optmzed Trells Coded Vector Quantzaton) algorthm. Examples of smulaton results for encodng memoryless Gaussan sources usng fractonal rate OTCVQ encoders are lsted n table 3. Table3 : Performances of the OTCVQ wth fractonal rates for the Gaussan source. Rate bps Vector Dm. Dm. k TCVQ Trellses Sze (State's Number) TCVQ Trellses Sze (State's Number) LBG- VQ D(R) 6..4 LBG- VQ D(R) Comparng these results wth those gven n table, we clearly notce the performance mprovements brought by the optmzaton of the TCVQ codebooks. 4 JOINT CODING BY THE CHANNEL OPTIMIZED VECTOR QUANTIZATION Vector quantzaton s currently used n varous practcal applcatons and snce some type of channel nose s present n any practcal communcaton system, the analyss and desgn of VQs for nosy channels s recevng ncreasng attenton. In ths work, we consdered the jont sourcechannel codng (JSCC) assocated specfcally wth the use of VQ n order to provde an mplct protecton to our quantzers. Partcularly, we were nterested on a category of JSCC relatng to quantzers optmzed by takng nto account the error probablty of channel. It's about the channel optmzed vector quantzaton [8], [8]. 4. COVQ system prncple: Modfed optmalty condtons A channel optmzed vector quantzer (COVQ) s a codng scheme based on the prncple of VQ generalzaton by takng nto account the present nose on the transmsson channel. The dea s to explot the knowledge about the channel n the codebook desgn process and the encodng algorthm. Thus, the operatons of source and channel codng are ntegrated jontly nto the same entty by ncorporatng the channel characterstcs n the desgn procedure. Indeed, the LBG-VQ s well approprate to a modfcaton n ths sense. The purpose then s to mnmze a modfed total average dstorton between the reconsttuted sgnal and the orgnal sgnal, gven the channel nose. The desgn of a COVQ encoder s carred out by a VQ verson extended to the nosy case [8], [8]. The COVQ scheme keeps the same VQ block structure (encoder/decoder, dmenson, bt rate). The dfference s n the formulaton of the necessary condtons of optmalty to mnmze a modfed expresson of the total average dstorton. Ths new dstorton s formulated by consderng smultaneously the dstorton due to vector quantzaton and channel errors [8], [9]: D = k L = R x) L j= j / ) d( x, y j ) dx, (4) where j/) s the channel transton probablty whch represents the probablty that the ndex j s receved gven that the ndex s transmtted. By comparng the Eq. (4) wth Eq. (), one can notce easly that these two equatons are equvalent, except that the Eq. (4) uses a modfed dstance measure (term n the braces). It about the same dstance d but wth weghtngs gven by the channel transton

5 probabltes j / ),, j =,..., L. The formulatons of optmalty necessary condtons of COVQ are also derved n two steps, accordng to the mnmzaton prncple of the modfed total average dstorton [8], [8], [9]. For a gven codebook Y = {y,..., y L } and by usng a squared Eucldean dstance measure, the optmal partton R (=,..., L ) for a nosy channel s such that : L L k R = x R : p ( j/ ) x yj p ( j/ l) x yj, l (5) j= j= Smlarly, the optmum codebook for a fxed partton s gven by: L = L = j / ) R y j =, j =,, L. (6) j / ) x). dx R x x). dx The codevector y j represents now the centrod of all nput vectors that are decoded nto the cell R j, even f the transmtted ndex s dfferent from j. The equatons (5) and (6) are respectvely referred as the generalzed nearest neghbour and centrod condtons wth a modfed dstorton measure. The optmal codevectors for nosy channel are thus lnear combnatons of those for the noseless case, weghted by the a posteror channel transton probabltes. In our applcatons, the communcaton channel consdered s a dscrete memoryless channel wth fnte nput and output alphabets. Precsely, we assumed a memoryless bnary symmetrc channel (BSC) model wth bt error (crossover) probablty p [6], [6]. For codewords (VQ ndces) of n bts, the BSC transton probabltes are descrbed by [9], [9]: j ) = ( p) n dh (, j) p dh (, j), (7) where d H (, j) ( d H (, j) n) s the Hammng dstance between the n-bts bnary codewords represented by ntegers and j. When the channel bt error probablty p s suffcently small, the probablty of multple bt errors n an ndex s very small relatve to the probablty of zero or one bt error [9], [8], [9]. To smplfy the numercal computatons, t s often adequate to consder only the effects of sngle bt errors on channel codewords. The BSC channel model can be then approxmated by [9]: p ( j ) = p np j ξ, j =, otherwse (8) where ξ s the set of all ntegers j, ( j L ), such that the bnary representaton of j s of Hammng dstance one from the bnary representaton of. In the case where the source dstrbuton s unknown, long tranng database of k-dmensonal vectors can be used for the quantzer desgn. Wth the approxmaton gven n Eq. (8), the equatons (4) and (6) wll be respectvely modfed as: N L D = j / t ) d( xt, y j ) N k, (9) t= j ξ and : y j ξ j ξ j j / ) l l: xl R j / ) R x / N =, () / N where N s the sze of the tranng base and R denotes the number of tranng vectors belongng to the cell R. 4. COVQ encoder desgn algorthm The desgn procedure of the COVQ encodng system s a straghtforward extenson of the LBG- VQ algorthm. An teratve optmzaton of the two modfed optmalty condtons s carred out such as the partton and the codebook codevectors are updated by usng the modfed dstorton ncludng the channel probablty [8], [8]. The steps of our verson of the COVQ algorthm are detaled n []. We suppose that a set of nput vectors s avalable (tranng base) and that the BSC channel error probablty ε s gven. Ths channel probablty, whch s often called desgn error probablty of COVQ codebook, s consdered as an nput parameter n the optmzaton process. At the begnnng ths desgn parameter s set temporarly at a low value; then gradually ncreased untl matchng the desred desgn error probablty. The choce of the ntal codebook s very mportant snce t can sgnfcantly mpact the fnal results. In our desgn, the ntal codebook s conceved for ε = (.e., for noseless channel). It s about a smple run of the conventonal LBG-VQ algorthm whch wll converge to a locally optmal codebook. Ths codebook wll be used as ntal

6 codebook of the COVQ algorthm. Then, for each stage of ε, the algorthm wll converge to an ntermedate codebook whch wll be used as ntal codebook of the next stage n the COVQ desgn process. The greatest dffculty n the COVQ system desgn s that the channel error probablty s a parameter n the optmzaton process. In real transmsson stuaton, ths parameter s dffcult to estmate. It may even vary n tme, makng the desgn accordng to a specfc value rather academc. Thus, accordng to the practcal stuaton and to the estmates of the real communcaton channel characterstcs, COVQ encoders can be selected to obtan the hghest degree of robustness. 4.3 COVQ encoder performances We now present numercal results on the performance of COVQ encodng system operatng over a BSC channel wth varable bt error probablty p. Examples of smulaton results of COVQ encoders, traned for varous values of the desgn probablty parameter ε (ε =.,.5,. and.5) are gven n table 4. These encoders, whose selected characterstcs are: k =, R = bps and L = 6, were appled to encode memoryless Gaussan source. For a comparatve evaluaton wth the conventonal VQ, the LBG-VQ (desgned for a noseless channel, ε =.) performances were also ncluded n the table. Table 4 : SNR Performances comparson between COVQ and VQ over BSC channel ε p In the case of transmssons over noser channels (hgher values of p), the results ndcate that COVQ performs better than LBG-VQ. For example, for a BSC of p =., a consderable SNR gan of 3.36 db was obtaned by the COVQ (traned for ε =.5) compared wth the LBG-VQ. One notce that when the channel probablty p does not match wth the desgn probablty ε, COVQ encoders traned for ε dentcal or close to p are those whch yelds the best performances. However, when the channel s noseless (p =.) the SNR-performances of COVQ encoders are suboptmal wth the ncrease of the desgn parameter ε. In ths case, the LBG-VQ ensures comparable performances or better than the COVQ. Same remarks when the channel error probablty s low (p <.5) wth a slght performances mprovement obtaned by COVQ encoders traned for a low value of the desgn parameter ε (example, COVQ for ε =.). 5 OPTIMIZED-TCVQ FOR LOW-BIT RATE ENCODING OF LSF PARAMETERS Usng the OTCVQ encodng technque, an encodng scheme for the LSF parameters s presented n ths secton. The am of ths encodng system, called "LSF-OTCVQ Encoder" [5], s to effcently quantze the LSF parameters of one frame usng only the dependences among the same parameters. For speech codng applcatons, the OTCVQ s used n block mode, where each block corresponds to an LSF vector of sze. In ths work, twodmensonal -D codebooks (k = ) are used for encodng the LSF vectors. Thus, each stage n the trells dagram s assocated wth -D of the LSF vector. Hence, there are fve stages n the LSF- OTCVQ trells wth two branches enterng and leavng each state. Snce the LSF parameters have dfferent means and varances, fve extended codebooks are then needed to encode an LSF vector. Knowng that choce of an approprate dstance measure s an mportant ssue n the desgn of any VQ system, we have used another dstance measure n the desgn and the operaton steps of the LSF- OTCVQ encoder. It's about the weghted Eucldean dstance measure. Based on the LSF parameters propertes, several weghted dstance measures have been proposed for the LSF encodng [], [4], []. In our applcatons, we used the weghted squared Eucldean dstance gven by: d ( f, fˆ) = c w ( f fˆ ), () = where f and fˆ are respectvely the th coeffcents of the orgnal f and quantzed fˆ LSF vectors; c and w represent respectvely the constant and varable weghts assgned to the th LSF coeffcent. These weghts are meant to provde a better quantzaton of LSF parameters n the formant regons. Many weghtng functons have been defned to calculate the varable weght vector w = [w,, w ]. Partcularly, we used the weghtng functon, known by the nverse harmonc mean (IHM) []: w = f f + f +, () f

7 where f = and f =.5. The constant weght vector c = [c,, c ] s expermentally determned []:., for 8 c =.8, for = 9 (3).4, for = The LSF quantzer performances are evaluated by the average spectral dstorton (SD) whch s often used as an objectve measure of the LSF encodng performance. Ths measure correlates well wth human percepton of dstorton. When calculated dscretely over a lmted bandwdth, the spectral dstorton for frame s gven, n decbels, by [4] : n jπn / N S( e ) log jπn / N n= n Sˆ( e ) SD = n n. (4) For speech sgnal sampled at 8 khz wth a 3 khz bandwdth, an N = 56 pont FFT s used to compute the orgnal S(e jπn/n ) and quantzed Ŝ(e jπn/n ) power spectra of the LPC synthess flter, assocated wth the th frame of speech. The spectral dstorton s thus computed dscretely wth a resoluton of 3.5 Hz per sample over 96 unformly spaced ponts from 5 Hz to 3.5 khz. The constants n and n n Eq. (4) correspond to and 96 respectvely. Generally, t s accepted that an average SD of about db ndcates neglgble audble dstorton has ncurred durng quantzaton. Ths value has been, n the past, suggested for transparent quantzaton qualty and used as a goal n desgnng many LPC quantzaton schemes. In [], Palwal and Atal establshed that the average SD s not suffcent to measure perceved qualty alone. They ntroduced the noton of spectral outlers frames. Consequently, we can get transparent qualty f we mantan the followng three condtons: ) The average SD s about db, ) The percentage of outler frames havng SD between and 4 db s less than %, 3) No frames must have SD greater than 4 db. Now, we evaluate the performances of our LSF- OTCVQ encoder operatng at dfferent bt rates. All smulaton results reported n ths secton were obtaned by usng four-state trells and -D codebooks. For each encodng rate, bts are thus assgned to represent the ntal state. When the remanng bts cannot be equally assgned to represent the fve -D codebooks, fewer bts are used n the last codebooks, snce t s known that human resoluton n the hgher frequency bands s less than n the lower frequency bands. We nvestgated the optmum bt allocatons for the LSF-OTCVQ encoder and found that the bt allocatons gven n table 5 yeld the best results. Table 5 : Bt allocatons of each LSF-OTCVQ trells stage codebook as a functon of bt rate Bts / LSF Trells Stage Number : Vector Bts / Stage codebook The speech data used n the experments of ths secton conssts of approxmately 43 mn of speech taken from the TIMIT speech database []. To construct the LSF database, we have used the same LPC analyss functon of the FS6 speech coder [3]. A -order LPC analyss, based on the autocorrelaton method, s performed every analyss frame of 3 ms usng a Hammng wndow. One part of the LSF database, consstng of 75 LSF vectors, s used for tranng and the remanng part, of 6 LSF vectors (dfferent from the tranng set), s used for test. For dfferent bt rates, the performances of the LSF-OTCVQ encoder are shown n table 6. These results have been obtaned by usng separately two dfferent dstorton measures (unweghted and Table 6: Performances of the LSF-OTCVQ encoder as a functon of bt rate. LSF-OTCVQ (unweghted dstance) LSF-OTCVQ (weghted dstance) Bts/frame Average SD Outlers (n %) Average SD Outlers (n %) SD (db) - 4 db > 4 db SD (db) - 4 db > 4 db

8 weghted dstances) n both the desgn and the operaton of the LSF-OTCVQ encoder. These comparatve results clearly show the mprovement of the LSF-OTCVQ performances, obtaned by usng the weghted dstance. The LSF- OTCVQ encoder, desgned wth a weghted dstance, need 7 bts/frame to get transparent quantzaton qualty. Compared to the encoder desgned wth the unweghted dstance, t can save about - bts/frame whle mantanng comparable performances. 6 EFFICIENT AND ROBUST CODING OF THE FS6 LSF PARAMETERS: APPLICATION OF THE LSF-OTCVQ In ths secton we use the LSF-OTCVQ encoder (wth weghted dstance) to quantze the LSF parameters of the FS6. For the moment, we suppose that the transmssons are done over a noseless deal channel. Recall that the US Federal Standard FS6 s a 4.8 kbts/s Code Excted Lnear Predcton (CELP) speech coder [3]. Accordng to the FS6 norm, the LSF parameters are encoded at the orgn by an SQ of 34 bts/frame. For the same test database (6 LSF vectors), ths 34 bts/frame LSF SQ results n an average SD of.7 db, 5.99 % outlers n the range -4 db, and.46 % outlers havng SD greater than 4 db. By comparng these results wth those gven n table 6, we can see that the LSF-OTCVQ encoder (for all studed lower rates) performs better than the 34 bts/frame SQ used at the orgn n the FS6. Thus, several bts per frame can be ganed by the applcaton of the LSF-OTCVQ n the LSF encodng process of the FS6. Subjectve lstenng tests of the 7 bts/frame LSF-OTCVQ encoder were also performed. Incorporatng ths encoder n the FS6, the bt rate for the quantzaton of the LSF parameters decreases to 9 bts/s and consequently the FS6 operate at a bt rate of 4.57 kbts/s. To carry out these tests, we generated for the same orgnal speech sgnal three versons of synthetc speech sgnals: one wth unquantzed LSFs and the two others wth quantzed LSFs usng respectvely the 7 bts/frame LSF- OTCVQ encoder and the 34 bts/frame SQ. Subjectve qualty evaluatons are done here through A-B comparson and MOS (Mean Opnon Score) tests usng 8 lsteners. Sx sentences from the TIMIT database (spoken by three male and three female speakers) are used for the subjectve evaluatons. The A-B comparson test nvolves presentng lsteners wth a sequence of two speech test sgnals (A and B). For each sentence, a comparson s done between the two synthetc sgnals: one A (or B) wth unquantzed LSFs and the other B (or A) wth LSFs quantzed by the LSF-OTCVQ encoder. The A-B sgnal pars are presented n a randomzed order. The lsteners choose ether one or the other of the two syntheszed versons, or ndcate no preference. For the MOS tests, the lsteners were requested to rate each synthetc speech sentence (wth LSF-OTCVQ quantzed LSFs) n a scale between (bad) and 5 (excellent). At the end, the average score of opnon (MOS) s calculated. Results from the A-B comparson tests show that the majorty of the lsteners (58.84 %) have no preference. The mean preference for speech sgnal coded wth LSF-OTCVQ quantzed LSFs (.83 %) s dentcal to that obtaned for the speech sgnal coded wth unquantzed LSFs. Roughly, we can conclude that the two consdered versons of coded speech are statstcally ndstngushable,.e., there are no perceptble dfferences and the quantzaton does not contrbute to audble dstorton. In terms of MOS, the consdered coded verson of speech exhbts a good score of Ths mples that good communcatons qualty and hgh levels of ntellgblty [] are obtaned usng the 7 bts/frame LSF-OTCVQ encoder n the FS6. In addton, n term of average segmental sgnalto-nose rato (SSNR), the synthetc speech sgnals wth unquantzed LSF parameters gave an average SSNR of.5 db; wth LSF-OTCVQ encodng of LSF parameters, the average SSNR obtaned s.3 db. In the case where LSF parameters are quantzed by the 34 bts SQ, an average SSNR of 9.59 db was obtaned. Thus, a reducton n codng rate wth an mprovement of the SSNR-performances of the FS6 was obtaned by applcaton of the LSF- OTCVQ encodng system. 6. Robustness of the COVQ-OTCVQ encoder: Transmsson over a nosy channel In a practcal communcaton system, the robustness of the LSF-OTCVQ encoder must be renforced so that the encoder wll be able to cope up wth channel errors. In ths part, we were nterested n mplct protecton of the encoders by applcaton of the JSCC-COVQ technque. We wll see frst how to apply the COVQ for the robust desgn of the LSF- OTCVQ encoder n order to provde an mplct protecton to some of ts ndces. To fnsh, we wll generalze the study wth the full protecton of all the ndces of the new LSF-OTCVQ encoder wth the COVQ technque. 6.. Desgn of the LSF-OTCVQ encoder wth JSCC-COVQ technque The desgn prncple of the LSF-OTCVQ encoder optmzed for nosy channel s based manly on the desgn algorthm of LSF-OTCVQ modfed accordng to the basc concept of the COVQ. In the applcatons, the fve extended codebooks of our new encodng system, denoted by: "COVQ-LSF-OTCVQ encoder", were optmzed for a desgn error

9 probablty ε =.5. The basc steps of our desgn algorthm of the 7 bts/frame COVQ-LSF-OTCVQ encoder are summarzed below. Notce that the trells states number of the encoder s always S = 4; consequently bts/frame are necessary to represent the ntal state. The remanng 5 bts are assgned for the 5 codebooks accordng to the bts allocaton gven n table 5. Let us specfy that at the begnnng the 5 ntal extended codebooks are desgned by the LBG- VQ algorthm (ε =.) usng the weghted Eucldean dstance. The codebooks desgn of COVQ-LSF-OTCVQ encoder s done usng the same tranng data base (75 LSF vectors). Thereafter, ths base s dvded nto 5 tranng subsets of -D LSF vector pars (LSF -, LSF 3-4, LSF 5-6, LSF 7-8 and LSF 9-). Desgn steps of COVQ-LSF-OTCVQ encoder : Step : Intal desgn Based on the 5 tranng subsets, use the COVQ (ε c =.5) algorthm to desgn the fve (-D) extended ntal codebooks of the encoder. Partton each ntal codebook n 4 sub-codebooks usng the set parttonng algorthm. Then, label the transtons of each trells stage wth the correspondng parttoned COVQ-codebook (.e., COVQ-codebook LSF- for stage, Set a stop threshold α to very small value. Step : TCVQ codng/decodng process For the gven LSF vectors tranng base, fnd the best possble reproducton LSF vectors through the trells by usng a modfed verson of Vterb procedure. Calculate the average SD between the orgnal and quantzed LSF vectors. Step 3: Termnaton Test If the relatve decrease of the average SD s below the threshold α, save the 5 optmzed codebooks of COVQ-LSF-OTCVQ encoder, stop. Otherwse, updates the 5 COVQ-codebooks usng a modfed verson of the optmzaton procedure and go to step. In step, the TCVQ encodng process of nput LSF vectors conssts to fnd the best possble sequence of codevectors (optmal path) through the trells. Ths research task s assured by the Vterb algorthm wth a slght modfcaton of the dstance computaton formula. Ths dstance, whch must be mnmzed durng the TCVQ search process of the optmal codevector, s formulated as follows: d( f, fˆ ) = j / ) cmwmd( f ( m) fˆ j ( m)) (5) k j ξ m= k where k s the dmenson of LSF vectors (k = for LSF's pars) and ξ s the set of the -neghbors such as d H (, j) =. Recall that after the encodng process, COVQ-LSF-OTCVQ encoder transmts two bnary sequences n addton to two bts representng the trells ntal state. In ths part, we must notce that only the ndces sequence of COVQ-LSF-OTCVQ codevectors (sequence of bts for the 5 ndces) s supposed to be protected mplctly by COVQ. Ths sequence results drectly from the COVQ search procedure through the 5 codebooks of the encoder. On the other hand, the other bnary sequences (ntal state, optmal path) are not delvered by VQ search process and consequently they are not protected mplctly aganst channel errors. 6.. Performances of the COVQ-LSF-OTCVQ system: Encodng of the FS6 LSF parameters We present now the performances of the 7 bts/frame COVQ-LSF-OTCVQ encoder (ε =.5) appled for the effcent and robust codng of FS6 LSF parameters. In these smulatons, the channel errors wll affect only the transmsson of LSF parameters. For the moment, only the sequences of bts/frame specfyng the COVQ-LSF-OTCVQ codevectors ndces are transmtted over a BSC channel of bt error probablty p varyng between and.5. The data base used n the followng evaluatons s composed of 3.69s speech sequences extracted from the test data base. Syntheszed speech sgnals of ths base were generated by the FS6, wth objectve evaluatons n terms of average SD for the LSF encoders and average SSNR for synthetc speech sgnals. The SD Performances of the 7 bts/frame systems: LSF-OTCVQ (wthout protecton) and COVQ-LSF-OTCVQ (ε =.5) are reported n table 7. These results show that when the channel error probablty becomes rather hgh (p > ε =.5), the COVQ yelds sgnfcant mprovement to the performances of LSF-OTCVQ encoder. Wthout protecton, the LSF-OTCVQ has ncurred more severe degradaton compared wth the protected LSF encoder. Ths degradaton s represented by a brutal ncrease n the average SD of the LSF-OTCVQ as well as the percentage of outlers frames havng SD> 4 db. Under these condtons, the COVQ (ε =.5) has permtted thus to LSF-OTCVQ to have a good robustness aganst channel errors by mantanng a reduced and slow ncrease of the average SD and the number of outlers frames (SD > 4 db).

10 Table 7: Performance comparsons between COVQ-LSF-OTCVQ/LSF-OTCVQ encoders of 7 bts/frame: Applcaton to the FS6 LSF parameters encodng However, when the transmssons are done over a noseless channel (p =.) or slghtly dsturbed (p ε), the performances of COVQ-LSF-OTCVQ become suboptmal by compromsng the transparent quantzaton qualty. On other hand, mportant observatons were noted concernng the SSNR objectve performances of the global FS6 encoder. Indeed, contrary to certan conclusons made before, the FS6 SSNR performances (wth LSF parameters coded by COVQ-LSF-OTCVQ) are also remarkable when the channel s slghtly dsturbed. The comparatve evaluaton of the FS6 objectve performances, wth LSFs coded by LSF-OTCVQ and COVQ-LSF- OTCVQ encoders, s presented n Fg.. Average SSNR (db) COVQ-LSF-OTCVQ Encoder BSC Average SD Outlers (n %) Probablty p SD (db) -4 db > 4 db FS6 wth LSF-OTCVQ FS6 wth COVQ-LSF-OTCVQ.,,.5 Error Probablty (p) Fgure : Average SSNR performances of the FS6 speech coder. For error probabltes p., these results show that the dstortons are neglgble for the two LSF encodng systems. We can conclude that the encodng system COVQ-LSF-OTCVQ (ε =.5) can provde a good mplct protecton to the FS6 LSF parameters wth suboptmal SD-performances when the channel s slghtly dsturbed. LSF-OTCVQ Encoder Average SD Outlers (n %) SD (db) -4 db > 4 db COVQ-LSF-OTCVQ encoder wth redundant channel codng Now, we generalze the study wth the full protecton of all transmsson ndces of the 7 bts/frame COVQ-LSF-OTCVQ encoder (ε =.5). By adequately explotng the bts ganed by ths encoder, a redundant channel codng s used to explctly protect the 7 bts/frame remanng wthout protecton. Snce n our smulatons the transmssons are done va BSC channel wth the assumpton of only one error bt domnatng by corrupted ndex (sngle error), a smple sngle error-correctng code s largely suffcent to correct all possble sngle errors whch wll affect the transmtted sequences of the encoder (5 bts of the optmal path and the bts of the ntal state). Notce, of course, that the bts/ frame representng the codevectors ndces of the optmal path are already protected by COVQ. To carry out the channel codng of the nonprotected 7 bts/frame, we used two error-correctng Hammng (7, 4, 3) codes belongng to the category of systematc lnear block codes. In ths paper, we wll not revew the desgn/operaton theory of the Hammng codes whch s generally well documented [6]. These codes were frst conceved to effectvely correct only one error per transmsson block (sngle error-correctng codes). In our desgn, the two Hammng (7, 4, 3) codes have the capacty to protect 8 bts by generatng together 4 bts. The 7 bts/frame COVQ-LSF-OTCVQ encoder, wth the two Hammng (7, 4, 3) codes, wll thus operate at a rate of 34 bts/frame. It s about the same number of bts allocated wth the orgnal codng of the FS6's LSF parameters. Thus, the global desgn of the FS6 wth COVQ-LSF-OTCVQ (plus the Hammng codes) of LSF parameters mantans the speech coder rate to ts orgnal value of 4.8 kbts/s. The performances of the non-protected LSF- OTCVQ compared wth those of the COVQ-LSF- OTCVQ (ε =.5) encoder wth Hammng (7, 4, 3)

11 Table 8 : Performances comparson between the LSF-OTCVQ encoder and the COVQ-LSF-OTCVQ (ε =.5) + Hammng (7, 4, 3) codes BSC Probablty p COVQ-LSF-OTCVQ Encoder + Hammng (7, 4, 3) codes Average SD Outlers (n %) SD (db) -4 db > 4 db LSF-OTCVQ Encoder wthout protecton Average SD Outlers (n %) SD (db) -4 db > 4 db codes are gven n table 8. For all error probablty varaton range, the results showed that the channel codng by Hammng codes (7, 4, 3) has clearly mproved the performances of the 7 bts/frame COVQ-LSF- OTCVQ encodng system. The global system thus has a good robustness aganst the errors of the nosy channel. On the other hand by comparng these results wth those gven n table 7, the LSF-OTCVQ encoder has ncurred larger degradaton n terms of average SD and outlers. Ths s due manly to the random nose effects of the bnary sequences specfyng the ntal state or the optmal path. Concernng the SSNR performances of the global FS6 (wth LSFs coded by COVQ-LSF- OTCVQ + Hammng (7, 4, 3) codes), the degradatons are very low and even neglgble for error probabltes p <.. The SSNR performances of the FS6, n the cases wth and wthout LSF protecton, are presented n Fg. 3. Average SSNR (db) FS6 wth non-protected LSF-OTCVQ FS6 wth COVQ-LSF-OTCVQ + Ham(7,4).,,.5 Error Probablty (p) 7 CONCLUSION In ths work, an optmzed trells coded vector quantzaton scheme has been developed and successfully appled for the effcent and robust encodng of the FS6 LSF spectral parameters. In the case of deal transmssons over a noseless channel, objectve and subjectve evaluaton results revealed that the 7 bts/frame LSF-OTCVQ encoder (wth weghted dstance) produced equvalent perceptual qualty to that when the LSF parameters are unquantzed. After, we used a JSCC-COVQ technque to protect mplctly the transmsson ndces of the LSF-OTCVQ encoder ncorporated n the FS6. The smulaton results showed that our new COVQ- LSF-OTCVQ encodng system has permtted to the basc LSF-OTCVQ encoder to have a good robustness aganst BSC channel errors especally when the transmsson errors probablty s hgh. To fnsh ths work, t was necessary to protect all the transmsson ndces of the COVQ-LSF-OTCVQ encoder snce only a part of ts ndces was protected mplctly by JSCC-COVQ. By usng adequately the bts per frame ganed by ths encoder, a redundant channel codng by Hammng codes was used to explctly protect the remanng bts wthout protecton. We showed that the COVQ-LSF- OTCVQ encoder, usng the Hammng codes (7, 4, 3), has contrbuted sgnfcantly to the mprovement of the encodng performances of the FS6's LSF parameters. We can conclude that our global COVQ-LSF- OTCVQ encodng system wth Hammng channel codes can ensure an effectve and robust codng of the LSF parameters of the FS6 operatng over nosy channel. Fgure 3: Average-SSNR performances of global FS6

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