University Road, Hsinchu 300, Taiwan, R.O.C. b Department of Communications Engineering, National Chiao Tung University, 1001

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1 This article was downloaded by: [National Chiao Tung University 國立交通大學 ] On: 25 April 2014, At: 06:40 Publisher: Taylor & Francis Infora Ltd Registered in England and Wales Registered Nuber: Registered office: Mortier House, Mortier Street, London W1T 3JH, UK Journal of the Chinese Institute of Engineers Publication details, including instructions for authors and subscription inforation: Channel optiized error itigation for distributed speech recognition over wireless networks Cheng Lung Lee a & Wen Whei Chang b a Departent of Counications Engineering, National Chiao Tung University, 1001 University Road, Hsinchu 300, Taiwan, R.O.C. b Departent of Counications Engineering, National Chiao Tung University, 1001 University Road, Hsinchu 300, Taiwan, R.O.C. Phone: E-ail: Published online: 04 Mar To cite this article: Cheng Lung Lee & Wen Whei Chang (2009 Channel optiized error itigation for distributed speech recognition over wireless networks, Journal of the Chinese Institute of Engineers, 32:1, 45-51, DOI: / To link to this article: PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis akes every effort to ensure the accuracy of all the inforation (the Content contained in the publications on our platfor. However, Taylor & Francis, our agents, and our licensors ake no representations or warranties whatsoever as to the accuracy, copleteness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with priary sources of inforation. Taylor and Francis shall not be liable for any losses, actions, clais, proceedings, deands, costs, expenses, daages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article ay be used for research, teaching, and private study purposes. Any substantial or systeatic reproduction, redistribution, reselling, loan, sub-licensing, systeatic supply, or distribution in any for to anyone is expressly forbidden. Ters & Conditions of access and use can be found at

2 Journal of the Chinese Institute of Engineers, Vol. 32, No. 1, pp ( CHANNEL-OPTIMIZED ERROR MITIGATION FOR DISTRIBUTED SPEECH RECOGNITION OVER WIRELESS NETWORKS Cheng-Lung Lee and Wen-Whei Chang* ABSTRACT This paper investigates the error itigation algoriths for distributed speech recognition over wireless channels. A MAP sybol decoding algorith which exploits the cobined a priori inforation of source and channel is proposed. This is used in conunction with a odified BCJR algorith for decoding convolutional codes based on sectionalized code trellises. Perforance is further enhanced by the use of the Gilbert channel odel that ore closely characterizes the statistical dependencies between channel bit errors. Experients on Mandarin digit string recognition task indicate that our proposed itigation schee achieves high robustness against channel errors. Key Words: channel error itigation, distributed speech recognition. I. INTRODUCTION The increasing use of obile and IP networks for speech counication has lead to distributed speech recognition (DSR systes being developed (ETSI ES v1.1.1., The basic idea of DSR consists of using a local front-end fro which speech features are extracted and transitted through a data channel to a reote back-end recognizer. F or transission, speech features are grouped into pairs and copressed via vector quantizers (VQs in order to eet bandwidth requireents. The VQ encoder operates by apping a large set of input vectors into a finite set of representative codevectors. The transitter sends the index of the nearest codevector to the receiver, while the receiver decodes the codevector associated with the received index and uses it as an approxiation of the input vector. Transitting VQ data over noisy channels changes the encoded inforation and consequently leads to degraded recognition perforance. In the case of packet-erasure channels, several packet loss copensation techniques such as interpolation (Bernard and Alwan, 2002 and error control coding (Boulis et al., 2002 have been introduced for DSR. For wireless channels, oint *Corresponding author. (Tel: ; Eail: The authors are with the Departent of Counications Engineering, National Chiao-Tung University, 1001 University Road, Hsinchu 300, Taiwan, R.O.C. source-channel decoding (JSCD techniques (Peinado et al., 2003; Reinhold and Valentin, 2004; Fingscheidt and Vary, 2001 have been shown effective for error itigation using source residual redundancy assisted by bit reliability inforation provided by the softoutput channel decoder. However, the usefulness of these techniques ay be restricted because they only exploit the bit-level source correlation on the basis of a eoryless AWGN channel assuption. In this paper, we attept to capitalize ore fully on the a priori knowledge of source and channel and then develop a DSR syste with increased robustness against channel errors. The first step toward realization is to use quantizer indexes rather than single index-bits as the bases for the JSCD, since the dependencies of quantizer indexes are stronger than the correlations of the index-bits. The next knowledge source to be exploited is the channel error characteristics. Transission errors encountered in ost real counication channels exhibit various degrees of statistical dependency that are contingent on the transission ediu and on the particular odulation technique used. A typical exaple occurs in digital obile radio channels, where speech paraeters suffer severe degradation fro error bursts due to the cobined effects of fading and ultipath propagation. A standard technique for robust VQ over a channel with eory is to use interleaving to render the channel eoryless and then design a decoding algorith for the eoryless channel. This approach, however, often introduces large

3 46 Journal of the Chinese Institute of Engineers, Vol. 32, No. 1 (2009 Table 1 Entropies for DSR feature pairs Paraeter (u t C 1, C 2 C 3, C 4 C 5, C 6 C 7, C 8 C 9, C 10 C 11, C 12 C 0, loge Bits/Codeword H(u t H(u t u t decoding delays and does not utilize the channel eory inforation. Further iproveent can be realized through a ore precise characterization of the channel on which the decoder design is based (Kanal and Sastry, For this investigation, we focused on the twostate Markov chain odel proposed by Gilbert (Gilbert, This odel has several practical advantages over the Gaussian channel (Peinado et al., 2003 and binary Markov channels (Wang and Moayeri, First, the Gilbert odel is relatively siple and can characterize a wide range of digital channels, as evidenced by its applicability to perforance analysis of various error control schees (Drukarev and Yiu, Second, as we shall see later, the channel transition probabilities of the Gilbert odel have a recursive forula that can be represented in ters of odel paraeters. II. DSR TRANSMISSION SYSTEM The standard, ETSI ES , describes the speech processing, transission, and quality aspects of a DSR syste. The local front-end consists of a feature extraction algorith and an encoding schee for speech input to be transitted to a reote recognizer. Each speech frae is represented by a 14-diension feature vector containing log-energy loge and 13 Melfrequency cepstral coefficients (MFCCs ranging fro C 0 to C 12. For the cepstral analysis speech signals are sapled at 8 khz and analyzed using a 25 s Haing window with 10 s frae shift. These features are further copressed based on a split vector codebook where the set of 14 features is split into 7 subsets with two features in each. Each feature pair is quantized using its own codebook. MFCCs C 1 to C 10 are quantized with 6 bits each pair, (C 11, C 12 is quantized with 5 bits, and (C 0, loge is quantized with 8 bits. Two quantized fraes are grouped together and protected by a 4-bit cyclic redundancy check creating a 92-bit frae-pair packet. Twelve of these fraepairs are cobined and appended with overhead bits resulting in an 1152-bit ultifrae packet representing 240 s of speech. Multifrae packets are concatenated into a bit-strea for transission via a data channel with an overall data rate of 4800 bits/s. This work is devoted to channel error itigation for DSR over burst error channels. Fig. 1 gives the block diagra of the transission schee for each Input signal ^ v t Feature extraction Paraeter estiation v t P[u t yt 1 ] VQ encoder and Bit apping Index APP coputation Channel encoder Channel Source a priori knowledge Channel inforation Fig. 1 Transission schee for each DSR feature pair DSR feature pair. Suppose at tie t, the input vector v t is quantized to obtain a codevector c t {c (i, i = 0, 1,..., 2 k 1} that, after bit apping, is represented by a k-bit cobination u t = (u t (1, u t (2,..., u t (k. Each bit cobination u t is assigned to a quantizer index i {0,1,..., 2 k 1} and we write for siplicity u t = u i t to denote that u t represents the i-th quantizer index. Due to constraints on coding coplexity and delay, the VQ encoder exhibits considerable redundancy within the encoded index sequence, either in ters of a non-unifor distribution or in ters of correlation. If only the non-unifor distribution is considered and the indexes are assued to be independent of each other, the redundancy is defined as the difference between the index length k and the entropy given by H(u t = Σ P(u t log 2 P(u t. (1 ut If inter-frae correlation of indexes is considered by using a first-order Markov odel with transition probabilities P(u t u t 1, the redundancy is then defined as the index length k and the conditional entropy given by H( u t u t 1 = Σ ut Σ P(u t, u t 1 log 2 P( u t u t 1. u t 1 (2 Table 1 shows the index lengths and entropies for the seven feature pairs of the ETSI DSR frond-end. For each colun in Table 1, the probabilities P(u t and P(u t u t 1 have to be estiated in advance fro a training speech database. Fro it we see that the DSR index sequence is better characterized by a first-order Markov process. For error protection individual index-bits are fed into a binary convolutional encoder consisting of M shift registers. The register shifts u t y t x t

4 C. L. Lee and W. W. Chang: Channel-Optiized Error Mitigation for Distributed Speech Recognition 47 Previous state 00 Stage 1 Stage 2 Next state 00 Previous state 00 Next state (a Bit-level trellis diagra (b Merged trellis diagra 11 Fig. 2 Trellis diagras used for (a the encoder and (b the MAP decoder one bit at a tie and its state is deterined by the M ost recent inputs. After channel encoding, the codebit cobination corresponding to the quantizer index u t is denoted by x t = (x t (1, x t (2,..., x t (n with the code rate R = k/n. One of the principal concerns in transitting VQ data over noisy channels is that channel errors corrupt the bits that convey inforation about quantizer indexes. Assue that a channel s input x t and output y t differ by an error pattern e t, so that the received bit cobination is y t = (y t (1, y t (2,..., y t (n in which y t (l = x t (l e t (l, l = 1, 2,..., n, and denotes the bitwise odulo-2 addition. At the receiver side, the JSCD decoder will find the ost probable transitted quantizer index given the received sequence. The decoding process starts with the foration of an a posteriori probability (APP for each of the possibly transitted indices u t = i, which is followed by choosing the index value ^ i that corresponds to the axiu a posteriori (MAP probability for that quantizer index. Once the MAP estiate of the quantizer index is deterined, its corresponding codevector becoes the decoded output ^ v t = c (^ i. The APP is the probability that a decoded index u t = i can be derived fro the oint probability P(ut, i s t, y 1, T where s t is the channel encoder state at tie t and y 1 T =(y 1, y 2,..., y T is the received sequence fro tie t = 1 through soe tie T. We have chosen the length T = 24 in copliance with the ETSI bit-streaing forat, where each ultifrae essage packages speech features fro 24 fraes. Proceeding in this way, the sybol APP can be obtained by suing the oint probability over all encoder states, as follows: P(u t = i y T P(u 1 = i t, s t, y T 1 Σ P(y T, i = 0, 1,..., 2 k 1. st 1 (3 III. MODIFIED BCJR ALGORITHM Depending upon the choice of the sybol APP calculator, a nuber of different MAP decoder ipleentations can be realized. For the transission schee with channel coding, a soft-output channel decoder can be used to provide both decoded bits and their reliability inforation for further processing to iprove the syste error perforance. The ost well-known soft-output decoding algorith is the BCJR algorith (Bahl et al., 1974 that was devised to iniize the bit error probability. This algorith is a trellis-based decoding algorith for both linear block and convolutional codes. The derivation presented in Bahl et al. led to a forward-backward recursive coputation on the basis of a bit-level code trellis. In a bit-level trellis diagra, there are two branches leaving each state and every branch represents a single index-bit. Proper sectionalization of a bit-level trellis ay result in useful trellis structural properties (Lin and Costello, 2004 and allow us to devise MAP decoding algoriths which exploit bitlevel as well as sybol-level source correlations. To advance with this, we propose a odified BCJR algorith which parses the received code-bit sequence into blocks of length n and coputes the APP for each quantizer index on a sybol-by-sybol basis. Unlike a conventional BCJR algorith that decodes one bit at a tie, our schee proceeds with decoding the quantizer indexes in a frae as nonbinary sybols according to their index length k. By parsing the codebit sequence into n-bit blocks, we are in essence erging k stages of the original bit-level code trellis into one. As an exaple, we illustrate in Fig. 2 two stages of the bit-level trellis diagra of a rate 1/2 convolutional encoder with generator polynoial (5, 7 8. The solid lines and dashed lines correspond to the input bits of 0 and 1, respectively. Fig. 2 also shows the decoding trellis diagra when two stages of the original bit-level trellis are erged together. In general, there are 2 k branches leaving and entering each state in a k-stage erged trellis diagra. Having defined the decoding trellis diagra as such, there will be one sybol APP corresponding to each branch which represents a particular quantizer index u t = i. For convenience, we say that the sectionalized trellis diagra fors a finite-state achine defined by its state transition function S(u i t, s t and output function X(u i t,

5 48 Journal of the Chinese Institute of Engineers, Vol. 32, No. 1 (2009 s t. Viewed fro this perspective, the code-bit cobination x t = X(u i t, s t is associated with the branch fro state s t to state s t + 1 = S(u i t, s t if the corresponding quantizer index at tie t is u t = i. We next odified the BCJR algorith based on sectionalized trellis to exploit the cobined a priori inforation of source and channel. We begin our developent of the odified BCJR algorith by rewriting the oint probability in Eq. (3 as follows: P(u i t, s t, y T 1 = α i t(s t β i t(s t, (4 where α i t(s t = P(u i t, s t, y t 1 and β i t(s t = P(y T t + 1 u i t, s t, y t 1. For the MAP sybol decoding algorith, the forward and backward recursions are to copute the following etrics: in which Σ Σ α i t (s t = P(u i t, s t, u t 1, s t 1, y t, yt 1 1 s t 1 Σ Σ = α t 1 (s t 1 γ i, (y t, s t, s t 1, (5 s t 1 Σ Σ β i t (s t = P(u t +1, s t +1, y t +1, yt t +2 u i t, s t, y t 1 s t +1 Σ Σ = β t +1 (s t +1 γ, i (y t +1, s t +1, s t, (6 s t +1 γ i, (y t, s t, s t 1 = P(u i t, s t, y t u t 1, s t 1, y 1 t 1 = P(s t u t 1, s t 1, y 1 t 1 P(u i t s t, u t 1, s t 1, y 1 t 1. P(y t u i t, s t, u t 1, s t 1, y 1 t 1. (7 Having a proper representation of the branch etric γ i, (y t, s t, s t 1 is the critical step in applying MAP sybol decoding to error itigation and one that conditions all subsequent steps of the ipleentation. As a practical anner, several additional factors ust be considered to take advantage of source correlation and channel eory. First, aking use of the sectionalized structure of a decoding trellis, we write the first ter in Eq. (7 as P( s t u t 1, s t 1, yt 1 1 =P( s t u t 1, s t 1 = 1, s t = S(u t 1, s t 1 0, othertwise. (8 The next knowledge source to be exploited is the residual redundancy reaining in the DSR features. Assuing that the quantizer index is odelled as a firstorder Markov process with transition probabilities P(u t u t 1, the second ter in Eq. (7 is reduced to P(u i t s t, u t 1, s t 1, y 1 t 1 = P(u t = i u t 1 =. (9 In addition to source a priori knowledge, specific knowledge about the channel eory ust be taken into consideration. There are any odels describing the correlation of bit error sequences. If no channel eory inforation is considered, which eans that the channel bit errors are assued to be rando, the third ter in Eq. (7 is reduced to P(y t u i t, s t, u t 1, s t 1, y 1 t 1 = P(y t x t = X(u i t, s t = P(e t = ε l (1 ε n 1, (10 where ε is the channel bit error rate (BER and l is the nuber of ones occurring in the error pattern e t. When intrafrae and interfrae eory of the channel are considered, the third ter in Eq. (7 becoes P(y t u i t, s t, u t 1, s t 1, y 1 t 1 b 1-b G B 1-g g Fig. 3 Gilbert channel odel = P(y t x t = X(u i t, s t, y t 1, x t 1 = X(u t 1, s t 1 = P(e t e t 1. (11 IV. PROBABILITY RECURSIONS FOR GILBERT CHANNEL Designing a robust DSR syste requires that paraeterized probabilistic odels be used to suarize soe of the ost relevant aspects of error statistics. It is apparent fro previous work on channel odelling (Kanal and Sastry, 1978 that we are confronted with contrasting requireents in selecting a good odel. A odel should be representative enough to describe real channel behavior and yet it should not be analytically coplicated. To perit theoretical analysis, we assued that the encoded bits of DSR features were subected to the saple error sequences typical of the Gilbert channel. The Gilbert channel odel consists of a Markov chain having an error-free state G and a bad state B, in which errors occur with the probability (1 h. The state transition probabilities are b and g for the G to B and B to G transitions, respectively. The odel state-transition diagra is shown in Fig. 3. The effective BER produced by the Gilbert channel is ε = (1 hb/(g + b. Notice that in the particular case of a Gilbert odel with paraeter values b = 1, g = 0, h = 1 ε,

6 C. L. Lee and W. W. Chang: Channel-Optiized Error Mitigation for Distributed Speech Recognition 49 the channel odel reduces to a eoryless binary syetric channel with the BER ε. The effectiveness of the MAP sybol decoding depends crucially on how well the error characteristics are incorporated into the calculation of channel transition probabilities P(e t e t 1. Although using channel eory inforation was previously proposed for MAP sybol decoding (Turin, 2001, the ephasis was placed upon channels with no interfrae eory. When only access to the intrafrae eory is available, it was shown that the channel transition probabilities of the Gilbert channel have closed-for expressions that can be represented in ters of odel paraeters {h, b, g}. Under such conditions, we can proceed with the MAP sybol decoding in a anner siilar to the work of (Turin, Extensions of these results to channels with both intrafrae and interfrae eory have been found difficult. Recognizing this, we next develop a general treatent of probability recursions for the Gilbert channel. The ain result is a recursive ipleentation of MAP sybol decoder being closer to the optial for channels with eory. For notational convenience, channel bit error e t (l will be denoted as r, in which the bit tie is related to the frae tie t as = n(t 1 + l, l = 1, 2,..., n. Let q {G, B} denote the Gilbert channel state at bit tie. The eory of the Gilbert channel is due to the Markov structure of the state transitions, which lead to a dependence of the current channel state q on the previous state q 1. To develop a recursive algorith, it is ore convenient to rewrite the channel transition probabilities as P( e t e t 1 nt Π = P(r =1r 1 0 r P(r =0r 0 = n(t r (12 where r 1 0 = (r 0, r 0 + 1,..., r 1 represents the bit error sequence starting fro bit 0 = n(t The following is devoted to a way of recursively coputing P(r = 1 r 1 0 fro P(r 1 = 1 r 2 0. The Gilbert channel has two properties, P(q q 1, r 1 0 = P(q q 1 and P(r q, r 1 0 = P(r q, which facilitate the probability recursions. By successively applying the Bayes rule and the Markovian property of the channel, we have in which P( r =1 r 1 0 = P( r =1 q = B, r 1 0 P( q = B r 1 0 = (1 hp( q = B r 1 0, (13, P( q = B r 1 0 = P( q = B q 1 = G, r 1 0 P( q 1 = G r P( q = B q 1 = B, r 1 0 P( q 1 = B r 1 0 = b P( q 1= G, r 1 r 2 0 P( r 1 r (1 g P( q 1= B, r 1 r 2 0 P( r 1 r 2 0 = b +(1 g b P( q 1= B, r 1 r 2 0 P( r 1 r 2 0 = b +(1 g b P( r 1 q 1 = B P( r 1 r 2 0 P( r 1=1 r 2 0. (14 1 h V. EXPERIMENTAL RESULTS Coputer siulations were conducted to evaluate three MAP-based error itigation schees for DSR over burst error channels. First a bit-level trellis MAP decoding schee BMAP is considered that uses the standard BCJR algorith to decode the index-bits. The decoders SMAP1 and SMAP2 exploit the sybol-level source redundancy by using a odified BCJR algorith based on a sectionalized trellis structure. The SMAP1 is designed for a eoryless binary syetric channel, whereas the SMAP2 exploits the channel eory though the Gilbert channel characterization. The channel transition probabilities to be used for the SMAP1 is P(e t in Eq. (10, and P(e t e t 1 in Eq. (11 for the SMAP2. For purposes of coparison, we also investigated an error itigation schee (Peinado et al., 2003 which applied the concept of softbit speech decoding (SBSD and achieved good recognition perforance for AWGN and burst channels. A preliinary experient was first perfored to evaluate various decoders for reconstruction of the feature pair (C 0, loge encoded with the DSR front-end. A rate R = 1/ 2 convolutional code with eory order M = 6 and the octal generator (46,72 8 is chosen as the channel code. Table 2 presents the signal-to-noise ratio (SNR obtained fro transission of the index-bits over Gilbert channel with BER ranging fro 10 3 to The results of these experients clearly deonstrate the iproved perforance achievable using the SMAP1 and SMAP2 in coparison to those of BMAP and SBSD. Furtherore, the iproveent has a tendency to increase for noisy channels with higher BER. This indicates that the residual redundancy of quantizer indexes is better exploited at the sybol level to achieve ore perforance iproveent. A coparison of

7 50 Journal of the Chinese Institute of Engineers, Vol. 32, No. 1 (2009 Table 2 SNR(dB perforance for various decoders on a Gilbert channel BER BMAP SBSD SMAP1 SMAP Table 3 Estiated Gilbert odel paraeters for GSM TCH/F4.8 data channels CIR(dB g b h the SMAP1 and SMAP2 also revealed the iportance of atching the real error characteristics to the channel odel on which the MAP sybol decoder design is based. The better perforance of SMAP2 can be attributed to its ability to copute the sybol APP taking interfrae and intrafrae eory of the channel into consideration, as opposed to the eoryless channel assuption ade in the SMAP1. We further validate the proposed decoding algoriths for the case where error sequences were generated using a coplete GSM siulation. The siulator is based on the CoCentric GSM library (CoCentric Syste Studio-Referenec Design Kits, 2003 with TCH/ F4.8 data and channel coding, interleaving, odulation, a channel odel, and equalization. The channel odel represents a typical case of a rural area with 6 propagation paths and a user speed of 50 k/h. Further, cochannel interference was siulated at various carrier-to-interference ratios (CIR. In using the SMAP1 and SMAP2 schees, the channel transition probabilities have to be cobined with a priori knowledge of Gilbert odel paraeters which can be estiated once in advance using the gradient iterative ethod (Chouinard et al., For each siulated error sequence, we first easured the error-gap distribution P(0 l 1 by coputing the probability that at least l successive error-free bits will be encountered next on the condition that an error bit has ust occurred. The optial identification of Gilbert odel paraeters was then forulated as the least square approxiation of the easured error-gap distribution by exponential curve fitting. Table 3 gives estiated Gilbert odel paraeters for the GSM TCH/F4.8 data channels operating at CIR = 1, 4, 7, 10 db. The next step in the present investigation concerned the perforance degradation that ay result fro using the SMAP2 schee under channel isatch conditions. In Table 4, CIR d refers to the Table 4 SNR perforance of the SMAP2 over the GSM data channel under channel isatch conditions CIR a = 1 CIR a = 4 CIR a = 7 CIR a = 10 CIR d = CIR d = CIR d = CIR d = Digit Accuracy (% SMAP2 SMAP1 SBSD BMAP BER (db Fig. 4 Recognition perforances for DSR transission over a Gilbert channel CIR value assued in the design process, and CIR a refers to the true CIR used for the evaluation. The best results are in the ain diagonal of the table, where channel-atched Gilbert odel paraeters are used for the channel transition probability coputation of Eq. (12. The perforance decreases in each colun below the ain diagonal when the CIR d is increased. The investigation further showed that the SMAP2 is not very sensitive to a channel isatch between the design and evaluation assuptions. We next considered the speaker-independent recognition of Mandarin digit strings as the task without restricting the string length. A Mandarin digit string database recorded by 50 ale and 50 feale speakers was used in our experients. Each speaker pronounced 10 utterances and 1-9 digits in each utterance. The speech of 90 speakers (45 ale and 45 feale was used as the training data, and the other 10 as test data. The total nubers of digits included in the training and test data were 6796 and 642, respectively. The reference recognizer is based on the HTK software package. A 38-diension feature vector used in the recognizer consisted of 12 MFCCs, delta-mfcc, delta-delta-mfcc, delta-energy and delta-delta-energy. The digits were odelled as whole word Hidden Markov Models (HMMs with 8 states per word and 64 ixtures for each state. In addition, a 3-state HMM was used to odel pauses before and after the utterance and a one-state HMM was used to odel pauses between digits. The DSR results obtained by various error itigation algoriths for the Gilbert channel are shown in Fig. 4. It

8 C. L. Lee and W. W. Chang: Channel-Optiized Error Mitigation for Distributed Speech Recognition 51 can be seen that eploying the source a priori inforation, sectionalized trellis MAP decoding, and channel eory constantly iproves the recognition accuracy. The SMAP2 schee perfors the best in all cases, showing the iportance of cobining the a priori knowledge of source and channel by eans of a sectionalized code trellis and Gilbert channel characterization. VI. CONCLUSIONS A JSCD schee which exploits the cobined source and channel statistics as an a priori inforation is proposed and applied to channel error itigation in DSR applications. We first investigate the residual redundancies existing in the DSR features and find ways to exploit these redundancies in the MAP sybol decoding process. Also proposed is a odified BCJR algorith based on sectionalized code trellises which uses Gilbert channel characterization for better decoding in addition to source a priori knowledge. Experients on Mandarin digit string recognition indicate that the proposed decoder achieved significant iproveents in recognition accuracy for DSR over burst error channels. ACKNOWLEDGEMENT This study was ointly supported by MediaTek Inc. and the National Science Council, Republic of China, under contract NSC E b B c t e t g G k s t u t v t x t y t ε NOMENCLATURE the probability for the state transition G to B the bad state of the Gilbert channel the codeword of the VQ at tie t the bit-error pattern at tie t the probability for the state transition B to G the good state of the Gilbert channel the length of u t the state of the channel encoder the binary index representing c t the source vector the code-bit cobination after channel encoding the received bit cobination at the receiver bit error rate of the noisy channel REFERENCES Bahl, L. R., Cocke, J., Jelinek, F., and Raviv, J., 1974, Optial Decoding of Linear Codes for Miniizing Sybol Error Rate, IEEE Transactions on Inforation Theory, Vol. IT-20, No. 2, pp Bernard, A., and Alwan, A., 2002, Low-bitrate Distributed Speech Recognition for Packet-based and Wireless Counication, IEEE Transactions on Speech and Audio Processing, Vol. 10, No. 8, pp Boulis, C., Ostendorf, M., Riskin, E., and Otterson, S., 2002, Graceful Degradation of Speech Recognition Perforance over Packet-erasure Networks, IEEE Transactions on Speech and Audio Processing, Vol. 10, No. 8, pp Chouinard, J. Y., Lecours M., and Delisle, G. Y., 1988, Estiation of Gilbert s and Fritchan s Models Paraeters Using the Gradient Method for Digital Mobile Radio Channels, IEEE Transactions on Vehicular Technology, Vol. 37, No. 3, pp CoCentric Syste Studio-Referenec Design Kits, 2003, Synopsys, Inc., Mountain View, CA, USA. Drukarev, A. I., and Yiu, K. P., 1986, Perforance of Error-correcting Codes on Channels with Meory, IEEE Transactions on Counications, Vol. COM-34, No. 6, pp ETSI ES v Digital Speech Recognition; Extended Advanced Front-end Feature Extraction Algorith; Copression Algoriths; Back-end Speech Reconstruction Algorith. Noveber Fingscheidt, T., and Vary, P., 2001, Softbit Speech Decoding: a New Approach to Error Concealent, IEEE Transaction on Speech and Audio Processing, Vol. 9, No. 3, pp Gilbert, E. N., 1960, Capacity of a Burst-noise Channel, The Bell Syste Technical Journal, Vol. 39, No. 1, pp Kanal, L. N., and Sastry, A. R. K., 1978, Models for Channels with Meory and their Applications to Error Control, Proceedings of IEEE, Vol. 66, No. 7, pp Lin, S., and Costello, D. J., 2004, Error Control Coding, Prentice Hall, NJ, USA. Peinado, A. M., Sanchez, V., Perez-Cordoba, J. L., and Torre, A., 2003, HMM-based Channel Error Mitigation and its Application to Distributed Speech Recognition, Speech Counication, Vol. 41, No. 2, pp Reinhold, H. U., and Valentin, I., 2004, Soft Features for Iproved Distributed Speech Recognition over Wireless Networks, Proceedings of 8 th International Conference on Spoken Language Processing, Jeu Island, Korea, pp Turin, W., 2001, MAP Sybol Decoding in Channels with Error Bursts, IEEE Transactions on Inforation Theory, Vol. 47, No. 5, pp Wang, H. S., and Moayeri, N., 1993, Modeling, Capacity, and Joint Source/Channel Coding for Rayleigh Fading Channels, Proceedings of IEEE Vehicular Technology Conference, Secaucus, NJ, USA, pp Manuscript Received: Oct. 23, 2007 Revision Received: June 30, 2008 and Accepted: July 30, 2008