N. Farvardin, "A study of vector quantization for noisy channels," IEEE Trans. Inform. Theory, vol. IT-36, pp. 799--809, July 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....bene cial to perform source compression and error protection jointly. Several methods have been proposed for joint source channel coding, which may be categorized as unequal error protection [2] 6] channel optimized scalar and vector quantization (COVQ) 7] 11] index assignment optimization [12, 13], and exploitation of the residual redundancy of the source coder via maximum a posteriori (MAP) decoding [14, 15] In this paper we present a COSQ based image coder for transmission of images over noisy channels with memory. Memory is an important property of many real life chan This work ....

N. Farvardin, \A study of vector quantization for noisy channels," IEEE Trans. Inform. Theory, vol. 36, pp. 799-809, July 1990.

....the above result assumes the availability of unlimited coding decoding delay and complexity. It is known that when there are delay and complexity constraints, it is more advantageous to employ joint source channel coding where the source and channel codes are designed in cohesion (e.g. 5] [15] [17] 20, 22] 30, 31, 37] There are three main approaches to joint source channel coding: the unequal error protection approach, the zero redundancy channel coding approach, and the combined source channel coding approach. In the unequal error protection approach, the output of the source ....

.... b( where b : C J N and J N = f1; Ng, the channel distortion can be formulated to be P(c i )P(b(c j )jb(c i ) kc i c j k where P(c i ) is the a priori probability of the codevector c i ; P(c i ) P(X 2 S i ) In view of this analysis and as suggested by Farvardin in [15], we can focus on minimizing the channel distortion c by appropriately choosing the index assignment function b( To choose an appropriate index assignment function b( we use a technique called simulated annealing. Simulated annealing belongs to a class of randomized algorithms, 34] ....

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N. Farvardin , \A study of vector quantization for noisy channels," IEEE Trans. Inform. Theory, Vol. 36,N0. 4, pp. 799-808, Jul. 1990. 119

.... [51] resulting in the so called channel optimized scalar quantizer (COSQ) Kumazawa et al. extended the COSQ to the high dimensional vector space or channel optimized vector quantizer (COVQ) 50] The performance and complexity of the COVQ system is studied by Farvardin and Vaishampayan [29] In [28], Farvardin also introduced the simulated annealing technique to the initial codebook design for the COVQ system. In [2, 62] Alajaji and Phamdo successfully implemented a COVQ system for AWGN and Rayleigh fading channels in conjunction with a q bit soft decision scalar quantizer at the channel ....

.... quantization originated by Linde, Buzo and Gray [52] is one of the most notable techniques in xed length source coding, and has been successfully applied to speech [55] and image coding [37] The channel optimized vector quantization (COVQ) studied by Kumazawa et al. 50] and Farvardin et al. [29, 28] incorporates the channel statistics in the vector quantization design, thus achieves high end to end performance over noisy channels. In this chapter, we design and implement a robust soft decision COVQ scheme for Turbo coded AWGN channels and Rayleigh fading channels with known side ....

N. Farvardin, \A study of vector quantization for noisy channels," IEEE Trans. Inform. Theory, vol. 36, pp. 799-809, Jul. 1990. 142

....Lloyd Max resulting in the so called channel optimized scalar quantizer (COSQ) 7] The COSQ is designed to operate over a binary symmetric channel with a particular error probability. The channel optimized quantizer algorithm was further extended by the same researchers to encode vector sources [8, 9], and is known as the channel optimized vector quantizer (COVQ) One of the first attempts to design a quantizer with soft reconstruction decoding was made by Vaishampayan and Farvardin by extending the COVQ design algorithm to include the modulation signal set [10] Phamdo and Alajaji also ....

.... of the code word probabilities multiplied with their corresponding reconstruction levels, i.e. x = R j P (u = u j jv) 3) The hard decision rule is essentially a threshold operation on the received vector v, and systems with this reconstruction rule are well established in the literature [7, 3, 4, 5, 8, 9]. The soft decision rule is a relatively new idea, where some earlier relevant results are described in [10, 11, 13, 16] 3 Quantizer and Reconstructor Design The quantizer reconstructor pair is designed using an iterative algorithm similar to [7, 3, 4] Consider a sample x which is transmitted ....

N. Farvardin, "A study of vector quantization for noisy channels," IEEE Transactions On Information Theory, vol. 36, no. 4, July 1990, pp. 799--809.

.... for a Gaussian source over a memoryless binary symmetric channel [8] More recently, the combined source channel coding in vector quantization has been studied by Faryardin, who gives an algorithm based on simulated annealing for assigning binary code words to the vector quantizer code vectors [9]. The present article is organized as follows: Section 2 gives an overview of the system under consideration. Section 3 describes the combined source channel cod ing algorithm. The bit allocation method is explained in Section 4. Section 5 presents some numerical results. Pinally, Section 6 is ....

N.Farvardin, "A Study of Vector Quantization for Noisy Channels", IEEE Transactions on In]ormation Theory, vol. IT-36, No. 4, pp. 799-809, July 1990.

....gespeichert werden muss. F ur COVQ nimmt dagegen entweder die Leistungsf ahigkeit bei nicht vorhandener Anpassung an den Kanalzustand stark ab, oder eine groe Anzahl von Codeb uchern muss im Encoder und im Decoder verf ugbar sein. 1 Introduction Channel optimized vector quantization (COVQ) [4, 5] achieves strong quality improvements over conventional vector quantization (VQ) if the transmission channel is noisy. Variations of COVQ in which simulated and deterministic annealing are used have been proposed, e.g. in [6, 10] the algorithms work superior to normal COVQ due to improvements ....

....dimension N y j Figure 1: Transmission system with a channel optimized vector quantizer. The idea of channel optimized vector quantization (COVQ) is to exploit the knowledge about the channel in the design of the codebook and in the encoding algorithm. The COVQ codebook design algorithm [4] can be regarded as an extension of the classical LBG algorithm [9] for noiseless channels. In the following, we use the performance of COVQ [4] as a reference for the approximations that are investigated in this paper. Note that the COVQ distance measure, which is used in both the codebook design ....

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N. Farvardin, "A study of vector quantization for noisy channels," IEEE Transactions on Information Theory, vol. 36, no. 4, pp. 799--809, July 1990.

....(MDSQ) where the indexes have a direct relationship to the amplitudes of the quantizer reproduction levels. Since the splitting method was used for the initialization of the LBG codebook training, most of the neighbouring indexes of the VQ codebook lie also relatively close in the signal space [7]. Therefore, the ML assignment is useful for the MD BSA as an initialization because it is already closer to a good assignment than some random initialization. The descriptions were transmitted over mutually independent erasure channels with the erasure probabilities p 1 , p 2 (0. 1) For ....

N. Farvardin, "A study of vector quantization for noisy channels," IEEE Transactions on Information Theory, vol. 36, no. 4, pp. 799--809, July 1990.

....The quantity Q jji is the conditional probability that the index of C j is received given that the index of C i was transmitted. By Equation 1, Q jji (D i W i jjC i 0 C j jj ) Q jji Q jji W i jjC i 0 C j jj (3) Equation 3 is the same as Equation 7 in Farvardin [4]. Because Q jji = 1, the first term of Equation 3 is exactly the average distortion when the codebook is used with a noiseless channel. We define this as D = For i k , which we define to differ from index i only in the k th bit, Q i k ji = Q ; 4) where Q = Q log 2 N j=1 (1 0 ffl j ....

....43 (correct 56 and introduce 13 ) of the errors in the second MSB, correct 27 (correct 46 and introduce 19 ) of the errors in the third MSB, and do not correct any errors in the fourth MSB. Having different error rates on each bit of the codeword index is related to work done by Farvardin [4] where he obtained unequal error probabilities through the use of channel coding and modified his VQ design accordingly. Simulations of progressive image transmission with a BER of 10 without and with MAP detection are shown in Fig. 12 and Fig. 13. We have selected a BER of 10 to better ....

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N. Farvardin. A study of vector quantization for noisy channels. IEEE Transactions on Information Theory, 36(4):799--809, July 1990.

....] 9) 3 The repetition matrix The repetition matrix R introduced in the previous section should be optimized for delay estimation performance. Since this optimization is a huge combinatorial optimization problem we take a simplifying approach based on the simulated annealing algorithm (see e.g. [4, 5]) However, for the simulated annealing algorithm to work well it is important to find a good criterion (energy function) In our case we derived a criterion using the Cramer Rao Bound (CRB) for the problem of jointly estimating the delay # and complex path gain # but with known encoded bits c. ....

N. Farvardin. A study of vector quantization for noisy channels. IEEE Transactions on Information Theory, 36(4):799--809, July 1990.

....transmission of information by separately designing the source and channel codes. It is however known that when there are delay and complexity constraints, it is more advantageous to employ joint source channel coding where the source and channel codes are designed in cohesion (e.g. 1] 2] [5] [7] 10] 15] 17] There are three main approaches to joint source channel coding: the unequal error protection approach, the zero redundancy channel coding approach, and the combined This work was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of ....

N. Farvardin, \A study of vector quantization for noisy channels," IEEE Trans. Inform. Theory, Vol. 36, pp. 799-808, Jul. 1990.

....with each codeword. Intuitively, the proper index assignment is the index assignment for which similar codewords have similar binary descriptions. In this case, the increase in distortion caused by likely codeword errors is kept small. Papers treating the index assignment problem include [15] [17] An alternate approach to the same problem is to redesign the source codebook to take into account the index crossover probabilities imposed by a noisy channel. Examples of work taking this approach include the channel optimized vector quantizer (COVQ) and its scalar variation [2] 3] ....

N. Farvardin, "A study of vector quantization for noisy channels," IEEE Trans. Inform. Theory, vol. 36, pp. 799--809, July 1990.

.... this distortion measure was proved in 1981 [135] and a Lloyd style design algorithm for such encoders provided in 1987 [19] A Lloyd algorithm for vector quantizers using the modified distortion measure was introduced in 1984 by Kumazawa, Kasahara, and Namekawa [303] and further studied in [157] [152], 153] The method has also been applied to tree 50 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 44, NO. 6, OCTOBER 1998 structured VQ [412] It can be combined with a maximum likelihood detector to further improve performance and permit progressive transmission over a noisy channel [411] ....

....INFORMATION THEORY, VOL. 44, NO. 6, OCTOBER 1998 structured VQ [412] It can be combined with a maximum likelihood detector to further improve performance and permit progressive transmission over a noisy channel [411] 523] Simulated annealing has also been used to design such quantizers [140] [152], 354] Another approach to joint source and channel coding based on a quantizer structure and not explicitly involving typical channel coding techniques is to design a scalar or vector quantizer for the source without regard to the channel, but then code the resulting indices in a way that ....

N. Farvardin, "A study of vector quantization for noisy channels, " IEEE Trans. Inform. Theory, vol. 36, pp. 799--809, July 1990.

....by the most frequent decoder errors is minimized. The optimization of IA is normally performed for some representative (typical or average) channel condition. However, the resulting IA is known to achieve robust performance over a large range of channel conditions. Channel optimized quantization [4], 19] assumes precise knowledge of the channel characteristics. This knowledge is used to modify the VQ codebook and the encoding rule so as to achieve optimal performance under the prescribed channel conditions. This class of methods is more 0090 6778 99 10.00 1999 IEEE 150 IEEE TRANSACTIONS ....

....be desirable in practice. 1 This paper is organized as follows: In Section II we briefly review the basic idea of TEA in the context of a VQ indexed by the natural binary code (NBC) Natural binary code is a codebook indexing obtained from VQ design using the splitting initialization, see, e.g. [4]. NBC is a convenient indexing for VQ codewords and its combination with TEA provides substantial improvements over standard pseudo Gray index assignment. However, NBC is not the optimal choice. In Section III we pose the problem of joint optimization of TEA and index assignment. We develop a ....

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N. Farvardin, "A study of vector quantization for noisy channels," IEEE Trans. Inform. Theory, vol. 36, pp. 799--809, July 1990.

....one bit error in a single codevector transmission, the distortion due to channel errors can be written as where, is the bit error rate for bit . The natural binary code (NBC) is a form of index assignment that is obtained when the splitting initialization is employed to design the VQ (see, e.g. [6]) An important consequence of employing NBC for VQ indexing is that it produces a large variation in bit sensitivities. We exploit this feature by providing optimal unequal error protection to the various bits. This is achieved as follows. Let denote the transmission energy allocated for binary ....

N. Farvardin, "A study of vector quantization for noisy channels," IEEE Trans. Inform. Theory, vol. IT-36, pp. 799--809, July 1990.

....The 2 b and the b factors in the denominator eliminate respectively the symmetric cases and the bit permutation cases. This results 8:3 Theta 10 499 distinct possible combinations for b = 8 bits. Evidently, the IA is a non polynomial (NP) complete task [20] Farvardin has observed [8] that when the splitting 4 technique [25] is used for VQ training, the resulting codebook has a natural ordering that can somehow protect the signal in the presence of channel errors. This is due to the splitting mechanism which makes sister codevectors behave similarly. However, this is not ....

....next section. 7 x IA Decoder Encoder BSC y q q p( p (i) i e e p i IA 1 1 1 (i) p( Figure 2: Block diagram of the VQ based coding system used over a noisy channel. 4. 1 Simulated Annealing Since IA is an NP complete problem, Farvardin used simulated annealing (SA) to solve it [8]. SA is a Monte Carlo algorithm which has been widely used to solve combinatorial problems [18] It imitates the physical process of annealing which finds a lower energetic equilibrium for the crystallization of steel. An appropriate temperature variable, T , is to be defined. This variable is ....

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N. Farvardin, "A Study of Vector Quantization for Noisy Channels", IEEE Transactions on Information Theory 36 (1990), no. 4, 799--809.

....is selected by the encoder. This observation allows direct extension of the known VQ design algorithms to this case. There is a long history of noisy channel quantizer design. In the 1960 s, a basic method was proposed for scalar quantizers [58] and was extended in many papers since [3] 24] [28], 30] 57] 109] These papers basically describe GLA type methods which alternate between enforcing the encoder and centroid (decoder) optimality conditions. One can similarly extend the DA approach to the noisy channel case [14] 72] We can write the expected overall source channel ....

N. Farvardin, "A study of vector quantization for noisy channels, " IEEE Trans. Inform. Theory, vol. 36, pp. 799--809, July 1990.

....used, i.e. assignments of quantizer codevectors to channel codewords. Another approach to source coding in the presence of channel noise has been to use, on a noisy channel, a source coder designed for a noiseless channel, but with an optimized index assignment and with no explicit channel coder [8], 20] 24] Other nonredundant methods exploiting specific quantizer structures can be found in [25] 27] In [28] a random coding argument is used to give analytic bounds on the performance of an optimal index assignment. One appealing feature of index assignments is that they require no ....

N. Farvardin, "A study of vector quantization for noisy channels," IEEE Trans. Inform. Theory, vol. 36, pp. 799--809, July 1990.

....and the bit permutation cases. For instance, for b = 8 bits, this results in 8:3 Theta 10 499 distinct possible combinations. Obviously, the index assignment is a non polynomial (NP) complete task [5] Several methods for reordering the indices have been proposed in the literature. Farvardin [2] suggests simulated annealing (SA) while Zeger and Gersho [11] propose binary switching algorithm (BSA) Both methods consist of pairwise swaps of the codewords to improve a given index assignment. A robust vector quantizer can be obtained also with competitive learning; as this method can ....

....sensible to this input vector. So, during the learning, a topological structure is created which later allows to obtain a more robust quantizer. 2. 2 Splitting The splitting technique [7] is shown to create a natural ordering that can somehow protect the signal in the presence of channel errors [2]. This is due to the fact that in the splitting mechanism, sister codevectors behave more or less similarly. We observed that the proposed system performs better if we use splitting in its training period. Of course, this natural order is not completely perfect, if one uses a classical algorithm ....

N. Farvardin, "A study of vector quantization for noisy channels", IEEE Transactions on Information

....much recent attention [1 10] The existing methods for VQ over noisy channels can be divided, roughly, into two main groups. In the rst, referred here to as robust VQ (RVQ) a VQ trained for a noiseless channel is made robust towards channel errors by means of an index assignment (IA) algorithm [4, 6, 7, 11, 12]. In the second, referred to as channel optimized VQ (COVQ) the VQ is designed assuming a known channel, taking the resulting channel distortion into consideration in the design [1 3,5,7,8] Ideally, the runtime channel parameters should then agree exactly with the ones assumed during training. ....

.... noiseless channel is made robust towards channel errors by means of an index assignment (IA) algorithm [4, 6, 7, 11, 12] In the second, referred to as channel optimized VQ (COVQ) the VQ is designed assuming a known channel, taking the resulting channel distortion into consideration in the design [1 3,5,7,8]. Ideally, the runtime channel parameters should then agree exactly with the ones assumed during training. In this paper we also wish to consider a third class of methods, here referred to as channel constrained VQ (CCVQ) where the VQ is trained for minimum quantization distortion under a ....

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N. Farvardin, \A study of vector quantization for noisy channels," IEEE Transactions on Information Theory, vol. 36, no. 4, pp. 799-809, July 1990. 16

....by channel noise. In [10] the authors focus on worst case performance, the performance criterion being the minimax distortion. The case of unequal probabilities of the codevectors has been considered in conjunction with: a fast greedy algorithm in [12] with simulated annealing techniques in [4, 5], and with genetic annealing algorithms in [9] Here we also use the reformultaion of the IA problem as a quadratic assignment problem, and use the ant system techniques developed for solving QAP to obtain an ecient solution for IA. Ant systems are heuristically motivated methods for nding ....

N. Farvardin. A study of vector quantization for noisy channels. IEEE Transactions on Information Theory, 36:799-809, July 1990.

....probability, and can be used as such for further processing. We also show some possible applications in joint sourcechannel coding schemes. 1 INTRODUCTION The eld of joint source channel coding (JSCC) has been studied in many di erent ways up to now and has lead to numerous di erent techniques [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. One of the problems of the joint study of source and channel codes is to obtain a coherent quality measure for these two coders. Many systems rely on the knowledge of a bit or symbol error probability of the channel but fail to take into account the presence of an error correcting code. We ....

Nariman Farvardin. A study of vector quantization for noisy channels. IEEE Transactions on Information Theory, 36(4):799-809, July 1990.

.... this distortion measure was proved in 1981 [135] and a Lloyd style design algorithm for such encoders provided in 1987 [19] A Lloyd algorithm for vector quantizers using the modified distortion measure was introduced in 1984 by Kumazawa, Kasahara, and Namekawa [303] and further studied in [157] [152], 153] The method has also been applied to tree 50 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 44, NO. 6, OCTOBER 1998 structured VQ [412] It can be combined with a maximum likelihood detector to further improve performance and permit progressive transmission over a noisy channel [411] ....

....INFORMATION THEORY, VOL. 44, NO. 6, OCTOBER 1998 structured VQ [412] It can be combined with a maximum likelihood detector to further improve performance and permit progressive transmission over a noisy channel [411] 523] Simulated annealing has also been used to design such quantizers [140] [152], 354] Another approach to joint source and channel coding based on a quantizer structure and not explicitly involving typical channel coding techniques is to design a scalar or vector quantizer for the source without regard to the channel, but then code the resulting indices in a way that ....

N. Farvardin, "A study of vector quantization for noisy channels, " IEEE Trans. Inform. Theory, vol. 36, pp. 799--809, July 1990.

....unequal error protection (UEP) schemes such as Rate Compatible Punctured Convolutional (RCPC) codes [5, 1, 2, 7, 6] With the exception of [1] which deals with speech, the remaining papers mentioned above explicitly require the source coder to adapt to the channel condition. As an example, in [8] a whole new codebook might have to be designed and used in order to optimally match each new channel condition. With the recent introduction of highly scalable video compression schemes such as [3] it is possible to generate one compressed bit stream, such that different subsets of it ....

N. Farvardin, "A Study of Vector Quantization for Noisy Channels", IEEE Transactions on Information Theory, Vol. 36, Nol. 4, July 1990, pp. 799 - 809.

....bits within a bitstream often varies, one can protect different source bits using unequal error protection (UEP) schemes such as Rate Compatible Punctured Convolutional (RCPC) codes [5] to further enhance performance. Indeed, several researchers have applied this idea to speech [1, 7] and image [6, 2, 8] transmission over wireless links. With the exception of [1] which deals with speech, the remaining papers mentioned above explicitly require the source coder to adapt to the channel condition. As an example, in [8] a whole new codebook might have to be designed and used in order to optimally ....

....Indeed, several researchers have applied this idea to speech [1, 7] and image [6, 2, 8] transmission over wireless links. With the exception of [1] which deals with speech, the remaining papers mentioned above explicitly require the source coder to adapt to the channel condition. As an example, in [8] a whole new codebook might have to be designed and used in order to optimally accommodate each new channel 2 condition. With highly scalable video compression schemes such as [3] it is possible to generate one compressed bitstream such that different subsets of the stream correspond to the ....

N. Farvardin, "A Study of Vector Quantization for Noisy Channels", IEEE Transactions on Information Theory, Vol. 36, Nol. 4, July 1990, pp. 799 - 809. 47

....of a larger ordered quantizer. While scalar quantizers have a natural ordering, vector quantizers as used for color quantization do not. Imposing an ordering, or organization, on a vector quantizer requires careful consideration. Binary index assignment for vector quantizers has been considered [19, 20, 21, 22] for joint source channel coding, progressive transmission, and in lossless compression of VQ indices. We adapt some of these binary index assignment techniques to order our color palettes. We use two observations of the scalar quantizer example of Figure 3 to motivate our ordering of color ....

N. Farvardin, "A study of vector quantization for noisy channels," IEEE Transactions on Information Theory, vol. 36, no. 4, pp. 799--809, July 1990.

....a joint source channel coder, complexity considerations have led numerous researchers to develop joint source channel coding techniques. To date, a majority of this effort has been for fixed rate codes because they do not suffer from the synchronization problems that occur with variable rate codes [9, 10, 11]. Notable exceptions that have considered joint source channel coding schemes for variable rate codes include work on reversible variable length codes that can be decoded in both directions [12] However, these codes can still have problems with synchronization. 3 SPIHT yields high compression ....

N. Farvardin, "A study of vector quantization for noisy channels," IEEE Transactions on Information Theory, vol. 36, pp. 799--809, July 1990.

.... separation theorem [19] states that for a noisy channel, the source and channel coders can be independently designed and cascaded with the same results as given by a joint source channel coder, complexity considerations have led numerous researchers develop joint source channel coding techniques [7, 25]. To date, a majority of this effort has been for fixed rate codes because they do not suffer from the synchronization problems that occur with variable rate codes. Notable exceptions that have considered joint source channel coding schemes for variable rate codes include work on reversible ....

N. Farvardin. A study of vector quantization for noisy channels. IEEE Transactions on Information Theory, 36(4):799--809, July 1990.

....the index of C i was transmitted. By Equation 1, D av = 1 W N01 X i=0 N01 X j=0 Q jji (D i W i jjC i 0 C j jj 2 ) and D av = 1 W N01 X i=0 D i N01 X j=0 Q jji 1 W N01 X i=0 N01 X j=0 Q jji W i jjC i 0 C j jj 2 (3) Equation 3 is the same as Equation 7 in Farvardin [4]. Because P N01 j=0 Q jji = 1, the first term of Equation 3 is exactly the average distortion when the codebook is used with a noiseless channel. We define this as D = P N01 i=0 D i W . For i k , which we define to differ from index i only in the k th bit, Q i k ji = Q ffl k 1 0 ffl k ; ....

....43 (correct 56 and introduce 13 ) of the errors in the second MSB, correct 27 (correct 46 and introduce 19 ) of the errors in the third MSB, and do not correct any errors in the fourth MSB. Having different error rates on each bit of the codeword index is related to work done by Farvardin [4] where he obtained unequal error probabilities through the use of channel coding and modified his VQ design accordingly. Simulations of progressive image transmission with a BER of 10 without and with MAP detection are shown in Fig. 12 and Fig. 13. We have selected a BER of 10 to better ....

[Article contains additional citation context not shown here]

N. Farvardin. A study of vector quantization for noisy channels. IEEE Transactions on Information Theory, 36(4):799--809, July 1990.

....the bit rate for speech parameters for the noisy channel scenario has not been extensively studied elsewhere. Various authors have attempted to design joint source channel coders for vector quantisation. The most notable work in the area has been done by Ayanoglu and Gray [38] and Farvardin [39] [40]. Each of the joint source channel coders perform well under the conditions they were designed for, that is, at a particular channel error rate. Secker [41] applied Ayanoglu s design algorithm to the encoding of LSP parameters. Although for a given bit rate significant performance improvement was ....

....and measures must be taken to increase the robustness in noisy channels. By taking the approach that the vector quantiser be designed in such a way as to cause minimum distortion at reconstruction time should the transmitted codebook index be corrupted, a degree of robustness can be obtained [39] [40] [42] A nice property of vector quantisation is that a stable synthesis filter configuration is always chosen albeit the incorrect one if one or bits were in error in the index. The work in this Chapter concentrated on designing a vector quantiser that required only moderate computational effort ....

[Article contains additional citation context not shown here]

N. Farvardin, "A Study of Vector Quantization for Noisy Channels", IEEE Trans. Inform. Theory, vol. IT-36, pp. 799--809, July 1990.

.... separation theorem [8] states that for a noisy channel, the source and channel coders can be independently designed and cascaded with the same results as given by a joint source channel coder, complexity considerations have led numerous researchers develop joint source channel coding techniques [9, 10]. To date, a majority of this effort has been for fixed rate codes because they do not suffer from the synchronization problems that occur with variable rate codes. Notable exceptions that have considered joint source channel coding schemes for variable rate codes include work on reversible ....

N. Farvardin, "A study of vector quantization for noisy channels," IEEE Transactions on Information Theory, vol. 36, pp. 799--809, July 1990.

....s;i ; R c;i ) 2) R s;i and R c;i denote the source and channel coding rates for the i th subband respectively. Under the conditions that the source codewords satisfy the centroid condition and that the channel errors are independent of the source codewords, the distortion may be decomposed as [2, 6] D i (R s;i ; R c;i ) D s;i (R s;i ) D c;i (R c;i ) 3) where D s;i (R s;i ) and D c;i (R c;i ) are distortions in the i th subband due to the source coder and channel, respectively. Therefore, the total distortion suffered by the source under these assumptions is D = M X i=1 D s;i (R ....

N.Farvardin, "A study of Vector Quantization for Noisy Channels," IEEE Trans. on Info. Theory, Vol.36, pp.799-809, July 1990.

....using variable length codes. Variable length codes allow the propagation of errors because errors in a code word can cause loss of synchronization. A simple way to prevent this, possibly at a cost of some coding efficiency is to use fixed length code words. This is done for vector quantization in [5] and for coding sparse data in [3] It is also possible to rearrange the variable length codes so that the code words start at known positions in the bitstream as done in [16] Unequal Error Protection In video coding, some information is more important than others. For example, loss of ....

N. Farvardin. A study of vector quantization for noisy channels. IEEE Trans. Inform. Theory, 36:799--809, 1990.

....memory methods. 3 3.2. COVQ Index assignment does not take into account any knowledge about the channel characteristics. If some knowledge about the channel can be incorporated in the design, performance can be significantly improved. This is usually referred to as channel optimized VQ (COVQ) [13]. The basic idea is to incorporate a distortion measure in the encoder that take the channel characteristics into consideration. As for the index assignment design a simultaneously optimized COVQ requires that all combinations of the codebooks are known already in the design procedure for the ....

N. Farvardin, "A Study of Vector Quantization for Noisy Channels", IEEE Transactions on Information Theory, vol. 36, no. 4, pp. 799-809, 1990.

....optimized for noisy channels. They also provide theoretical predictions for performance and rate distortion theoretic bounds based on an image model. There has been a large body of work on robust vector quantization for transmission over noisy channels. These include the work on index assignment [4] and channeloptimized VQ (COVQ) 5, 6] Some approaches have used bit sensitivity calculations to design UEP schemes using variable rate channel codes. Ruf and Modestino [7] use bit sensitivity analysis to optimally allocate source and channel coding rates for image transmission over noisy ....

....farther away in Euclidean distance. Interleaving helps in this situation because codeword indices that are received erroneously are only a small Hamming distance away from the correct indices. Interleaving would be even more advantageous if optimal index assignment strategies (along the lines of [4]) are used. Furthermore, interleaving aids in the analytical computation of the channel induced distortion by making the equivalent channel (the channel as seen by the source encoder and decoder) memoryless. For this system, we derive operational rate distortion curves for each subband which ....

[Article contains additional citation context not shown here]

N. Farvardin, "A study of vector quantization for noisy channels," IEEE Transactions on Information Theory, vol. 36, no. 4, pp. 799--809, July 1990.

....rule (ME) 23] 16] can be derived within the framework of robust encoding under di#erent sources of noise and bandwidth variations or limitations. It has previously been noticed that source channel coding may lead to a topological ordering of prototypes very similar to the SOFM [24] 14] [25], 13] The major contribution of this work is to demonstrate how generalized versions of the NG algorithm and ME learning fit into this framework. For several reasons, it is important to understand how di#erent soft competition schemes are related to the empirical risk minimization framework ....

....of receiving index # after sending # through the channel. The objective functions H vq generalizes to H svq (c, Y; X ) 1 n n # i=1 m # #=1 s # c i D(x i , y # ) 7) It has been noticed that source channel coding may lead to a topological ordering of prototypes [24] [25], 14] 13] If s # # is high, it is advantageous to place y# and y # close to each other in order to limit the detrimental e#ect of a reconstruction from corrupted indices. This is directly expressed by the stationary equations c i = arg min # D S i# , n # i=1 s # c i #D(x i , y # ) #y ....

M. Farvardin, "A study of vector quantization for noisy channels, " IEEE Trans Information Theory, vol. 36, pp. 799--809, 1990.

....1. INTRODUCTION Vector quantization (VQ) can be used for obtaining high compression ratios in speech coders, and is particularly suitable for quantization of LPC sets. Regretfully, a VQ is very sensitive towards transmission errors if the index assignment (IA) is not designed properly. In [2] it is shown how a robust IA for a binary symetric channel (BSC) can be obtained by using simulated annealing, and how a VQ can be optimized for a channel with a particular bit error rate (BER) giving a channel optimized VQ (COVQ) Obtaining a robust IA is important also for COVQ design. Physical ....

N. Farvardin, "A study of vector quantization for noisy channels," IEEE Trans. Infor. Th, vol. 36, pp. 799--809, July 1990.

....: Mg, then the problem is a M ary sequential detection problem with Bayes penalties C i;j = ks i Gammas j k 2 . This problem has been studied in the context of signal detection (e.g. 3] The non sequential analog in the context of joint source channel coding has also been studied (e.g. [4]) For our simulations we used the collection of all convex combinations of source encoder centroids s i as the reproduction codebook C. This set includes the Minimum Mean Squared Error (MMSE) estimate of the sourceencoder centroids. 5. Optimal Sequential Design Let n i (y n 1 ) denote the ....

N. Farvardin, "A study of vector quantization for noisy channels," IEEE Trans. Info. Theory, vol. 36, pp. 799-- 809, July 1990.

....transmission over noisy channels have been the main motivation for studying the sensitivity of a vector quantizer (VQ) to channel noise. These studies have led to the development of techniques for making a VQ robust with respect to channel noise, either by an appropriate binary codeword assignment [1, 2] or by a complete redesign of the VQ partition and codebook, resulting in the so called channel optimized vector quantizer (COVQ) 3, 4] Previous studies on the subject have concentrated on the design of a COVQ for memoryless binary symmetric channels (BSCs) 3, 4] and finite state channels ....

....i ) 2 ] Table 1: PSNR Results for a log normal fading channel (average CSNR=10 dB) 512 Theta 512 Lenna. COVQ Rate Dim. VQ Average Optimal DA (bpp) BER NA K = 2 2 4 24.49 26.33 27.00 27.27 1 8 23.96 25.80 26.25 26.46 0. 5 16 23.54 25.14 25.59 25.84 annealing is used to assign binary code words [1] to the code vectors of VQ, thus making the comparison between different schemes meaningful. Note that f ffl and I are derived for the log normal fading channel by assuming a BPSK modulation scheme and the corresponding BER given by Equation (1) This is straightforward due to the fact that BER as ....

N. Farvardin, "A Study of Vector Quantization for Noisy Channels," IEEE Trans. Inform. Theory, vol. 36, pp. 799-- 809, July 1990.

....stages, even for noiseless channels, is not optimal [2] Tables 1 and 2 show the performance of HTVQ, VQ, CM HTVQ, and COVQ for a memoryless Gaussian source at rates 0.5 and 1 bit sample (compression ratio (CR) 16:1 and 8:1) respectively. We have used simulated annealing to assign indices [5] to the codevectors of VQ and HTVQ. The source consists of samples from a memoryless Gaussian source quantized using an 8 bit Lloyd Max scalar quantizer. As it is clear from the tables, the difference between the performance of COVQ and CM HTVQ is less than the gap between VQ and HTVQ for a ....

N. Farvardin, "A Study of Vector Quantization for Noisy Channels," IEEE Trans. on Inf. Theory, vol. 36, pp. 799--809, July 1990.

....part independently of the error control part without losing the optimality. But this is an asymptotic result and it has been demonstrated that for finite delay, finite complexity systems, a combined design of the source coding and channel coding parts can yield better end to end performance e.g. [4]. In situations, where the source coding application (e.g. one residing in a personal computer) interacts with an external transmission system (e.g a cellular network) the protocols for the transmission system may not offer the full flexibility to implement the optimal combined source channel ....

N. Farvardin, "A study of vector quantization for noisy channels," IEEE Trans. Info. Theory, vol. 36, pp. 799--809, July 1990.

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N. Farvardin, "A study of vector quantization for noisy channels," IEEE Trans. Inform. Theory, vol. IT-36, pp. 799--809, July 1990.

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N. Farvardin, "A study of vector quantization for noisy channels," IEEE Trans. Inform. Theory, vol. 36, p. 799809, July 1990.

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N. Farvardin, \A study of vector quantization for noisy channels," IEEE Trans. Inform. Theory, vol. 36, pp. 799-809, July 1990.

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N. Farvardin, "A study of vector quantization for noisy channels," IEEE Transactions on Information Theory, vol. 36, no. 4, pp. 799 809, July 1990.

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N. Farvardin. A study of vector quantization for noisy channels. IEEE Transactions on Information Theory, 36(4):799--809, July 1990.

No context found.

N. Farvardin. A study of vector quantization for noisy channels. IEEE Trans. Inform. Th., 36(4):79909, July 1990.

No context found.

N. Farvardin, "A study of vector quantization for noisy channels," IEEE Trans. Inform. Theory, vol. 36, pp. 799--809, July 1990.

No context found.

N. Farvardin. A study of vector quantization for noisy channels. IEEE Transactions on Information Theory, 36:799--809, July 1990.

No context found.

N. Farvardin. A study of vector quantization for noisy channels. IEEE Transactions on Information Theory, 36(4):799--809, July 1990.

No context found.

N. Farvardin, "A Study of Vector Quantization for Noisy Channels," IEEE Transactions on Information Theory, vol. 36, no. 4, pp. 799--809, July 1990.

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