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

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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.

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