M. W. Marcellin and T. R. Fischer, "Trellis coded quantization of memoryless and Gauss--Markov sources," IEEE Trans. Commun., vol. 38, pp. 82--93, Jan. 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....In general, the uncoded scheme can be modified to use a code, C, by changing the uniform scalar quanfizer, F(X ) into a quanfizer which quanfizes X to the nearest codeword in C. To illustrate this procedure we describe a construction using lattices based on trellis codes. As shown in [13] [14], 15] these lattices are superior to the integer lattice both in terms of reducing the quantization distortion and increasing the distance between codewords. We use the same encoding scheme as shown in Figure 3 except that the uniform scalar quantizer is replaced with a trellis quantizer ....

....to the integer lattice both in terms of reducing the quantization distortion and increasing the distance between codewords. We use the same encoding scheme as shown in Figure 3 except that the uniform scalar quantizer is replaced with a trellis quantizer designed for a uniform source as in [14]. The tag bits are then computed and embedded into the least significant bits of the codeword as before t and the resulting codeword is reconstructed to obtain the encoded signal Y . The decoding operation is the same as in the uncoded case except the scalar quantizer is replaced with the trellis ....

M. W. Marcellin and T. R. Fischer, "Trellis coded quantization of memoryless and Gauss-Markov sources," IEEE Transactions on Communications 38, pp. 82-93, January 1990.

....showing improvement with respect to the schemes of [12] The key point in [13] is to decompose the underlying operations into the lower dimensional subspaces. This decomposition avoids the exponential growth of the complexity. Trellis coded quantization (TCQ) introduced by Marcellin and Fischer [14], is based on applying the Ungerboeck notion of set partitioning to the partitions of a scalar quantizer where a trellis structure is used to prune the expanded number of quantization levels down to the desired encoding rate. Entropy constrained TCQ [15,16] is based on using a distance measure ....

....which was introduced in [18] In order to solve the resulting zero one integer program, we approximated it to a simple linear program. The result is a Lagrangian formulation adjoining the distortion and length of codewords. In order to achieve some packing gain, we combine the trellis encoding [14] and the new proposed FEVQ. For the important special case of a source with a monotonically decreasing density, we present a second method with negligible complexity, The rest of article is organized as follows: Section II contains a brief description of the linear program formulation and the ....

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M. W. Marcellin and T. R. Fischer, "Trellis-coded quantization of memoryless and Gauss-Markov sources," IEEE Trans. Commun. vol. 38, pp. 82--93, Nov. 1990.

....presence of long range dependencies of data as, for example, in a bimodal distribution. The goal of this paper is to use the adaptive quantization technique of [4] as a building block in quantization schemes, such as the scalar vector quan tizer (SVq) 5] and the trellis coded quantizer (TCq) [6], which are constructed based on an underlying scalar quantizer (USQ) Our motivation is to demon strate how adaptivity can be added and provide good results for popular quantization techniques such as TCQ and SVQ both of which have useful properties. We will introduce the adaptive scalar vector ....

....scalar quantizer (ECSQ) while quantizing the input vectors at a fixed rate and retaining structural and computational simplicity. The fixed rate approach is attractive to avoid the potential problems of transmitting variable rate quantizer data over channels with error. The popu larity of the TCQ [6] stems from the fact that it can outperform scalar quantizers with an encoding complexity which is still far less than that of vector quan tizers. The paper is organized as follows: In Section 2, we introduce the adaptive scalar quantization scheme used. Then we explain how adaptivity can be ....

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M. Marcellin and T. Fischer, "Trellis coded quantiza- tion of memoryless and Gauss-Markov sources," IEEE Trans. Commun, vol. 38, pp. 82-93, Jan. 1990.

....use an upper bound that is possibly not tight. This yields a R D bound for the Type 1 strategy that might not be representative of its actual performance. 4. Practical Implementation In this section, we develop a practical and feasible compression scheme based on trellis coded quantization (TCQ) [6]. TCQ allows efficient quantization of Gaussian random variables, and its optimization structure is easily adapted for lossy compression of Bernoulli random variables. Although TCQ encodes a sequence of variables one symbol at a time, it achieves compression efficiency by 11 10 00 01 10 00 ....

....I: Magnitude Optimization Stage I assumes that fB i g has been coded lossily to f b B i g, and it attempts to find the optimal trellis coding for fX i g with a desired rate of RX bits per symbol. Our algorithm uses the Ungerboeck trellis and is identical to the Gaussian TCQ algorithm presented in [6]; the only difference in our implementation is the distortion function which is minimized. At each node, we set b Y i = b X i ( b B i ; 1 b B i ) Instead of minimizing the distortion of the Gaussian itself, we choose a trellis path for f b X i g to minimize the distortion of f b Y i g. As in ....

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Michael W. Marcellin and Thomas R. Fischer, "Trellis coded quantization of memoryless and Gauss-Markov sources," IEEE Trans. on Communication, vol. 38, no. 1, January 1990.

....scheme. In general, the uncoded scheme can be modified to use a code, by changing the uniform scalar quanfizer, F(X) into a quantizer which quantizes X to the nearest codeword in . To illustrate this procedure we describe a construction using lattices based on trellis codes. As shown in [13] [14], 15] these lattices are superior to the integer lattice both in terms of reducing the quantization distortion and increasing the distance between codewords. We use the same encoding scheme as shown in Figure 3 except that the uniform scalar quantizer is replaced with a trellis quantizer ....

....to the integer lattice both in terms of reducing the quantization distortion and increasing the distance between codewords. We use the same encoding scheme as shown in Figure 3 except that the uniform scalar quantizer is replaced with a trellis quantizer designed for a uniform source as in [14]. The tag bits are then computed and embedded into the least significant bits of the codeword as before t and the resulting codeword is reconstructed to obtain the encoded signal Y L The decoding operation is the same as in the uncoded case except the scalar quantizer is replaced with the trellis ....

M. W. Marcellin and T. R. Fischer, "Trellis coded quantization of memoryless and Gauss-Markov sources," IEEE Transactions on Communications 38, pp. 82-93, January 1990.

.... encoder without feedback must be used for trellis generation [4] Fortunately, for every convolutional encoder with feedback, there exists a feedback free encoder, for which any given input bit can affect no more that 1 log 2 (N ) outputs, where N is defined as the number of trellis states [5]. A feedback free convolutional encoder produces a similar trellis with the branch bits labeled differently. This construction bounds the diversion from the correct trellis path caused by a bit error and allows the intended path to be recovered. 3. PREDICTION FILTERS The prediction filters used ....

M. W. Marcellin and T. R. Fischer. Trellis coded quantization of memoryless and Gauss-Markov sources. IEEE Transactions on Communications, 38(1):82--93, January 1990.

....data using a finite set of quantized symbols. Notions used in TCQ are similar to that of trellis coded modulation (TCM) widely used today for the design of voice line modems [96] In its simple form, TCQ exploits a codebook of codewords when coding a given source at a bit rate of bits symbol [97]. This is twice the number of codewords needed in a conventional quantization mechanism. It is possible to show that this doubling of number of codewords allows one to obtain nearly all the theoretical gain possible over a B bits symol Lloyd Max quantizers. The codebook is partitioned into ....

M. W. Marcellin and T. R. Fischer, "Trellis coded quantization of memoryless and Gauss-Markov sources," IEEE Trans. Commun., vol. COM-38, pp. 82--93, Jan. 1990.

....the uncoded scheme can be modi ed to use a code, C, by changing the uniform scalar quantizer, F (X n 1 ) into a quantizer which quantizes X n 1 to the nearest codeword in C. To illustrate this procedure we describe a construction using lattices based on trellis codes. As shown in [13] [14], 15] these lattices are superior to the integer lattice both in terms of reducing the quantization distortion and increasing the distance between codewords. We use the same encoding scheme as shown in Figure 3 except that the uniform scalar quantizer is replaced with a trellis quantizer ....

....to the integer lattice both in terms of reducing the quantization distortion and increasing the distance between codewords. We use the same encoding scheme as shown in Figure 3 except that the uniform scalar quantizer is replaced with a trellis quantizer designed for a uniform source as in [14]. The tag bits are then computed and embedded into the least signi cant bits of the codeword as before y and the resulting codeword is reconstructed to obtain the encoded signal Y n 1 . The decoding operation is the same as in the uncoded case except the scalar quantizer is replaced with the ....

M. W. Marcellin and T. R. Fischer, \Trellis coded quantization of memoryless and Gauss-Markov sources," IEEE Transactions on Communications 38, pp. 82-93, January 1990.

....The next question in robust image coding is how to choose the quantization scheme. There has been extensive research on quantization, and many schemes have been proposed, including various scalar quantizations and vector quantizations. One recently proposed scheme, trellis coded quantization (TCQ) [7], is shown to be relatively insensitive to the channel errors with moderate complexity. One bit error a ects no more than 1#log # N outputs, where N is the number of trellis states. Therefore TCQ is selected in this research as the quantization scheme and will be discussed in detail in Section ....

....Chen, Z. Sun Signal Processing: Image Communication 14 (1999) 575 584 577 Fig. 2. Four state trellis with four subsets. quantized to #r # #### ### bits sample, and reconstructed as #x( # #### ### . 3. Fixed rate uniform threshold trellis coded quantization Trellis coded quantization [7] is a nite state quantizer that employs a scalar codebook and a Viterbi encoding algorithm and labels the trellis branches with subsets of the codebook. This quantization scheme has low complexity with excellent mean square error (MSE) performance and is also insensitive to channel noise. TCQ ....

M.W. Marcellin, T.R. Fischer, Trellis coded quantization of memoryless and Gauss-Markov sources, IEEE Trans. Commun. 38 (1990) 82}93.

....as possible, while maintaining symmetry among the cosets. In the following, a trellis based partitioning is considered based on convolutional codes and set partitioning rules as in Trellis Coded Modulation (TCM) 11] Note that this is not to be confused with the Trellis Coded Quantization (TCQ) [12] framework: we still use scalar quantization but use trellises to build coset sequences. A bit stream with R bits unit time is used to partition 2 R 1 codevectors taking values in R. The set r is partitioned into 4 subsets (for the sake of clarity) as before. We use Ungerboeck s 4 state trellis ....

M. W. Marcellin and T. R. Fischer, "Trellis coded quantization of memoryless and Gauss-Markov sources," IEEE Trans. on Comm., vol. 38, pp. 82--93, Jan. 1990.

....are straightforward) Let us consider a simple fixed length, 8 level, uniform scalar quantizer with step size Delta = 1:0. Suppose R 1 = R 2 = 2 bits source sample. Let r = fr 0 ; r 1 ; r 7 g be the set of reconstruction levels of the scalar quantizer. Consider the Ungerboeck trellis [13, 14, 11] built on r. We have a finite state machine operating on a bit stream at the rate of 2 bits unit time. It has a rate 2=3 3 It can be noted that this problem is not the same as the quantization followed by coding in the binary space. 5 convolutional encoder, set partitioning rules and a mapping ....

M. W. Marcellin and T. R. Fischer, "Trellis coded quantization of memoryless and Gauss-Markov sources," IEEE Trans. on Comm., vol. 38, pp. 82--93, Jan. 1990.

....such as the Viterbi algorithm. Trellis Coded Quantization Trellis coded quantization, both scalar and vector, improves upon traditional trellis encoded systems by labeling the trellis branches with entire subcodebooks (or subsets ) rather than with individual reproduction levels [345] [344], 166] 167] 522] 343] 478] 514] The primary gain resulting is a reduction in encoder complexity for a given level of performance. As the original trellis encoding systems were motivated by convolutional channel codes with Viterbi decoders, trellis coded quantization was motivated by ....

M. W. Marcellin and T. R. Fischer, "Trellis coded quantization of memoryless and Gauss-Markov sources," IEEE Trans. Comm., vol. 38, pp. 82--93, January 1990.

....has been widely applied to many decoding and estimation applications in communications and signal processing. It can be used to perform maximum likelihood decoding for convolutional codes, or maximum likelihood estimation on Trellis Coded Modulation (TCM) 2] and Trellis Coded Quantization (TCQ) [3, 4]. Trellis Coded Modulation has evolved over the past decade as a combined coding and modulation technique for digital transmission over band limited channels. Trellis Coded Quantization was recently introduced as an effective scheme for encoding memoryless sources with low to moderate complexity. ....

M.W. Marcellin, T.R. Fischer, Trellis Coded Quantization of Memoryless and Gauss-Markov sources, IEEE Trans. Commun., v. 28, pp.92-93, Jan 1990.

....the best path (the maximum likelihood sequence) through a trellis in a dynamic manner through the study of the output sequence of a convolutional encoder received from a noisy channel. Other applications of the Viterbi algorithm are related to communications (TCM) 3] and image compression (TCQ) [4]. In order to establish a notation and briefly introduce the operation of the decoder, it is convenient to start by describing the encoder. A convolutional encoder consists of a shift register with K stages and n binary function generators. We denote as state the content of the K 1 least ....

M.W. Marcellin, T.R. Fischer, Trellis Coded Quantization of Memoryless and Gauss-Markov sources, IEEE Trans. Commun., vol 28, pp.92-93, Jan 1990.

....formal model that permits obtaining a regular and modular design solution optimal for a particular set of area and or speed constraints. 1. INTRODUCTION Trellis Coded Quantization (TCQ) was introduced as an effective scheme for encoding monochrome and color images with low to moderate complexity [1, 2]. For a given encoding rate of R bits per sample, it is possible to obtain nearly all of the theorically possible gain over the R bit per sample Loyd Max quantizer using an encoder with an output alphabet consisting of the output points of the R 1 bit per sample Lloy Max quantizer [2] The ....

.... complexity [1, 2] For a given encoding rate of R bits per sample, it is possible to obtain nearly all of the theorically possible gain over the R bit per sample Loyd Max quantizer using an encoder with an output alphabet consisting of the output points of the R 1 bit per sample Lloy Max quantizer [2]. The fixed rate TCQ applied to images can be improved with entropy constrained schemes and vector quantization. In TCQ systems an expanded codebook is partitioned into subsets, and these subsets are used to label the branches of an appropriate trellis, where a trellis is a transition diagram for ....

[Article contains additional citation context not shown here]

M.W. Marcellin, T.R. Fischer, Trellis Coded Quantization of Memoryless and Gauss-Markov sources, IEEE Trans. Commun., v. 28, pp.92-93, Jan 1990.

....transforming the image with better frequency separation. In order to further speed up the overall algorithm, the factorized nonseparable fast filters, such as the ones proposed in [5] can be used. Trellis coded quantization (TCQ) has shown to be performing quite effectively for image compression [29, 30]. A move from the uniform scalar quantization towards the TCQ might be worthwhile. In order to achieve the objective of lossless compression, the lifting scheme [21] has been used [31] since the main hurdle in lossless compression otherwise is the floating point coefficients generated by the ....

M. W. Marcellin and T. R. Fischer. Trellis Coded Quantization of Memoryless and Gauss-Markov Sources. IEEE Transactions on Communications, 38:82--93, 1990.

....such as the Viterbi algorithm. Trellis Coded Quantization Trellis coded quantization, both scalar and vector, improves upon traditional trellis encoded systems by labeling the trellis branches with entire subcodebooks (or subsets ) rather than with individual reproduction levels [345] [344], 166] 167] 522] 343] 478] 514] The primary gain resulting is a reduction in encoder complexity for a given level of performance. As the original trellis encoding systems were motivated by convolutional channel codes with Viterbi decoders, trellis coded quantization was motivated by ....

M. W. Marcellin and T. R. Fischer, "Trellis coded quantization of memoryless and Gauss-Markov sources," IEEE Trans. Comm., vol. 38, pp. 82--93, January 1990.

....quantizers use a cartesian product reproduction codebook, which often can be rapidly searched. Examples include polar vector quantizers [291, 292, 47, 376, 345, 346, 339, 342, 344] mean removed vector quantizers [18, 19] and shape gain vector quantizers [313, 281] Trellis coded quantizers [249, 247, 123, 124, 248, 324] use a Viterbi algorithm encoder matched to a reproduction codebook with a trellis structure. Hierarchical table lookup vector quantizers provide fixed rate vector quantizers with minimal computational complexity, both lossy encoder and reproduction decoder being accomplished by table lookups [69, ....

....trellis search algorithm such as the Viterbi algorithm. Trellis Coded Quantization Trellis coded quantization, both scalar and vector, improve upon traditional encoded systems by labeling the trellis branches with entire subcodebooks (or subsets ) rather than with individual reproduction levels [249, 247, 123, 124, 369, 248, 324]. The primary gain resulting is a reduction in encoder complexity for a given level of performance. As the original trellis encoding systems were motivated by convolutional channel codes with Viterbi decoders, trellis coded quantization was motivated by Ungerboeck s enormously successful coded ....

M. W. Marcellin and T. R. Fischer, "Trellis coded quantization of memoryless and Gauss-Markov sources," IEEE Trans. on Communications, Vol. 38, pp. 82--93, 1990.

.... 2 p k q (p) 6= 0 (12) 2. 2 Trellis Coded Quantization Trellis Coded Quantization (TCQ) is based on the ideas of an expanded signal set and set partioning from coded modulation, and has been shown to be an ecient method with modest complexity for encoding of memoryless sources [1]. As mentioned previously, TCQ is included in JPEG2000 Part II. A trellis is nothing more than a state transition diagram (that takes time into account) for a nite state machine. Trellises are used to study sequences of state transitions, or equivalently, sequences of states. A typical trellis ....

M. W. Marcellin, T. R. Fischer, Trellis coded quantization of memoryless and Gauss-Markov sources, IEEE Transactions on Communications 38 (1990) 82-93.

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M. W. Marcellin, T. R. Fischer, "Trellis coded quantization of memoryless and Gauss-Markov sources," IEEE Trans. Commun., January, 1990.

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M. W. Marcellin and T. R. Fischer, "Trellis coded quantization of memoryless and Gauss--Markov sources," IEEE Trans. Commun., vol. 38, pp. 82--93, Jan. 1990.

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M. W. Marcellin and T. R. Fischer, "Trellis-coded quantization of memoryless and Gauss-Markov sources," IEEE Trans. Commun., vol. 38, pp. 82--93, 1993.

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M. W. Marcellin and Fischer T. R., "Trellis coded quantization of memoryless and gauss-markov sources," IEEE Trans. on Commun., vol. COM-38, pp. 82--93, Jan. 1990.

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M. W. Marcellin and T. R. Fischer. Trellis coded quantization of memoryless and gauss-markov sources. IEEE Transactions on Communications, 38(1):82-- 93, January 1990.

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M.W. Marcellin and T.R. Fischer, "Trellis coded quantization of memoryless and Gauss-Markov sources," IEEE Trans. Commun., vol. 38, pp. 82-93, Jan. 1990.

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