• Journal of the Institute of Electronics Engineers of Korea SP
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• v.49 no.2
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• pp.18-27
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• 2012

Optimal quantizers in conducting the entropy-constrained quantization for high bit rates have the lattice structure. The quantization process is simple due to the regular structure and various quantization algorithms are proposed depending on the lattice. In this paper, such a lattice vector quantization is implemented by using the sample-adaptive product quantizer (SAPQ). It is shown that several important lattices can be implemented by SAPQ and the lattice vector quantization can be performed by using a simple integer-transform function of scalar values within SAPQ. The performance of the proposed lattice SAPQ is compared to the entropy-constrained scalar quantizer and the entropy-constrained SAPQ (ECSAPQ) at a similar encoding complexity. Even though ECSAPQ shows a good performance at low bit-rates, lattice SAPQ shows better performance than the ECSAPQ case for a wide range of bit rates.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.12B
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• pp.2382-2390
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• 1999

In this paper, we employed a new quantization scheme called sample-adaptive product quantizer (SAPQ) to quantize image data based on the differential pulse code modulation (DPCM) coder, which has fixed length outputs and high bit rates. In order to improve the performance of traditional DPCM coders, the scalar quantizer should be replaced by the vector quantizer (VQ). As the bit rate increases, it will be nearly impossible to implement a conventional VQ or modified VQ, such as the tree-structured VQ, even if the modified VQ can significantly reduce the encoding complexity. SAPQ has a form of the feed-forward adaptive scalar quantizer having a short adaptation period. However, since SAPQ is a structurally constrained VQ, SAPQ can achieve VQ-level performance with a low encoding complexity. Since SAPQ has a scalar quantizer structure, by using the traditional scalar value predictors, we can easily apply SAPQ to DPCM coders. For synthetic data and real images, by employing SAPQ as the quantizer part of DPCM coders, we obtained a 2~3 dB improvement over the DPCM coders, which are based on the Lloyd-Max scalar quantizers, for data rates above 4 b/point.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.49 no.1
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• pp.19-30
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• 2012

For digital data compression, the quantization is the main part of the lossy source coding. In order to improve the performance of quantization, the vector quantizer(VQ) can be employed. The encoding complexity, however, exponentially increases as the vector dimension or bit rate gets large. Much research has been conducted to alleviate such problems of VQ. Especially for high bit rates, a constrained VQ, which is called the sample-adaptive product quantizer(SAPQ), has been proposed for reducing the hugh encoding complexity of regular VQs. SAPQ has very similar structure as to the product VQ(PQ). However, the quantizer performance can be better than the PQ case. Further, the encoding complexity and the memory requirement for the codebooks are lower than the regular full-search VQ case. Among SAPQs, 1-SAPQ has a simple quantizer structure, where each product codebook is symmetric with respect to the diagonal line in the underlying vector space. It is known that 1-SAPQ shows a good performance for i.i.d. sources. In this paper, a study on designing 1-SAPQ for the first-order Markov process. For an efficient design of 1-SAPQ, an algorithm for the initial codebook is proposed, and through the numerical analysis it is shown that 1-SAPQ shows better quantizer distortion than the VQ case, of which encoding complexity is similar to that of 1-SAPQ, and shows distortions, which are close to that of the DPCM(differential pulse coded modulation) scheme with the Lloyd-Max quantizer.

• Journal of the Institute of Electronics and Information Engineers
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• v.49 no.9
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• pp.67-75
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• 2012

Optimal quantizers in conducting the entropy-constrained quantization for high bit rates have the lattice structure. The quantization process is simple due to the regular structure, and various quantization algorithms are proposed depending on the lattice. Such a lattice vector quantizer (VQ) can be implemented by using the sample-adaptive product quantizer (SAPQ) and its output can also be easily entropy encoded. In this paper, the entropy encoding scheme for the lattice VQ is proposed based on SAPQ, and the performance of the proposed lattice VQ, which is based on SAPQ with the entropy coder, is asymptotically compared as the rate increases. It is shown by experiment that the gain for the memoryless Gaussian source also approaches the theoretic gain for the uniform density case.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.42 no.3 s.303
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• pp.81-90
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• 2005

When we transmit signals, which are quantized by the vector quantizer (VQ), through noisy channels, the overall performance of the coding system is very dependent on the employed quantization scheme and the channel error effect. In order to design an optimal coding system, the source and channel coding scheme should be jointly optimized as in the channel-optimized VQ. As a suboptimal approach, we may consider the robust VQ (RVQ). In RVQ, we consider developing an index assignment function for mapping the output of quantizers to channel symbols so that the effect of the channel errors is minimized. Recently, a VQ, which can reduce the encoding complexity and is called the sample-adaptive product quantizer (SAPQ), has been proposed. SAPQ has very similar quantizer structure as to the product quantizer (PQ). However, the quantization performance can be better than PQ. Further, the encoding complexity and the memory requirement for the codebooks are lower than the regular full-search VQ case. In this paper, SAPQ is employed in order to design an RVQ to channel errors by reducing the vector dimension. Discussions on the codebook structure of SAPQ and experiments are introduced in an aspect of robustness to noisy channels.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.12B
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• pp.2391-2400
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• 1999

Vector quantizer (VQ) is an efficient data compression technique for low bit rate applications. However, the major disadvantage of VQ is its encoding complexity which increases dramatically as the vector dimension and bit rate increase. Even though one can use a modified VQ to reduce the encoding complexity, it is nearly impossible to implement such a VQ at a high bit rate or for a large vector dimension because of the enormously large memory requirement for the codebook and the very large training sequence (TS) size. To overcome this difficulty, in this paper we propose a novel structurally constrained VQ for the high bit rate and the large vector dimension cases in order to obtain VQ-level performance. Furthermore, this VQ can be extended to the low bit rate applications. The proposed quantization scheme has a form of feed-forward adaptive quantizer with a short adaptation period. Hence, we call this quantization scheme sample-adaptive product quantizer (SAPQ). SAPQ can provide a 2 ~3dB improvement over the Lloyd-Max scalar quantizers.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.49 no.1
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• pp.11-18
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• 2012

In this paper, an entropy constrained vector quantizer for high bit-rates is proposed. The sample-adaptive product quantizer (SAPQ), which is based on the product codebooks, is employed, and a design algorithm for the entropy constrained sample adaptive product quantizer (ECSAPQ) is proposed. The performance of the proposed ECSAPQ is better than the case of the entropy constrained vector quantizer by 0.5dB. It is also shown that the ECSAPQ distortion curve, which is based on the scalar quantizer, is lower than the high-rate theoretical curve of the entropy constrained scalar quantizer, where the theoretical curve have 1.53dB difference from Shannon's lower bound.