An iteration method for calculating the relative capacity

Jimbo, Masakazu; Kunisawa, Kiyonori

doi:10.1016/s0019-9958(79)90719-8

Cited by 29 publications

(18 citation statements)

References 8 publications

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“…When the block lengths in the SC have bounded finite length and the duplication distribution has finite support, then the corresponding matrix is finite. In this case, capacity per unit cost given a matrix can be computed numerically, using a variation of the Blahut-Arimoto algorithm for calculating the capacity, under the conditions that we are dealing with finite alphabets and positive symbol costs, as is the case here [6]. This approach does not give an actual efficient coding scheme, but yields a distribution of block lengths, from which the capacity per unit cost can be derived.…”

Section: Lower Boundsmentioning

confidence: 99%

Capacity Bounds for Sticky Channels

Mitzenmacher

2008

IEEE Trans. Inform. Theory

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Section: Lower Boundsmentioning

confidence: 99%

Capacity Bounds for Sticky Channels

Mitzenmacher

2008

IEEE Trans. Inform. Theory

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“…Discussion [Comparison with other bounds]: To compare Theorem 2 with the numerical results reported by [9] for sticky channels, the upper and lower bounds proposed by [9] have to be implemented using the Jimbo-Kunisawa iterative algorithm [13]. These bounds are based on a mapping that transforms a sticky channel into a discrete memory channel with integer alphabets.…”

Section: Resultsmentioning

confidence: 99%

On the Capacity of Duplication Channels

Ramezani

Ardakani

2013

IEEE Trans. Commun.

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“…In general, for a channel C, with information alphabet X, we can calculate an associated unit-cost capacity C(C; |X|), and determine optimal capacity-achieving input probabilities. The capacity achieving distribution p(x) can be obtained by JimboKunisawa algorithm [15]. The distribution transformer is readily achieved by employing arithmetic decoder, which is widely used in source coding applications [16].…”

Section: B Distribution Transformermentioning

confidence: 99%

“…5. shows the capacity estimates of this channels for various values of p and alphabet size |X| obtained by the Jimbo-Kunisawa algorithm [15]. The region of low channel deletion probability is of practical interest as in this case the watermark can be efficiently protected by a code.…”

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confidence: 99%

Simplification Resilient LDPC-Coded Sparse-QIM Watermarking for 3D-Meshes

Vasic

Vasić

2013

IEEE Trans. Multimedia

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Abstract-We propose a blind watermarking scheme for 3-D meshes that combines sparse quantization index modulation (QIM) with deletion correction codes. The QIM operates on the vertices in rough concave regions of the surface thus ensuring impeccability, while the deletion correction code recovers the data hidden in the vertices, which is removed by mesh optimization and/or simplification. The proposed scheme offers two orders of magnitude better performance in terms of recovered watermark bit error rate compared to the existing schemes of similar payloads and fidelity constraints.Index Terms-3-D mesh, data hiding, error correction, deletion channels, watermarking, low-density parity check codes, iterative decoding, quantization index modulation. I. INTRODUCTIONIGITAL watermarking, i.e. hiding a digital signal (watermark) into the original signal (cover signal or host signal) has been widely used for copy-protection of digital media. A good watermarking scheme must adequately balance the conflicting requirements of fidelity, and capacity, while ensuring robustness and security. Roughly speaking, fidelity referrers to the perceptual closeness of the watermarked cover signal to the original cover signal, and capacity is the amount of hidden data per bit of the host data. Security is a measure of inability of an adversary to alter or remove a watermark, and the robustness is the probability of detecting a watermark data under common operations on the watermark cover signal such as compression and affine transformations. Another common requirement is that watermarking is blind, i.e., the original cover signal is not required for watermark detection.In the past decade, watermarking of audio, video and images has been widely studied and numerous techniques have been developed. On the contrary, blind watermarking of threedimensional (3D) mesh objects is in its infancy, although the use of 3D models is growing rapidly. Watermark as copyright protection of these models is significant due to their mass use in virtual reality, modern computer games, and recently in Manuscript received April 4, 2012, revised October 9, 2012. This work is funded in part by NSF, Grant CCF-0963726.Bata Vasic is with the Department of Electronics, Faculty of Electronic Engineering Nis, University of Nis, 18000 Nis, Republic of Serbia (phone: +381-63-417-696; fax: +381-18-588-399; e-mail: bata.vasic@ elfak.ni.ac.rs).Bane Vasic is with the Department of Electrical and Computer Engineering, University of Arizona, Tucson, AZ, 85721 USA (e-mail: vasic@ece.arizona.edu).digital cinematography as well as in computer-aided design (CAD), architectural and medical simulations. One of main difficulties in 3D watermarking is that even common signal processing operations for manipulation and editing 3D objects involve a number of complex geometric and topological operations very different from the transformations of signals in one dimension (1D) and two dimensions (2D). These transformations include mesh simplification and optimization, which are used to acce...

show abstract

An iteration method for calculating the relative capacity

Cited by 29 publications

References 8 publications

Capacity Bounds for Sticky Channels

Capacity Bounds for Sticky Channels

On the Capacity of Duplication Channels

Simplification Resilient LDPC-Coded Sparse-QIM Watermarking for 3D-Meshes

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