Indexing algorithms for Z/sub n/, A/sub n/, D/sub n/, and D/sub n//sup ++/ lattice vector quantizers

Rault, Patrick X.; Guillemot, Christine

doi:10.1109/6046.966111

Cited by 10 publications

(7 citation statements)

References 16 publications

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“…Indexing of suffix is usually done according to two different techniques. The method proposed in [2] and [3] are based on leader's indexing. Elementary vectors of hypersurface called leaders are the vectors that lead to all the other vectors lying on the hypersurface which are generated by permutations and sign changes.…”

Section: Introductionmentioning

confidence: 99%

Implementation of Direct Indexing and 2-V Golomb Coding of Lattice Vectors for Image Compression

Khandelwal¹,

Purohit²

2019

IJITEE

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Indexing of code vectors is a most difficult task in lattice vector quantization. In this work we focus on the problem of efficient indexing and coding of indexes. Index assignment to the quantized lattice vectors is computed by direct indexing method, through which a vector can be represented by a scalar quantity which represents the index of that vector. This eliminates the need of calculating the prefix i.e. index of the radius ( R) or norm and suffix i.e. the index of the position of vector on the shell of radius R, also eliminates index assignment to the suffix based on lattice point enumeration or leader’s indexing . Two value golomb coding is used to enumerate indices of quantized lattice vectors. We use analytical means to emphasize the dominance of two value golomb code over one value golomb code. This method is applied to achieve image compression. Indexes of particular subband of test images like barbara, peppers and boat are coded using 2-value golomb coding (2-V GC) and compression ratio is calculated. We demonstrate the effectiveness of the 2-V GC while the input is scanned columnwise as compare to rowwise. Experimentally we also show that good compression ratio is achieved when only higher order bits of the indexes are encoded instead of complete bits

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Section: Introductionmentioning

confidence: 99%

Implementation of Direct Indexing and 2-V Golomb Coding of Lattice Vectors for Image Compression

Khandelwal¹,

Purohit²

2019

IJITEE

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show abstract

“…Practical solutions to this problem have been the grouping of codevectors into sets (i.e. shells or leader classes) and entropy encoding of the index of the set while the vector index within the set is encoded using enumerative coding (Vasilache & Tabus, 2001), (Rault & Guillemot, 2001), (Moureaux et al, 1998), (Loyer et al, 2003). However, the large number of leader classes for some particular truncation shapes, makes their use less practical.…”

Section: Lattice Entropy Codingmentioning

confidence: 99%

“…In (Vasilache & Tabus, 2002) a method based on leader vectors for lattices that can be defined as unions of leader classes (including Z n , D n , D * n and D + n lattices) has been proposed. Rault and Guillemot (Rault & Guillemot, 2001) have presented an enumeration based on signed leaders or generated signed leaders valid for a large class of lattices (Z n , A n , D n and D ++ n ). The principle of the methods based on leaders, is to count the signed permutations generating the vectors in a leader class.…”

Section: Indexing the Vectors In Truncated Latticesmentioning

confidence: 99%

“…A second method of counting the points from a truncated lattice is based on the notion of leader classes: from the definition of the leader class, the number of vectors belonging to that class can be easily deduced using polynomial coefficients (Moureaux et al, 1998), (Rault & Guillemot, 2001). This approach is also more appropriate for applications where the indexing of lattice points is also required.…”

Section: Counting Lattice Pointsmentioning

confidence: 99%

“…The principle of the methods based on leaders, is to count the signed permutations generating the vectors in a leader class. The methods described in (Moureaux et al, 1998) and (Rault & Guillemot, 2001) are based on the lexicographical or inverse lexicographical order of vectors. The methods proposed in (Vasilache & Tabus, 2002) utilize also a second possible order of the vectors within a leader class, based on binomial coefficients.…”

Section: Indexing the Vectors In Truncated Latticesmentioning

confidence: 99%

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New Directions in Lattice Based Lossy Compression

Vasilache¹

2010

Signal Processing

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Fast lexicographical order-based encoder for lattice vector quantization of Generalized Gaussian sources using pre-computedn-balls cardinalities

Guillemot

Moureaux

2018

Signal Processing: Image Communication

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Indexing algorithms for Z/sub n/, A/sub n/, D/sub n/, and D/sub n//sup ++/ lattice vector quantizers

Cited by 10 publications

References 16 publications

Implementation of Direct Indexing and 2-V Golomb Coding of Lattice Vectors for Image Compression

Implementation of Direct Indexing and 2-V Golomb Coding of Lattice Vectors for Image Compression

New Directions in Lattice Based Lossy Compression

Fast lexicographical order-based encoder for lattice vector quantization of Generalized Gaussian sources using pre-computedn-balls cardinalities

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