The Redundancy of Multi-resolution Coding for Successively Refinable Sources

Yang, Jun; Zhang, Zhen

doi:10.1109/itw2.2006.323814

Cited by 1 publication

(3 citation statements)

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“…The redundancy of a code is the gap between its expected distortion and the Shannon distortion-rate function. An upper bound is derived in [31] on the redundancy of successive refinement codes. This bound grows linearly in the number of stages L. Though our results bound the probability of excess distortion rather than the redundancy, they suggest that the upper bound in [31] may not be tight.…”

Section: B Successive Refinement Interpretationmentioning

confidence: 99%

“…An upper bound is derived in [31] on the redundancy of successive refinement codes. This bound grows linearly in the number of stages L. Though our results bound the probability of excess distortion rather than the redundancy, they suggest that the upper bound in [31] may not be tight. Determining the 3 For L = 1, the factor M L that multiplies the exponential term in p 2 can be eliminated via a sharper analysis.…”

Section: B Successive Refinement Interpretationmentioning

confidence: 99%

“…An upper bound is derived in [31] on the redundancy of successive refinement codes. This bound grows linearly in the number of stages L. Though our results bound the probability of excess distortion rather than the redundancy, they suggest that the upper bound in [31] may not be tight. Determining the We emphasize that the successive refinement interpretation is only true for the proposed encoding algorithm, and is not an inherent feature of the sparse regression codebook.…”

Section: B Successive Refinement Interpretationmentioning

confidence: 99%

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Lossy Compression via Sparse Linear Regression: Computationally Efficient Encoding and Decoding

Venkataramanan

Sarkar

Tatikonda

2014

IEEE Trans. Inform. Theory

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We propose computationally efficient encoders and decoders for lossy compression using a Sparse Regression Code. The codebook is defined by a design matrix and codewords are structured linear combinations of columns of this matrix. The proposed encoding algorithm sequentially chooses columns of the design matrix to successively approximate the source sequence. It is shown to achieve the optimal distortion-rate function for i.i.d Gaussian sources under the squared-error distortion criterion. For a given rate, the parameters of the design matrix can be varied to trade off distortion performance with encoding complexity. An example of such a trade-off as a function of the block length n is the following. With computational resource (space or time) per source sample of O((n/ log n) 2 ), for a fixed distortion-level above the Gaussian distortion-rate function, the probability of excess distortion decays exponentially in n. The Sparse Regression Code is robust in the following sense: for any ergodic source, the proposed encoder achieves the optimal distortion-rate function of an i.i.d Gaussian source with the same variance. Simulations show that the encoder has good empirical performance, especially at low and moderate rates. ).Communicated by M. Elad, Associate Editor for Signal Processing. 1 The error exponent of a compression code measures how fast the probability of excess distortion decays to zero with growing block length.The Sparse Regression codebook is constructed based on the statistical framework of high-dimensional linear regression, and was proposed recently by Barron and Joseph for communication over the AWGN channel at rates approaching the channel capacity [4], [5]. The codewords are sparse linear combinations of columns of an n × N design matrix or 'dictionary', where n is the block-length and N is a loworder polynomial in n. This structure enables the design of computationally efficient encoders based on sparse approximation ideas (e.g., [6], [7]). We propose one such encoding algorithm and analyze it performance.

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Section: B Successive Refinement Interpretationmentioning

confidence: 99%

Section: B Successive Refinement Interpretationmentioning

confidence: 99%

“…An upper bound is derived in [31] on the redundancy of successive refinement codes. This bound grows linearly in the number of stages L. Though our results bound the probability of excess distortion rather than the redundancy, they suggest that the upper bound in [31] may not be tight. Determining the We emphasize that the successive refinement interpretation is only true for the proposed encoding algorithm, and is not an inherent feature of the sparse regression codebook.…”

Section: B Successive Refinement Interpretationmentioning

confidence: 99%

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