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Entropy 2016, 18(12), 449;

Entropy-Constrained Scalar Quantization with a Lossy-Compressed Bit

Universidad Carlos III de Madrid, Madrid 28911, Spain
Gregorio Marañón Health Research Institute, Madrid 28007, Spain
Stevens Institute of Technology, Hoboken, NJ 07030, USA
Authors to whom correspondence should be addressed.
Academic Editor: Raúl Alcaraz Martínez
Received: 8 September 2016 / Revised: 7 December 2016 / Accepted: 12 December 2016 / Published: 16 December 2016
(This article belongs to the Section Information Theory, Probability and Statistics)
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We consider the compression of a continuous real-valued source X using scalar quantizers and average squared error distortion D. Using lossless compression of the quantizer’s output, Gish and Pierce showed that uniform quantizing yields the smallest output entropy in the limit D 0 , resulting in a rate penalty of 0.255 bits/sample above the Shannon Lower Bound (SLB). We present a scalar quantization scheme named lossy-bit entropy-constrained scalar quantization (Lb-ECSQ) that is able to reduce the D 0 gap to SLB to 0.251 bits/sample by combining both lossless and binary lossy compression of the quantizer’s output. We also study the low-resolution regime and show that Lb-ECSQ significantly outperforms ECSQ in the case of 1-bit quantization. View Full-Text
Keywords: source coding; scalar quantization source coding; scalar quantization

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Pradier, M.F.; Olmos, P.M.; Perez-Cruz, F. Entropy-Constrained Scalar Quantization with a Lossy-Compressed Bit. Entropy 2016, 18, 449.

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