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
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
, 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
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.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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MDPI and ACS Style
Pradier, M.F.; Olmos, P.M.; Perez-Cruz, F. Entropy-Constrained Scalar Quantization with a Lossy-Compressed Bit. Entropy 2016, 18, 449.
Pradier MF, Olmos PM, Perez-Cruz F. Entropy-Constrained Scalar Quantization with a Lossy-Compressed Bit. Entropy. 2016; 18(12):449.
Pradier, Melanie F.; Olmos, Pablo M.; Perez-Cruz, Fernando. 2016. "Entropy-Constrained Scalar Quantization with a Lossy-Compressed Bit." Entropy 18, no. 12: 449.
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