A Generalized Run-Length Representation Scheme for Vector Source Coding

doi:10.1109/tsp.2026.3700629

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A Generalized Run-Length Representation Scheme for Vector Source Coding

2026-06-09

PRE

Leah Woldemariam

Hang Liu

Anna Scaglione

DOI：10.1109/tsp.2026.3700629

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Abstract

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Although data compression is a well-studied area, the research topic is still alive today due to the growing amount of data, their distributed nature, and the growing utility gained from acquiring them. Classical entropy coding schemes for discrete sources may sometimes yield sub-optimal results because they are tailored to data drawn from a specific underlying distribution or data with certain properties. For continuous sources, a typical approach is to quantize data into sparse representations and achieve compression gains due to the preponderance of zeros in the sequence to transmit. In this paper, we focus on leveraging a generalization of this property that is a common trademark of discrete, or quantized, compressible data vectors: most outcomes appear rarely. Our novel encoding scheme is tailored to data that are drawn from unknown distributions and utilizes the frequency and spatial information of the data to obtain a compressed representation. We first analyze the asymptotic behavior of our scheme for discrete sources and study its properties considering sources whose Probability Mass Function (PMF) is $c$-dominant. We then consider continuous sources and study how to create a set of quantization levels that balances error and entropy. Finally, we convey the wide applicability of our scheme with several experiments that reflect performance competitive with widely-used encoding schemes in multiple domains.

Keywords:

Source coding

entropy coding

compression

Golomb coding

run-length coding