The Twelvefold Way of Non-Sequential Lossless Compression

by   Taha Ameen ur Rahman, et al.

Many information sources are not just sequences of distinguishable symbols but rather have invariances governed by alternative counting paradigms such as permutations, combinations, and partitions. We consider an entire classification of these invariances called the twelvefold way in enumerative combinatorics and develop a method to characterize lossless compression limits. Explicit computations for all twelve settings are carried out for i.i.d. uniform and Bernoulli distributions. Comparisons among settings provide quantitative insight.


page 1

page 2

page 3

page 4


Sequential Universal Modeling for Non-Binary Sequences with Constrained Distributions

Sequential probability assignment and universal compression go hand in h...

Dv2v: A Dynamic Variable-to-Variable Compressor

We present Dv2v, a new dynamic (one-pass) variable-to-variable compresso...

Fundamental Limits of Lossless Data Compression with Side Information

The problem of lossless data compression with side information available...

Crowd Counting on Heavily Compressed Images with Curriculum Pre-Training

JPEG image compression algorithm is a widely used technique for image si...

A Distributed Computationally Aware Quantizer Design via Hyper Binning

We design a distributed function aware quantization scheme for distribut...

Estimating the Fundamental Limits is Easier than Achieving the Fundamental Limits

We show through case studies that it is easier to estimate the fundament...

Please sign up or login with your details

Forgot password? Click here to reset