The Zero Cubes Free and Cubes Unique Multidimensional Constraints

Sagi Marcovich, Eitan Yaakobi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


This paper studies two families of constraints for two-dimensional and multidimensional arrays. The first family requires that a multidimensional array will not contain a cube of zeros of some fixed size and the second constraint imposes that there will not be two identical cubes of a given size in the array. These constraints are natural extensions of their one-dimensional counterpart that have been rigorously studied recently. For both of these constraints we present conditions of the size of the cube for which the asymptotic rate of the set of valid arrays approaches 1 as well as conditions for the redundancy to be at most a single symbol. For the first family, we present an efficient encoding algorithm that uses a single symbol to encode arbitrary information into a valid array and for the second family we present a similar encoder for the two-dimensional case. The results in the paper are also extended to similar constraints where the subarray is not necessarily a cube, but a box of arbitrary dimensions and only its volume is bounded.

Original languageEnglish
Title of host publication2022 IEEE Information Theory Workshop, ITW 2022
Number of pages6
ISBN (Electronic)9781665483414
StatePublished - 2022
Event2022 IEEE Information Theory Workshop, ITW 2022 - Mumbai, India
Duration: 1 Nov 20229 Nov 2022

Publication series

Name2022 IEEE Information Theory Workshop, ITW 2022


Conference2022 IEEE Information Theory Workshop, ITW 2022

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Artificial Intelligence
  • Computational Theory and Mathematics
  • Computer Networks and Communications


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