Sharper upper bounds for unbalanced uniquely decodable code pairs

Per Austrin, Petteri Kaski, Mikko Koivisto, Jesper Nederlof

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)

Abstract

Two sets of 0-1 vectors of fixed length form a uniquely decodeable code pair if their Cartesian product is of the same size as their sumset, where the addition is pointwise over integers. For the size of the sumset of such a pair, van Tilborg has given an upper bound in the general case. Urbanke and Li, and later Ordentlich and Shayevitz, have given better bounds in the unbalanced case, that is, when either of the two sets is sufficiently large. Improvements to the latter bounds are presented.

Original languageEnglish
Article number7888502
Pages (from-to)1368-1373
Number of pages6
JournalIEEE Transactions on Information Theory
Volume64
Issue number2
DOIs
Publication statusPublished - 1 Feb 2018

Bibliographical note

to appear

Keywords

  • Additive combinatorics
  • Binary adder channel
  • Isoperimetric inequality
  • Uniquely decodeable code pair
  • Zero-error capacity

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