Sharper upper bounds for unbalanced uniquely decodable code pairs

Per Austrin, Petteri Kaski, Mikko Koivisto*, Jesper Nederlof

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)
26 Downloads (Pure)


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
Issue number2
Publication statusPublished - 1 Feb 2018
MoE publication typeA1 Journal article-refereed


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

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