Coding for the ℓ-Limited Permutation Channel

Michael Langberg, Moshe Schwartz, Eitan Yaakobi

Research output: Contribution to journalArticlepeer-review


We consider the communication of information in the presence of synchronization errors. Specifically, we consider permutation channels in which a transmitted codeword x=(x1,..,xn) is corrupted by a permutation π Sn to yield the received word y=(y1,..,yn), where yi=xπ (i). We initiate the study of worst case (or zero-error) communication over permutation channels that distort the information by applying permutations π, which are limited to displacing any symbol by at most r locations, i.e., permutations π with weight at most r in the ℓmetric. We present direct and recursive constructions, as well as bounds on the rate of such channels for binary and general alphabets. Specific attention is given to the case of r=1.

Original languageEnglish
Article number8067503
Pages (from-to)7676-7686
Number of pages11
JournalIEEE Transactions on Information Theory
Issue number12
StatePublished - Dec 2017
Externally publishedYes

Bibliographical note

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  • Permutation channel
  • ℓ-metric


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