Coding for the ℓ∞-Limited Permutation Channel

In this work 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 l∞-metric. 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.

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