Abstract

Interleaving codewords is an important method not only for combatting burst-errors, but also for flexible data-retrieving. This paper defines the Multi-Cluster Interleaving (MCI) problem, an interleaving problem for parallel data-retrieving. The MCI problems on linear arrays and rings are studied. The following problem is completely solved: how to interleave integers on a linear array or ring such that any m (m ≥ 2) non-overlapping segments of length 2 in the array or ring have at least 3 distinct integers. We then present a scheme using a ‘hierarchical-chain structure’ to solve the following more general problem for linear arrays: how to interleave integers on a linear array such that any m (m ≥ 2) non-overlapping segments of length L (L ≥ 2) in the array have at least L + 1 distinct integers. It is shown that the scheme using the ‘hierarchical-chain structure’ solves the second interleaving problem for arrays that are asymptotically as long as the longest array on which an MCI exists, and clearly, for shorter arrays as well.

Citations