Two-dimensional interleaving using the set partitioning technique

We propose an efficient two-dimensional interleaving technique which spreads a cluster of errors having a circular shape. As a consequence of this technique, simple random-error-correcting codes can be used to correct cluster of errors, instead of the more complex burst-error-correcting codes. Interleaving techniques are mainly used in channels with memory. The combination of coding and interleaving, in general, leads to memoryless channels where modelling and performance analysis are amenable. The motivation for the use of this technique is related to applications such as in magnetic and optical data storage, or in digital image transmission, where a cluster of errors occurs in the first case due to dust particles, or defective regions, and in the second case due to noise. The 2D interleaving technique is used to separate the neighbors of any given point in a Q×Q square array, by a minimum squared Euclidean distance, d_min⩽Q, where Q is the order of the array. When d_min⩽=Q, we say that the interleaving is perfect, or it realizes a maximum distance spreading of points. We show by an example, the effectiveness of the interleaving scheme