NDLI: Basis arrays and successive packing for M-D interleaving

Content Provider	Springer Nature Link
Author	Zhang, Xi Min Xu, Wen Qing Shi, Yun Qing Basu, Sankar
Copyright Year	2010
Abstract	In this paper, we first present a novel concept of 2-D basis interleaving array (also referred to as basis array for short). That is, an m × m interleaved array is said to be a basis array if the shortest distance among all pairs of elements in each of the so-called m-equivalent sets within the m × m array reaches the maximum. It is shown that this maximum is given by $${\lfloor \sqrt{2m} \rfloor}$$ and an m × m basis array can be constructed by using a simple cyclic translation method. The previously developed concept of successive packing is then generalized in the sense that it can be applied to any basis array to generate an interleaved array with a larger size. Except that optimality cannot be guaranteed, the concept of basis arrays and successive packing are extended to M-D cases. It is shown that for any M ≥ 2, the proposed technique can spread any error burst of block size $${m_{1}^{k} \times m_{2}^{k} \times \cdots \times m_{M}^{k}}$$ within an $${ m_{1}^{n} \times m_{2}^{n} \times \cdots \times m_{M}^{n}}$$ array (1 ≤ k ≤ n−1) so effectively that the error burst can be corrected with some simple random error-correcting code (provided the error-correcting code is available). It is shown that important prior results in M-D interleaving such as the t-interleaved array based approach by Blaum et al. and the successive packing approach by Shi and Zhang now become special cases of the framework based on basis arrays and successive packing, proposed in this paper.
Starting Page	237
Ending Page	257
Page Count	21
File Format	PDF
ISSN	09236082
Journal	Multidimensional Systems and Signal Processing
Volume Number	22
Issue Number	1-3
e-ISSN	15730824
Language	English
Publisher	Springer US
Publisher Date	2010-09-04
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Successive packing Basis interleaving arrays M-D interleaving Error burst Random error-correction codes Artificial Intelligence (incl. Robotics) Signal, Image and Speech Processing Electrical Engineering Circuits and Systems
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Artificial Intelligence Signal Processing Information Systems Computer Science Applications Software Hardware and Architecture

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