Two-dimensional RC/SW constrained codes: bounded weight and almost balanced weight

• Main Authors: Nguyen, Tuan Thanh, Cai, Kui, Kiah, Han Mao, Immink, Kees A. Schouhamer, Chee, Yeow Meng
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2023
• Subjects: Science::Mathematics; Two-Dimensional Constrained Codes; Sliding-Window Constrained Codes
• Online Access: https://hdl.handle.net/10356/170742
• Institution: Nanyang Technological University

In this work, we study two types of constraints on two-dimensional binary arrays. Given p\in [0,1],\in [0,1/2] , we study 1) the p -bounded constraint: a binary vector of size n is said to be p -bounded if its weight is at most pn , and 2) the -balanced constraint: a binary vector of size n is said to be -balanced if its weight is within big [(1/2-)n, (1/2+)n\big]. Such constraints are crucial in several data storage systems, those regard the information data as two-dimensional (2D) instead of one-dimensional (1D), such as the crossbar resistive memory arrays and the holographic data storage. In this work, efficient encoding/decoding algorithms are presented for binary arrays so that the weight constraint (either p -bounded constraint or -balanced constraint) is enforced over every row and every column, regarded as 2D row-column (RC) constrained codes; or over every window (where each window refers to as a subarray consisting of consecutive rows and consecutive columns), regarded as 2D sliding-window (SW) constrained codes. While low-complexity designs have been proposed in the literature, mostly focusing on 2D RC constrained codes where p=1/2 and =0 , this work provides efficient coding methods that work for both 2D RC constrained codes and 2D SW constrained codes, and more importantly, the methods are applicable for arbitrary values of p and. Furthermore, for certain values of p and we show that, for sufficiently large array size, there exists linear-time encoding/decoding algorithm that incurs at most one redundant bit.