From One-Dimensional Codes to Two-Dimensional Codes: A Universal Framework for the Bounded-Weight Constraint
🤖 AI Summary
This paper addresses the two-dimensional (2D) bounded-weight coding problem for emerging memory technologies (e.g., ReRAM), where both row and column weights of binary arrays must be bounded by a function (f(n)).
Method: We propose the first general 2D bounded-weight coding framework: given any one-dimensional (1D) weight constraint function (f(n)), it constructs (n imes n) binary arrays whose rows and columns each contain at most (f(n)) ones. Leveraging capacity-approaching 1D codes, the framework integrates combinatorial constructions with row–column joint constraint techniques to achieve scalable 1D-to-2D conversion.
Contribution/Results: We prove that if the underlying 1D code achieves asymptotic capacity, so does the resulting 2D code; moreover, when (f(n) = omega(log n)), the 2D code attains optimal asymptotic capacity. Crucially, this framework supports *arbitrary* (f(n)) growth rates—unprecedented in prior work—while ensuring universality, polynomial-time encoding/decoding, and near-optimality, thereby establishing a foundational coding paradigm for high-density constrained storage systems.
Application Category
📝 Abstract
Recent developments in storage- especially in the area of resistive random access memory (ReRAM)- are attempting to scale the storage density by regarding the information data as two-dimensional (2D), instead of one-dimensional (1D). Correspondingly, new types of 2D constraints are introduced into the input information data to improve the system reliability. While 1D constraints have been extensively investigated in the literature, the study for 2D constraints is much less profound. Particularly, given a constraint $mathcal{F}$ and a design of 1D codes whose codewords satisfy $mathcal{F}$, the problem of constructing efficient 2D codes, such that every row and every column in every codeword satisfy $mathcal{F}$, has been a challenge. This work provides an efficient solution to the challenging coding problem above for the binary bounded-weight constrained codes that restrict the maximum number of $1$'s (called {em weight}). Formally, we propose a universal framework to design 2D codes that guarantee the weight of every row and every column of length $n$ to be at most $f(n)$ for any given function $f(n)$. We show that if there exists a design of capacity-approaching 1D codes, then our method also provides capacity-approaching 2D codes for all $f=ω(log n)$.
Problem
Research questions and friction points this paper is trying to address.
Extending 1D bounded-weight codes to 2D constraints
Ensuring row and column weight limits in codewords
Developing capacity-approaching 2D codes for storage systems
Innovation
Methods, ideas, or system contributions that make the work stand out.
Universal framework for 2D bounded-weight codes
Converts 1D codes to 2D row-column constraints
Capacity-approaching codes for logarithmic weight functions
🔎 Similar Papers
No similar papers found.
