Approaching Miscorrection-free Performance of Product and Generalized Product Codes

Miscorrection-free Decoding of Staircase Codes

We propose a novel decoding algorithm for staircase codes which reduces the effect of undetected component code miscorrections. The algorithm significantly improves performance, while retaining a low-complexity implementation suitable for high-speed optical transport networks.

On the Grobner Basis of a Family of Quasi-Cyclic LDPC Codes

A Tensor-Product Parity Code for Magnetic Recording

In magnetic recording channels, a standard code architecture consists of an outer Reed-Solomon code in concatenation with an inner parity code. The inner parity code is used to detect and correct commonly occurring error events. Generally, a parity code with short block length performs better, as multiple error events within one block and, consequently, miscorrection are less likely. In this pa...

Linear Resolutions of Powers of Generalized Mixed Product Ideals

Let L be the generalized mixed product ideal induced by a monomial ideal I. In this paper we compute powers of the genearlized mixed product ideals and show that Lk  have a linear resolution if and only if Ik have a linear resolution for all k. We also introduce the generalized mixed polymatroidal ideals and prove that powers and monomial localizations of a generalized mixed polymatroidal ideal...

On Generalized Injective Spaces in Generalized Topologies

In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, int...