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In many experimental designs -- split-plots, blocked or nested layouts, fractional factorials, and studies with missing or unequal replication -- standard ANOVA procedures no longer tell us exactly how many independent pieces of information…
This paper addresses optimal feedback selection for generic arbitrary pole placement of structured systems when each feedback edge is associated with a cost. Given a structured system and a feedback cost matrix, our aim is to find a…
A novel fast recursive coding technique is proposed. It operates with only integer values not longer 8 bits and is multiplication free. Recursion the algorithm is based on indirectly provides rather effective coding of symbols for very…
This paper presents a flexible irregular model for heterogeneous cloud storage systems and investigates how the cost of repairing failed nodes can be minimized. The fractional repetition code, originally designed for minimizing repair…
We consider the design of regenerating codes for distributed storage systems that enjoy the property of local, exact and uncoded repair, i.e., (a) upon failure, a node can be regenerated by simply downloading packets from the surviving…
We recently showed in [1] the superiority of certain structured coding matrices ensembles (such as partial row-orthogonal) for sparse superposition codes when compared with purely random matrices with i.i.d. entries, both…
Shaping codes are used to generate code sequences in which the symbols obey a prescribed probability distribution. They arise naturally in the context of source coding for noiseless channels with unequal symbol costs. Recently, shaping…
A rateless code-i.e., a rate-compatible family of codes-has the property that codewords of the higher rate codes are prefixes of those of the lower rate ones. A perfect family of such codes is one in which each of the codes in the family is…
This paper investigates fundamental properties of nonlinear binary codes by looking at the codebook matrix not row-wise (codewords), but column-wise. The family of weak flip codes is presented and shown to contain many beautiful properties.…
Digital System Research has pioneered the mathematics and design for a new class of computing machine using residue numbers. Unlike prior art, the new breakthrough provides methods and apparatus for general purpose computation using several…
Partial spread is important in finite geometry and can be used to construct linear codes. From the results in (Designs, Codes and Cryptography 90:1-15, 2022) by Xia Li, Qin Yue and Deng Tang, we know that if the number of the elements in a…
The minimum aberration criterion has been frequently used in the selection of fractional factorial designs with nominal factors. For designs with quantitative factors, however, level permutation of factors could alter their geometrical…
In a distributed storage network, reliability and bandwidth optimization can be provided by regenerating codes. Recently table based regenerating codes viz. DRESS (Distributed Replication-based Exact Simple Storage) codes has been proposed…
In a distributed storage systems (DSS), regenerating codes are used to optimize bandwidth in the repair process of a failed node. To optimize other DSS parameters such as computation and disk I/O, Distributed Replication-based Simple…
Modern distributed storage systems apply redundancy coding techniques to stored data. One form of redundancy is based on regenerating codes, which can minimize the repair bandwidth, i.e., the amount of data transferred when repairing a…
In distributed storage systems built using commodity hardware, it is necessary to have data redundancy in order to ensure system reliability. In such systems, it is also often desirable to be able to quickly repair storage nodes that fail.…
Shaping codes are used to encode information for use on channels with cost constraints. Applications include data transmission with a power constraint and, more recently, data storage on flash memories with a constraint on memory cell wear.…
A covering code is a subset $\mathcal{C} \subseteq \{0,1\}^n$ with the property that any $z \in \{0,1\}^n$ is close to some $c \in \mathcal{C}$ in Hamming distance. For every $\epsilon,\delta>0$, we show a construction of a family of codes…
Redundancy is related to the amount of functionality that the structure can sustain in the worst-case scenario of structural degradation. This paper proposes a widely-applicable concept of redundancy optimization of finite-dimensional…
Reliability is an inherent challenge for the emerging nonvolatile technology of racetrack memories, and there exists a fundamental relationship between codes designed for racetrack memories and codes with constrained periodicity. Previous…