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This paper studies the problem of encoding messages into sequences which can be uniquely recovered from some noisy observations about their substrings. The observed reads comprise consecutive substrings with some given minimum overlap. This…
A new achievable rate region is given for the Gaussian cognitive many-to-one interference channel. The proposed novel coding scheme is based on the compute-and-forward approach with lattice codes. Using the idea of decoding sums of…
Locally repairable codes for distributed storage systems have gained a lot of interest recently, and various constructions can be found in the literature. However, most of the constructions result in either large field sizes and hence too…
This paper introduces a structured memory which can be easily integrated into a neural network. The memory is very large by design and significantly increases the capacity of the architecture, by up to a billion parameters with a negligible…
Reducing the threshold voltage of electronic devices increases their sensitivity to electromagnetic radiation dramatically, increasing the probability of changing the memory cells' content. Designers mitigate failures using techniques such…
This work deals with error correction for non-volatile memories that are partially defective at some levels. Such memory cells can only store incomplete information since some of their levels cannot be utilized entirely due to, e.g.,…
A new concept of a multi-valued associative memory is introduced, generalizing a similar one in fuzzy neural networks. We expand the results on fuzzy associative memory with thresholds, to the case of a multi-valued one: we introduce the…
In this paper, we use a simple discrete dynamical model to study integer partitions and their lattice. The set of reachable configurations of the model, with the order induced by the transition rule defined on it, is the lattice of all…
In the framework of write-once memory (WOM) codes, it is important to distinguish between codes that can be decoded directly and those that require that the decoder knows the current generation to successfully decode the state of the…
Vector perturbation is an encoding method for broadcast channels in which the transmitter solves a shortest vector problem in a lattice to create a perturbation vector, which is then added to the data before transmission. In this work, we…
Linear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in…
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…
The significant advancements in integrated photonics have enabled high-speed and energy efficient systems for various applications from data communications and high-performance computing, to medical diagnosis, sensing and ranging. However,…
Designs and methods for nested lattice codes using Construction D' lattices for coding and convolutional code lattices for shaping are described. Two encoding methods and a decoding algorithm for Construction D' coding lattices that can be…
An ultra fast bit addressing scheme for magnetic random access memories (MRAM) in a crossed wire geometry is proposed. In the addressing scheme a word of cells is programmed simultaneously by sub nanosecond field pulses making use of the…
We present a precise characterization of linear functional-repair storage codes in terms of {\em admissible states/}, with each state made up from a collection of vector spaces over some fixed finite field. To illustrate the usefulness of…
A primary source of increased read time on NAND flash comes from the fact that in the presence of noise, the flash medium must be read several times using different read threshold voltages for the decoder to succeed. This paper proposes an…
Batch codes are of potential use for load balancing and private information retrieval in distributed data storage systems. Recently, a special case of batch codes, termed functional batch codes, was proposed in the literature. In functional…
The future of main memory appears to lie in the direction of new non-volatile memory technologies that provide strong capacity-to-performance ratios, but have write operations that are much more expensive than reads in terms of energy,…
Memristor, one of the fundamental circuit elements, has promising applications in non-volatile memory and storage technology as it can theoretically achieve infinite states. Information can be stored independently in these states and…