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Flash memory devices are winning the competition for storage density against magnetic recording devices. This outcome results from advances in physics that allow storage of more than one bit per cell, coupled with advances in signal processing that reduce the effect of physical instabilities. Constrained codes are used in storage to avoid problematic patterns. Recently, we introduced binary symmetric lexicographically-ordered constrained codes (LOCO codes) for data storage and transmission. This paper introduces simple constrained codes that support non-binary physical gates in multi, triple, quad, and the currently-in-development penta-level cell (M/T/Q/P-LC) Flash memories. The new codes can be easily modified if problematic patterns change with time. These codes are designed to mitigate inter-cell interference, which is a critical source of error in Flash devices. The new codes are called q-ary asymmetric LOCO codes (QA-LOCO codes), and the construction subsumes codes previously designed for single-level cell (SLC) Flash devices (ALOCO codes). QA-LOCO codes work for a Flash device with any number, q, of levels per cell. For q ≥ 4, we show that QA-LOCO codes can achieve rates greater than 0.95log 2 q information bits per coded symbol. Capacity-achieving rates, affordable encoding-decoding complexity, and ease of reconfigurability support the growing improvement of M/T/Q/P-LC Flash memory devices, as well as lifecycle management as the characteristics of these devices change with time. 

The continuous rise of the blockchain technology is moving various information systems towards decentralization. Blockchain-based decentralized storage networks (DSNs) offer significantly higher privacy and lower costs to customers compared with centralized cloud storage associated with specific vendors. Coding is required to retrieve data stored on failing components. While coding solutions for centralized storage have been intensely studied, those for DSNs have not yet been discussed. In this paper, we propose a coding scheme where each node receives extra protection through cooperation with nodes in its neighborhood in a heterogeneous DSN with any given topology. Our scheme can achieve faster recovery speed compared with existing network coding methods, and can correct more erasure patterns compared with our previous work. 

In data storage and data transmission, certain patterns are more likely to be subject to error when written (transmitted) onto the media. In magnetic recording systems with binary data and bipolar non-return-to-zero signaling, patterns that have insufficient separation between consecutive transitions exacerbate inter-symbol interference. Constrained codes are used to eliminate such error-prone patterns. A recent example is a new family of capacity-achieving constrained codes, named lexicographically-ordered constrained codes (LOCO codes). LOCO codes are symmetric, that is, the set of forbidden patterns is closed under taking pattern complements. LOCO codes are suboptimal in terms of rate when used in Flash devices where block erasure is employed since the complement of an error-prone pattern is not detrimental in these devices. This paper introduces asymmetric LOCO codes (A-LOCO codes), which are lexicographically-ordered constrained codes that forbid only those patterns that are detrimental for Flash performance. A-LOCO codes are also capacity-achieving, and at finite-lengths, they offer higher rates than the available state-of-the-art constrained codes designed for the same goal. The mapping-demapping between the index and the codeword in A-LOCO codes allows low-complexity encoding and decoding algorithms that are simpler than their LOCO counterparts. 

In order to accommodate the ever-growing data from various, possibly independent, sources and the dynamic nature of data usage rates in practical applications, modern cloud data storage systems are required to be scalable, flexible, and heterogeneous. Codes with hierarchical locality have been intensively studied due to their effectiveness in reducing the average reading time in cloud storage. In this paper, we present the first codes with hierarchical locality that achieve scalability and flexibility in heterogeneous cloud storage using small field size. We propose a double- level construction utilizing so-called Cauchy Reed-Solomon codes. We then develop a triple-level construction based on this double-level code; this construction can be easily generalized into any hierarchical structure with a greater number of layers since it naturally achieves scalability in the cloud storage systems. 

In order to meet the demands of data-hungry applications, data storage devices are required to be increasingly denser. Various sources of error appear with this increase in density. Multi-dimensional (MD) graph-based codes are capable of mitigating error sources like interference and channel non-uniformity in dense storage devices. Recently, a technique was proposed to enhance the performance of MD spatially-coupled codes that are based on circulants. The technique carefully relocates circulants to minimize the number of short cycles. However, cycles become more detrimental when they combine together to form more advanced objects, e.g., absorbing sets, including low-weight codewords. In this paper, we show how MD relocations can be exploited to minimize the number of detrimental objects in the graph of an MD code. Moreover, we demonstrate the savings in the number of relocation arrangements earned by focusing on objects rather than cycles. Our technique is applicable to a wide variety of one-dimensional (OD) codes. Simulation results reveal significant lifetime gains in practical Flash systems achieved by MD codes designed using our technique compared with OD codes having similar parameters.