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Due to its high data density and longevity, DNA is considered a promising medium for satisfying ever-increasing data storage needs. However, the diversity of errors that occur in DNA sequences makes efficient error-correction a challenging…
Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless.…
A construction using the E8 lattice and Reed-Solomon codes for error-correction in flash memory is given. Since E8 lattice decoding errors are bursty, a Reed-Solomon code over GF($2^8$) is well suited. This is a type of coded modulation,…
The most important challenge in the scaling down of flash memory is its increased inter-cell interference (ICI). If side information about ICI is known to the encoder, the flash memory channel can be viewed as similar to Costa's "writing on…
Determining the exact decoding error probability of linear block codes is an interesting problem. For binary BCH codes, McEliece derived methods to estimate the error probability of a simple bounded distance decoding (BDD) for BCH codes.…
The idea of computational error correction has been around for over half a century. The motivation has largely been to mitigate unreliable devices, manufacturing defects or harsh environments, primarily as a mandatory measure to preserve…
We present a constraint-coding scheme to correct asymmetric magnitude-$1$ errors in multi-level non-volatile memories. For large numbers of such errors, the scheme is shown to deliver better correction capability compared to known…
Fractional repetition (FR) codes are a class of repair efficient erasure codes that can recover a failed storage node with both optimal repair bandwidth and complexity. In this paper, we study the minimum distance of FR codes, which is the…
In this paper we study codes for correcting deletable errors in binary words, where each bit is either retained, substituted, erased or deleted and the total number of errors is much smaller compared to the length of the codeword. We…
Residue codes have been traditionally used for compute error correction rather than storage error correction. In this paper, we use these codes for storage error correction with surprising results. We find that adapting residue codes to…
Dynamic random access memory failures are a threat to the reliability of data centres as they lead to data loss and system crashes. Timely predictions of memory failures allow for taking preventive measures such as server migration and…
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 study error-correcting codes for permutations under the infinity norm, motivated by a novel storage scheme for flash memories call rank modulation. In this scheme, a set of $n$ flash cells are combined to create a single virtual…
Reed-Muller codes encode an $m$-variate polynomial of degree $r$ by evaluating it on all points in $\{0,1\}^m$. We denote this code by $RM(m,r)$. The minimal distance of $RM(m,r)$ is $2^{m-r}$ and so it cannot correct more than half that…
We consider the problem of constructing codes that can correct deletions that are localized within a certain part of the codeword that is unknown a priori. Namely, the model that we study is when at most $k$ deletions occur in a window of…
We introduce a new class of exact Minimum-Bandwidth Regenerating (MBR) codes for distributed storage systems, characterized by a low-complexity uncoded repair process that can tolerate multiple node failures. These codes consist of the…
Undetected errors are important for linear codes, which are the only type of errors after hard decision and automatic-repeat-request (ARQ), but do not receive much attention on their correction. In concatenated channel coding, suboptimal…
We propose an architecture for a quantum memory distributed over a $2 \times L$ array of modules equipped with a cyclic shift implemented via flying qubits. The logical information is distributed across the first row of $L$ modules and…
Arbitrarily long quantum computations require quantum memories that can be repeatedly measured without being corrupted. Here, we preserve the state of a quantum memory, notably with the additional use of flagged error events. All error…
In this paper, we derive analytic expressions for the success probability of decoding (Partial) Unit Memory codes in memoryless channels. An applications of this result is that these codes outperform individual block codes in certain…