Related papers: Multilayer crisscross error and erasure correction
Locally repairable codes (LRCs) were originally introduced to enable efficient recovery from erasures in distributed storage systems by accessing only a small number of other symbols. While their structural properties-such as bounds and…
We investigate the minimum distance of structured binary Low-Density Parity-Check (LDPC) codes whose parity-check matrices are of the form $[\mathbf{C} \vert \mathbf{M}]$ where $\mathbf{C}$ is circulant and of column weight $2$, and…
This paper focuses on error-correcting codes that can handle a predefined set of specific error patterns. The need for such codes arises in many settings of practical interest, including wireless communication and flash memory systems. In…
Constructing Reed-Solomon (RS) codes that can correct insertion and deletion (ins-del) errors has been the focus of several recent studies. However, efficient decoding algorithms for such codes have received less attention and remain a…
The performance of maximum-likelihood (ML) decoded binary linear block codes is addressed via the derivation of tightened upper bounds on their decoding error probability. The upper bounds on the block and bit error probabilities are valid…
We derive improved bounds on the error and erasure rate for spherical codes and for binary linear codes under Forney's erasure/list decoding scheme and prove some related results.
Despite the great performance of deep learning models in many areas, they still make mistakes and underperform on certain subsets of data, i.e. error slices. Given a trained model, it is important to identify its semantically coherent error…
In order to scale economically, data centers are increasingly evolving their data storage methods from the use of simple data replication to the use of more powerful erasure codes, which provide the same level of reliability as replication…
We derive a linear programming bound on the maximum cardinality of error-correcting codes in the sum-rank metric. Based on computational experiments on relatively small instances, we observe that the obtained bounds outperform all…
Rank-metric codes, defined as sets of matrices over a finite field with the rank distance, have gained significant attention due to their applications in network coding and connections to diverse mathematical areas. Initially studied by…
Maximum distance separable (MDS) codes are optimal where the minimum distance cannot be improved for a given length and code size. Twisted Reed-Solomon codes over finite fields were introduced in 2017, which are generalization of…
The explosion in the volumes of data being stored online has resulted in distributed storage systems transitioning to erasure coding based schemes. Local Reconstruction Codes (LRCs) have emerged as the codes of choice for these…
The masked projection techniques are popular in the area of non-linear model reduction. Quantifying and minimizing the error in model reduction, particularly from masked projections, is important. The exact error expressions are often…
The hull of linear codes have promising utilization in coding theory and quantum coding theory. In this paper, we study the hull of generalized Reed-Solomon codes and extended generalized Reed-Solomon codes over finite fields with respect…
A new algorithm for efficient exact maximum likelihood decoding of polar codes (which may be CRC augmented), transmitted over the binary erasure channel, is presented. The algorithm applies a matrix triangulation process on a sparse polar…
This paper introduces a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes, this…
We compare the performance of short-length linear binary codes on the binary erasure channel and the binary-input Gaussian channel. We use a universal decoder that can decode any linear binary block code: Gaussian-elimination based…
Several methods of triclustering of three dimensional data require the specification of the cluster size in each dimension. This introduces a certain degree of arbitrariness. To address this issue, we propose a new method, namely the…
We study linear exact repair for $(n,k,\ell)$ MDS array codes over $\mathbb{F}_q$, with redundancy $r=n-k$, in the regime where $q$, $r$, and $\ell$ are fixed and the code length $n$ varies. A recent projective counting argument gives a…
In this paper, we introduce a deep multiple description coding (MDC) framework optimized by minimizing multiple description (MD) compressive loss. First, MD multi-scale-dilated encoder network generates multiple description tensors, which…