Related papers: Improved Torn Paper Coding via Local Alignment
In distributed storage systems, locally repairable codes (LRCs) are designed to reduce disk I/O and repair costs by enabling recovery of each code symbol from a small number of other symbols. To handle multiple node failures,…
Expander (Tanner) codes combine sparse graphs with local constraints, enabling linear-time decoding and asymptotically good distance--rate tradeoffs. A standard constraint-counting argument yields the global-rate lower bound $R\ge 2r-1$ for…
We study exact decoding for the toric code and for planar and rotated surface codes under the standard independent \(X/Z\) noise model, focusing on Separate Minimum Weight (SMW) decoding and Separate Most Likely Coset (SMLC) decoding. For…
Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…
Tensor ring (TR) decomposition is a simple but effective tensor network for analyzing and interpreting latent patterns of tensors. In this work, we propose a doubly randomized optimization framework for computing TR decomposition. It can be…
The problem of low complexity, close to optimal, channel decoding of linear codes with short to moderate block length is considered. It is shown that deep learning methods can be used to improve a standard belief propagation decoder,…
Emerging applications in manufacturing, wireless communication, and molecular data storage require robust coding schemes that remain effective under physical distortions where codewords may be arbitrarily fragmented and partially missing.…
Locally repairable convolutional codes (LRCCs) for distributed storage systems (DSSs) are introduced in this work. They enable local repair, for a single node erasure (or more generally, $ \partial - 1 $ erasures per local group), and…
Shaping gain is attained in schemes where a shaped subcode is chosen from a larger codebook by a codeword selection process. This includes the popular method of Trellis Shaping (TS), originally proposed by Forney for average power…
The design of optimal linear block codes capable of being efficiently decoded is of major concern, especially for short block lengths. As near capacity-approaching codes, Low-Density Parity-Check (LDPC) codes possess several advantages over…
Mitigating errors in computing and communication systems has seen a great deal of research since the beginning of the widespread use of these technologies. However, as we develop new methods to do computation or communication, we also need…
It was pointed out in [JSW+25] that widely-studied optimization problems such as D-regular max-k-XORSAT can be reduced to decoding of LDPC codes, using quantum algorithms related to Regev's reduction. LDPC codes have very good decoders,…
In the age of data revolution, a modern storage~or transmission system typically requires different levels of protection. For example, the coding technique used to fortify data in a modern storage system when the device is fresh cannot be…
Batched sparse (BATS) codes were proposed as a reliable communication solution for networks with packet loss. In the finite-length regime, the error probability of BATS codes under belief propagation (BP) decoding has been studied in the…
Relative entropy coding (REC) algorithms encode a random sample following a target distribution $Q$, using a coding distribution $P$ shared between the sender and receiver. Sadly, general REC algorithms suffer from prohibitive encoding…
Repetition code forms a fundamental basis for quantum error correction experiments. To date, it stands as the sole code that has achieved large distances and extremely low error rates. Its applications span the spectrum of evaluating…
Coded computation is a framework which provides redundancy in distributed computing systems to speed up largescale tasks. Although most existing works assume an error-free scenarios in a master-worker setup, the link failures are common in…
Locally Decodable Codes (LDCs) are error correcting codes that admit efficient decoding of individual message symbols without decoding the entire message. Unfortunately, known LDC constructions offer a sub-optimal trade-off between rate,…
Locally repairable codes (LRC) have recently been a subject of intense research due to theoretical appeal and their application in distributed storage systems. In an LRC, any coordinate of a codeword can be recovered by accessing only few…
Local learning, which trains a network through layer-wise local targets and losses, has been studied as an alternative to backpropagation (BP) in neural computation. However, its algorithms often become more complex or require additional…