Related papers: Private and Resource-Bounded Locally Decodable Cod…
Consider two remote nodes (encoder and decoder), each with a binary sequence. The encoder's sequence $X$ differs from the decoder's sequence $Y$ by a small number of edits (deletions and insertions). The goal is to construct a message $M$,…
Data encoding is a fundamental step in emerging computing paradigms, particularly in stochastic computing (SC) and hyperdimensional computing (HDC), where it plays a crucial role in determining the overall system performance and hardware…
Error control is significant to network coding, since when unchecked, errors greatly deteriorate the throughput gains of network coding and seriously undermine both reliability and security of data. Two families of codes, subspace and rank…
We show for invertible problems that transform data from a source domain (for example, Logic Condition Tables (LCTs)) to a destination domain (for example, Hardware Description Language (HDL) code), an approach of using Large Language…
We consider the problem of transmitting correlated data after independent encoding to a central receiver through orthogonal channels. We assume that the channel state information is not known at the transmitter. The receiver has access to…
This paper aims to go beyond resilience into the study of security and local-repairability for distributed storage systems (DSS). Security and local-repairability are both important as features of an efficient storage system, and this paper…
Locally decodable codes (LDCs) are error correcting codes that allow for decoding of a single message bit using a small number of queries to a corrupted encoding. Despite decades of study, the optimal trade-off between query complexity and…
This paper presents an algorithm for decoding homogeneous interleaved codes of high interleaving order in the rank metric. The new decoder is an adaption of the Hamming-metric decoder by Metzner and Kapturowski (1990) and guarantees to…
We propose without loss of generality strategies to achieve a high-throughput FPGA-based architecture for a QC-LDPC code based on a circulant-1 identity matrix construction. We present a novel representation of the parity-check matrix (PCM)…
Error correction codes are a crucial part of the physical communication layer, ensuring the reliable transfer of data over noisy channels. The design of optimal linear block codes capable of being efficiently decoded is of major concern,…
A general multi-terminal source code and a general multi-terminal channel code are presented. Constrained-random-number generators with sparse matrices, which are building blocks for the code construction, are used in the construction of…
Raptor codes are rateless codes that achieve the capacity on the binary erasure channels. However the maximum degree of optimal output degree distribution is unbounded. This leads to a computational complexity problem both at encoders and…
Low Rank Parity Check (LRPC) codes form a class of rank-metric error-correcting codes that was purposely introduced to design public-key encryption schemes. An LRPC code is defined from a parity check matrix whose entries belong to a…
Information-theoretic security is considered in the paradigm of network coding in the presence of wiretappers, who can access one arbitrary edge subset up to a certain size, also referred to as the security level. Secure network coding is…
We show that spatially coupled low-density parity-check (LDPC) codes yield robust performance over changing intersymbol interfere (ISI) channels with optimal and suboptimal detectors. We compare the performance with classical LDPC code…
We study the performance of binary spatially-coupled low-density parity-check codes (SC-LDPC) when used with bit-interleaved coded-modulation (BICM) schemes. This paper considers the cases when transmission takes place over additive white…
Recently, locally repairable codes (LRCs) with local erasure correction constraints that are unequal and disjoint have been proposed. In this work, we study the same topic and provide some improved and additional results.
Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. A traditional approach is to look for codes which simultaneously maximize error tolerance and minimize storage space consumption. However, this…
Characterizing the decoding failure rate of iteratively decoded Low- and Moderate-Density Parity Check (LDPC/MDPC) codes is paramount to build cryptosystems based on them, able to achieve indistinguishability under adaptive chosen…
Large Language Models (LLMs) that can be deployed locally have recently gained popularity for privacy-sensitive tasks, with companies such as Meta, Google, and Intel playing significant roles in their development. However, the security of…