Related papers: Function-Correcting Partition Codes
Spatially-coupled (SC) codes are a family of graph-based codes that have attracted significant attention thanks to their capacity approaching performance and low decoding latency. An SC code is constructed by partitioning an underlying…
Functional principal components (FPC's) provide the most important and most extensively used tool for dimension reduction and inference for functional data. The selection of the number, d, of the FPC's to be used in a specific procedure has…
This paper investigates the theoretical analysis of intrinsic message passing decoding for generalized product codes (GPCs) with irregular degree distributions, a generalization of product codes that allows every code bit to be protected by…
In recent years, several integer programming (IP) approaches were developed for maximum-likelihood decoding and minimum distance computation for binary linear codes. Two aspects in particular have been demonstrated to improve the…
We introduce the class of partition-balanced families of codes, and show how to exploit their combinatorial invariants to obtain upper and lower bounds on the number of codes that have a prescribed property. In particular, we derive precise…
Recently introduced Fair-Density Parity-Check (FDPC) codes, targeting high-rate applications, offer superior error-correction performance (ECP) compared to 5G Low-Density Parity-Check (LDPC) codes, given the same number of message-passing…
The subblock energy-constrained codes (SECCs) and sliding window-constrained codes (SWCCs) have recently attracted attention due to various applications in communcation systems such as simultaneous energy and information transfer. In a…
Federated computing (FC) enables collaborative computation such as machine learning, analytics, or data processing across distributed organizations keeping raw data local. Built on four architectural pillars, distributed data assets,…
A new class of spatially-coupled turbo-like codes (SC-TCs), dubbed generalized spatially coupled parallel concatenated codes (GSC-PCCs), is introduced. These codes are constructed by applying spatial coupling on parallel concatenated codes…
Coherent parity check (CPC) codes are a new framework for the construction of quantum error correction codes that encode multiple qubits per logical block. CPC codes have a canonical structure involving successive rounds of bit and phase…
Storage codes are used to ensure reliable storage of data in distributed systems. Here we consider functional repair codes, where individual storage nodes that fail may be repaired efficiently and the ability to recover original data and to…
Generalized product codes (GPCs) are extensions of product codes (PCs) where code symbols are protected by two component codes but not necessarily arranged in a rectangular array. We consider a deterministic construction of GPCs (as opposed…
The complexity-performance trade-off is a fundamental aspect of the design of low-density parity-check (LDPC) codes. In this paper, we consider LDPC codes for the binary erasure channel (BEC), use code rate for performance metric, and…
Function-correcting codes with data protection simultaneously protect both the data and a function of the data at distinct error-correction levels. When the function receives strictly stronger protection than the data, such a code is called…
Using first principles from inference, we design a set of functionals for the purposes of \textit{ranking} joint probability distributions with respect to their correlations. Starting with a general functional, we impose its desired…
This paper presents a theoretical study of a new type of LDPC codes motivated by practical storage applications. LDPCL codes (suffix L represents locality) are LDPC codes that can be decoded either as usual over the full code block, or…
In this paper, we propose a new rateless coded cooperation scheme for a general multi-user cooperative wireless system. We develop cooperation methods based on Raptor codes with the assumption that the channels face erasure with specific…
Spatially-coupled (SC) codes, known for their threshold saturation phenomenon and low-latency windowed decoding algorithms, are ideal for streaming applications and data storage systems. SC codes are constructed by partitioning an…
The Theory of Functional Connections (TFC) is a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The functionals derived from this method, called \emph{constrained expressions},…
Algorithms for partition refinement are actively studied for a variety of systems, often with the optimisation called Hopcroft's trick. However, the low-level description of those algorithms in the literature often obscures the essence of…