Publications related to Hamming code

A Generalized Adjusted Min-Sum Decoder for 5G LDPC Codes: Algorithm and Implementation

Andreas Peter Burg, Alexios Konstantinos Balatsoukas Stimming, Yifei Shen, Yuqing Ren, Hassan Harb

5G New Radio (NR) has stringent demands on both performance and complexity for the design of low-density parity-check (LDPC) decoding algorithms and corresponding VLSI implementations. Furthermore, decoders must fully support the wide range of all 5G NR bl ...

Ieee-Inst Electrical Electronics Engineers Inc2024

Analysis of the influence of errors in DNA-based image coding

Touradj Ebrahimi, Michela Testolina, Davi Nachtigall Lazzarotto

In the last decade, DNA has been increasingly investigated as an alternative medium for cold data storage, presenting several advantages over standard hard drives such as a higher density, longer lifespan and lower energy consumption. However, such coding ...

2023

Critical Schrodinger Cat Qubit

Vincenzo Savona, Fabrizio Minganti, Luca Gravina

Encoding quantum information onto bosonic systems is a promising route to quantum error correc-tion. In a cat code, this encoding relies on the confinement of the dynamics of the system onto the two-dimensional manifold spanned by Schrodinger cats of oppos ...

AMER PHYSICAL SOC2023

Individual and combined benefits of different nonequilibrium proofreading mechanisms

Paolo De Los Rios, Daniel Maria Busiello, Stefano Zamuner, Adélaïde Alice Mohr

Genome duplication, transcription, and translation are among many crucial cellular processes that need to be performed with high fidelity. However, those extremely low error rates cannot be explained with simple equilibrium thermodynamic considerations. Th ...

Amer Physical Soc2023

Low Power LDPC Decoding by Reliable Voltage Down-Scaling

Andreas Peter Burg

Low-Density Parity-Check (LDPC) decoder is among the power hungry building blocks of wireless communication systems. Voltage scaling down to Near-Threshold (NT) voltages substantially improves energy efficiency, in theory up 10x. However, tuning the voltag ...

IEEE2023

Ultra-High-Throughput EMS NB-LDPC Decoder with Full-Parallel Node Processing

Hassan Harb

This paper presents an ultra-high-throughput decoder architecture for NB-LDPC codes based on the Hybrid Extended Min-Sum algorithm. We introduce a new processing block that updates a check node and its associated variable nodes in a fully pipelined way, th ...

SPRINGER2022

Symmetry in design and decoding of polar-like codes

Kirill Ivanov

The beginning of 21st century provided us with many answers about how to reach the channel capacity. Polarization and spatial coupling are two techniques for achieving the capacity of binary memoryless symmetric channels under low-complexity decoding algor ...

EPFL2022

Relaxed Locally Correctable Codes With Nearly-Linear Block Length And Constant Query Complexity

Alessandro Chiesa

Locally correctable codes (LCCs) are error correcting codes C : \Sigmak \rightarrow \Sigman which admit local algorithms that correct any individual symbol of a corrupted codeword via a minuscule number of queries. For systematic codes, this notion is stro ...

SIAM PUBLICATIONS2022

List Ordered Statistics Decoders for Polar Codes

Andreas Peter Burg, Yifei Shen, Chuan Zhang

The de-facto standard decoding algorithm for polar codes, successive cancellation list (SCL) decoding, is a breadth-first search algorithm. By keeping a list of candidate codewords, SCL decoding improves the performance as the list size L increases. Howeve ...

IEEE2022

Almost impossible E_8 and Leech lattices

Maryna Viazovska

We start this short note by introducing two remarkable mathematical objects: the E8E8 root lattice Lambda8Lambda8 in 8-dimensional Euclidean space and the Leech lattice Lambda24Lambda24 in 24-dimensional space. These two lattices stand out among their lat ...

2021

The Stability of Low-Density Parity-Check Codes and Some of its Consequences

Rüdiger Urbanke, Wei Liu

We study the stability of low-density parity-check codes under blockwise or bitwise maximum a posteriori decoding, where transmission takes place over a binary-input memoryless output-symmetric channel. Our study stems from the consideration of constructin ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

An Explicit Construction of Optimal Streaming Codes for Channels With Burst and Arbitrary Erasures

Damian Dudzicz

This paper presents a new construction of error correcting codes which achieves optimal recovery of a streaming source over a packet erasure channel. The channel model considered is the sliding-window erasure model, with burst and arbitrary losses, introdu ...

2020

On the Universality of Low-Density Parity-Check Block Codes

Rüdiger Urbanke, Wei Liu

An important class of modern channel codes is the capacity-achieving sequences of low-density parity-check block codes. Such sequences are usually designed for the binary erasure channel and are decoded by iterative message-passing algorithms. In this pape ...

IEEE2020

Minimum-Error Classes for Matching Parts

Thomas Alois Weber

This paper examines the binning of two types of parts with random characteristics, so that a componentwise monotonic evaluation criterion exhibits a minimum deviation to a given target value over all possible realizations. The optimal matching classes are ...

2021

Design and Decoding of Irregular LDPC Codes Based on Discrete Message Passing

Andreas Peter Burg

We consider discrete message passing (MP) decoding of low-density parity check (LDPC) codes based on information-optimal symmetric look-up table (LUT). A link between discrete message labels and the associated log-likelihood ratio values (defined in terms ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

On the Computational Complexity of Blind Detection of Binary Linear Codes

Alexios Konstantinos Balatsoukas Stimming, Aris Filos Ratsikas

In this work, we study the computational complexity of the Minimum Distance Code Detection problem. In this problem, we are given a set of noisy codeword observations and we wish to find a code in a set of linear codes C of a given dimension k, for which t ...

IEEE2019

New Results On The Pseudoredundancy

Jens Markus Zumbrägel, Zihui Liu

The concepts of pseudocodeword and pseudoweight play a fundamental role in the finite-length analysis of LDPC codes. The pseudoredundancy of a binary linear code is defined as the minimum number of rows in a parity-check matrix such that the corresponding ...

2019

Deep Unfolding for Communications Systems: A Survey and Some New Directions

Alexios Konstantinos Balatsoukas Stimming, Christoph Studer

Deep unfolding is a method of growing popularity that fuses iterative optimization algorithms with tools from neural networks to efficiently solve a range of tasks in machine learning, signal and image processing, and communication systems. This survey sum ...

IEEE2019

Improved decoding of second-order Reed-Muller codes

Rüdiger Urbanke, Kirill Ivanov

In this paper, we consider low-complexity decoding of second-order Reed-Muller codes. A class of polynomial-time algorithms, based on the projections onto first-order codes, is studied. An old representative of this class, originally developed for binary s ...

IEEE2019

Universal Sparse Superposition Codes With Spatial Coupling and GAMP Decoding

Nicolas Macris, Jean François Emmanuel Barbier, Mohamad Baker Dia

Sparse superposition codes, or sparse regression codes, constitute a new class of codes, which was first introduced for communication over the additive white Gaussian noise (AWGN) channel. It has been shown that such codes are capacity-achieving over the A ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019