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On the Minimum Distance of Non Binary LDPC Codes

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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

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

Recursive Projection-Aggregation Decoding of Reed-Muller Codes

Emmanuel Abbé, Min Ye

We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels. The algorithms are based on projecting the code on its cosets, recursively decoding the projected codes (which are lower-order RM code ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

System and method for decoding reed-muller codes

Emmanuel Abbé, Min Ye

Various embodiments are directed to Reed-Muller decoding systems and methods based on recursive projections and aggregations of cosets decoding, exploiting the self-similarity of RM codes, and extended with list-decoding procedures and with outer-code conc ...

2020

New Results On The Pseudoredundancy

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

From LDPC Block to LDPC Convolutional Codes: Capacity, Stability, and Universality

Wei Liu

In his landmark paper "A Mathematical Theory of Communication," the founding father of information theory and coding theory, Claude E. Shannon, established the largest rate at which reliable communication is possible and he revealed that the key to this re ...

EPFL2019

Compute–Forward Multiple Access (CFMA): Practical Implementations

Michael Christoph Gastpar, Sung Hoon Lim, Jingge Zhu, Erixhen Sula, Adriano Pastore

We present a practical strategy that aims to attain rate points on the dominant face of the multiple access channel capacity using a standard low complexity decoder. This technique is built upon recent theoretical developments of Zhu and Gastpar on compute ...

2019

Design rules for optimizing unipolar coded Brillouin optical time-domain analyzers

Luc Thévenaz, Marcelo Alfonso Soto Hernandez, Zhisheng Yang, Simon Adrien Zaslawski, Zonglei Li

The performance of unipolar unicolor coded Brillouin optical time-domain analysis (BOTDA) is evaluated based on both Simplex and Golay codes. Four major detrimental factors that limit the system performance, including decoded-gain trace distortion, coding ...

2018

A Formally Verified NAT Stack

George Candea, Solal Vincenzo Pirelli, Arseniy Zaostrovnykh

Prior work proved a stateful NAT network function to be semantically correct, crash-free, and memory safe. Their toolchain verifies the network function code while assuming the underlying kernel-bypass framework, drivers, operating system, and hardware to ...

2018

A Formally Verified NAT Stack

George Candea, Solal Vincenzo Pirelli, Arseniy Zaostrovnykh

Prior work proved a stateful NAT network function to be, crash-free, memory safe and semantically correct [29]. Their toolchain verifies the network function code while assuming the underlying kernel-bypass framework, drivers, operating system, and hardwar ...

ASSOC COMPUTING MACHINERY2018