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A Scaling Law to Predict the Finite-Length Performance of Spatially-Coupled LDPC Codes

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Towards a metabolic theory of catchments: scaling of water and carbon fluxes with size

Sara Bonetti, Francesca Bassani

Allometric scaling relations are widely used to link biological processes in nature. They are typically expressed as power laws, postulating that the metabolic rate of an organism scales as its mass to the power of an allometric exponent, which ranges betw ...

2024

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

Seeing the forest for the trees through metabolic scaling

Andrea Rinaldo, Amos Maritan

We demonstrate that when power scaling occurs for an individual tree and in a forest, there is great resulting simplicity notwithstanding the underlying complexity characterizing the system over many size scales. Our scaling framework unifies seemingly dis ...

2022

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

Permutation-based Decoding of Reed-Muller Codes in Binary Erasure Channel

Rüdiger Urbanke, Kirill Ivanov

In this paper, we consider the problem of decoding Reed-Muller (RM) codes in binary erasure channel. We propose a novel algorithm, which exploits several techniques, such as list recursive (successive cancellation) decoding based on Plotkin decomposition, ...

IEEE2019

Displacement Convexity in Spatially Coupled Scalar Recursions

Rüdiger Urbanke, Nicolas Macris, Rafah El-Khatib

We introduce a technique for the analysis of general spatially coupled systems that are governed by scalar recursions. Such systems can be expressed in variational form in terms of a potential function. We show, under mild conditions, that the potential fu ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

Bits through Time

Elie Najm

In any communication system, there exist two dimensions through which the information at the source becomes distorted before reaching the destination: the noisy channel and time. Messages transmitted through a noisy channel are susceptible to modification ...

EPFL2019

Almost Optimal Scaling of Reed-Muller Codes on BEC and BSC Channels

Rüdiger Urbanke, Seyed Hamed Hassani, Shrinivas Kudekar, Yury Polyanskiy

Consider a binary linear code of length N, minimum distance d(min), transmission over the binary erasure channel with parameter 0 < epsilon < 1 or the binary symmetric channel with parameter 0 < epsilon < 1/2, and block-MAP decoding. It was shown by Tillic ...

IEEE2018

Coding for Communications and Secrecy

Mani Bastaniparizi

Shannon, in his landmark 1948 paper, developed a framework for characterizing the fundamental limits of information transmission. Among other results, he showed that reliable communication over a channel is possible at any rate below its capacity. In 2008, ...

EPFL2017

Wave-Like Solutions of General 1-D Spatially Coupled Systems

Rüdiger Urbanke, Shrinivas Kudekar

We establish the existence of wave-like solutions to spatially coupled graphical models which, in the large size limit, can be characterized by a 1-D real-valued state. This is extended to a proof of the threshold saturation phenomenon for all such models, ...

Ieee-Inst Electrical Electronics Engineers Inc2015