Hamming code

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Related publications (31)

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

Optimal errors and phase transitions in high-dimensional generalized linear models

Nicolas Macris, Jean François Emmanuel Barbier, Florent Gérard Krzakala, Lenka Zdeborová

Generalized linear models (GLMs) are used in high-dimensional machine learning, statistics, communications, and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing, error-corre ...

National Academy of Sciences2019

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

LDPC Coded Multiuser Shaping for the Gaussian Multiple Access Channel

Alexios Konstantinos Balatsoukas Stimming

The joint design of input constellation and low-density parity-check (LDPC) codes to approach the symmetric capacity of the two-user Gaussian multiple access channel is studied. More specifically, multilevel coding is employed at each user to construct a h ...

IEEE2019

Gaussian channel transmission of images and audio files using cryptcoding

Vladimir Ilievski

Random codes based on quasigroups (RCBQ) are cryptcodes, i.e. they are error-correcting codes, which provide information security. Cut-Decoding and 4-Sets-Cut-Decoding algorithms for these codes are defined elsewhere. Also, the performance of these codes f ...

2019

Impact of Memory Voltage Scaling on Accuracy and Resilience of Deep Learning Based Edge Devices

David Atienza Alonso, Andreas Peter Burg, Miguel Peon Quiros, Andrea Bonetti, Martino Ruggiero, Benoît Walter Denkinger, Flavio Ponzina, Soumya Subhra Basu, Szabolcs Balási

Energy consumption is a significant obstacle to integrate deep learning into edge devices. Two common techniques to curve it are quantization, which reduces the size of the memories (static energy) and the number of accesses (dynamic energy), and voltage s ...

2020

Broadband Efficient Soliton Microcombs in Pulse-Driven Photonic Microresonators

Tobias Kippenberg, Junqiu Liu, Tobias Herr, Miles Henry Anderson, Sylvain Karlen

Broadband single-soliton based frequency combs, with a detectable repetition rate of 28 GHz, are efficiently generated through pulse-driving of a chip-based Si3N4 microresonator. We observe an influence of the pulse-driving rate on the comb mode linewidth. ...

IEEE2019

Cluster perturbation theory. III. Perturbation series for coupled cluster singles and doubles excitation energies

Jógvan Magnus Olsen, Pablo Jonas Baudin

The cluster perturbation series, CPS(D), for coupled cluster singles and doubles excitation energies is considered. It is demonstrated that the second-order model CPS(D-2) is identical to the configuration interaction singles with perturbative doubles, CIS ...

AMER INST PHYSICS2019

Scaling Functional Synthesis and Repair

Emmanouil Koukoutos

Program synthesis was first proposed a few decades ago, but in the last decade it has gained increased momentum in the research community. The increasing complexity of software has dictated the urgent need for improved supporting tools that verify the soft ...

EPFL2019

The Stability Condition of LDPC Codes Under MAP Decoding

Rüdiger Urbanke, Wei Liu

We determine the stability condition of low-density parity-check codes under both bitwise and blockwise maximum a posteriori decoding. As a consequence, we prove that the stability condition determines an upper bound on both the bitwise and the blockwise m ...

IEEE2018

The Velocity of the Propagating Wave for Spatially Coupled Systems With Applications to LDPC Codes

Nicolas Macris, Rafah El-Khatib

We consider the dynamics of message passing for spatially coupled codes and, in particular, the set of density evolution equations that tracks the profile of decoding errors along the spatial direction of coupling. It is known that, for suitable boundary c ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2018

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