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Linear Universal Decoder for Compound Discrete Memoryless Channels

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Finite-Level Quantization Procedures for Construction and Decoding of Polar Codes

Emre Telatar, Yunus Inan

We consider finite-level, symmetric quantization procedures for construction and decoding of polar codes. Whether polarization occurs in the presence of quantization is not known in general. Hassani and Urbanke have shown that a simple three-level quantiza ...

2020

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

Reed-Muller codes polarize

Emmanuel Abbé, Min Ye

Reed-Muller (RM) codes were introduced in 1954 and have long been conjectured to achieve Shannon's capacity on symmetric channels. The activity on this conjecture has recently been revived with the emergence of polar codes. RM codes and polar codes are gen ...

IEEE COMPUTER SOC2019

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

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

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

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

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

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