Publications related to A family of non-binary TLDPC codes: density evolution, convergence and thresholds

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Secure Network Coding With Erasures and Feedback

Christina Fragouli, Suhas Diggavi, László Czap, Vinod Malathidevi Prabhakaran

Secure network coding assumes that the underlying network channels are error-free; thus, if our channels introduce errors, we need to first apply a channel code to correct them, and then build security on top of the resulting error-free network. In this pa ...

Ieee-Inst Electrical Electronics Engineers Inc2015

Asynchronous Decoding of LDPC Codes over BEC

Amin Karbasi, Amir Hesam Salavati, Saeid Haghighatshoar

LDPC codes are typically decoded by running a synchronous message passing algorithm over the corresponding bipartite factor graph (made of variable and check nodes). More specifically, each synchronous round consists of 1) updating all variable nodes based ...

2015

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

LDPC Codes for 2D Arrays

Mohammad Amin Shokrollahi, Yuval Cassuto

Binary codes over 2D arrays are very useful in data storage, where each array column represents a storage device or unit that may suffer failure. In this paper, we propose a new framework for probabilistic construction of codes on 2D arrays. Instead of a p ...

Institute of Electrical and Electronics Engineers2014

Density Evolution for Min-Sum Decoding of LDPC Codes Under Unreliable Message Storage

Andreas Peter Burg, Alexios Konstantinos Balatsoukas Stimming

We analyze the performance of quantized min-sum decoding of low-density parity-check codes under unreliable message storage. To this end, we introduce a simple bit-level error model and show that decoder symmetry is preserved under this model. Subsequently ...

Institute of Electrical and Electronics Engineers2014

From Polar to Reed-Muller Codes: a Technique to Improve the Finite-Length Performance

Rüdiger Urbanke, Seyed Hamed Hassani, Marco Mondelli

We explore the relationship between polar and RM codes and we describe a coding scheme which improves upon the performance of the standard polar code at practical block lengths. Our starting point is the experimental observation that RM codes have a smalle ...

2014

Linear Programming Decoding of Spatially Coupled Codes

Rüdiger Urbanke, Badih Ghazi

For a given family of spatially coupled codes, we prove that the linear programming (LP) threshold on the binary-symmetric channel (BSC) of the tail-biting graph cover ensemble is the same as the LP threshold on the BSC of the derived spatially coupled ens ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Universal Polar Codes

Rüdiger Urbanke, Seyed Hamed Hassani

Polar codes, invented by Arikan in 2009, are known to achieve the capacity of any binary-input memoryless outputsymmetric channel. Further, both the encoding and the decoding can be accomplished in O(N log(N)) real operations, where N is the blocklength. O ...

Ieee2014

A family of non-binary TLDPC codes: density evolution, convergence and thresholds

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Re-proving Channel Polarization Theorems

Secure Network Coding With Erasures and Feedback

Asynchronous Decoding of LDPC Codes over BEC

Non-malleable Reductions and Applications

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

LDPC Codes for 2D Arrays

Density Evolution for Min-Sum Decoding of LDPC Codes Under Unreliable Message Storage

From Polar to Reed-Muller Codes: a Technique to Improve the Finite-Length Performance

Linear Programming Decoding of Spatially Coupled Codes

Universal Polar Codes

Re-proving Channel Polarization Theorems

Secure Network Coding With Erasures and Feedback

LDPC Codes for 2D Arrays

From Polar to Reed-Muller Codes: a Technique to Improve the Finite-Length Performance

Universal Polar Codes

Density Evolution for Min-Sum Decoding of LDPC Codes Under Unreliable Message Storage

Linear Programming Decoding of Spatially Coupled Codes

Asynchronous Decoding of LDPC Codes over BEC

Non-malleable Reductions and Applications

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