Publications related to Statistical physics methods for sparse graph codes

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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

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

Polarization Improves E-0

Emre Telatar, Mine Alsan

We prove that channel combining and splitting via Arikan's polarization transformation improves Gallager's reliability function E-0 for binary input channels. In this sense, polarization creates E-0. This observation gives yet another justification as to w ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Threshold Saturation for Spatially Coupled LDPC and LDGM Codes on BMS Channels

Nicolas Macris, Henry Pfister

Spatially-coupled low-density parity-check (LDPC) codes, which were first introduced as LDPC convolutional codes, have been shown to exhibit excellent performance under low-complexity belief-propagation decoding. This phenomenon is now termed threshold sat ...

Institute of Electrical and Electronics Engineers2014

A Fast Hadamard Transform for Signals with Sub-linear Sparsity

Martin Vetterli, Robin Scheibler, Saeid Haghighatshoar

A new iterative low complexity algorithm has been presented for computing the Walsh-Hadamard transform (WHT) of an N dimensional signal with a K-sparse WHT, where N is a power of two and K = O(N^α), scales sub- linearly in N for some 0 < α < 1. Assuming a ...

2013

Iterative Coding for Network Coding

Rüdiger Urbanke, Andrea Montanari

We consider communication over a noisy network under randomized linear network coding. Possible error mechanisms include node-or link-failures, Byzantine behavior of nodes, or an overestimate of the network min-cut. Building on the work of Kotter and Kschi ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Windowed Decoding of Spatially Coupled Codes

Rüdiger Urbanke

Spatially coupled codes have been of interest recently owing to their superior performance over memoryless binary-input channels. The performance is good both asymptotically, since the belief propagation thresholds approach the Shannon limit, as well as fo ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Spatially Coupled Ensembles Universally Achieve Capacity Under Belief Propagation

Rüdiger Urbanke, Shrinivas Kudekar

We investigate spatially coupled code ensembles. For transmission over the binary erasure channel, it was recently shown that spatial coupling increases the belief propagation threshold of the ensemble to essentially the maximum a priori threshold of the u ...

Institute of Electrical and Electronics Engineers2013

Approximate Decoding Approaches for Network Coded Correlated Data

Pascal Frossard, Nikolaos Thomos, Hyung Gon Park

This paper considers a framework where data from correlated sources are transmitted with help of network coding in ad-hoc network topologies. The correlated data are encoded independently at sensors and network coding is employed in the intermediate nodes ...

Institute of Electrical and Electronics Engineers2013

Statistical physics methods for sparse graph codes

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

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

Polarization Improves E-0

Threshold Saturation for Spatially Coupled LDPC and LDGM Codes on BMS Channels

A Fast Hadamard Transform for Signals with Sub-linear Sparsity

Iterative Coding for Network Coding

Polarization and Spatial Coupling

Windowed Decoding of Spatially Coupled Codes

Spatially Coupled Ensembles Universally Achieve Capacity Under Belief Propagation

Approximate Decoding Approaches for Network Coded Correlated Data

A Fast Hadamard Transform for Signals with Sub-linear Sparsity

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

Iterative Coding for Network Coding

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

Spatially Coupled Ensembles Universally Achieve Capacity Under Belief Propagation

Windowed Decoding of Spatially Coupled Codes

Polarization and Spatial Coupling

Threshold Saturation for Spatially Coupled LDPC and LDGM Codes on BMS Channels

Approximate Decoding Approaches for Network Coded Correlated Data

Polarization Improves E-0