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Weight Distribution of Low-Density Parity-Check Codes

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Polar Codes For Broadcast Channels

Michael Christoph Gastpar, Emmanuel Abbé, Naveen Goela

Building on polar code constructions proposed by the authors for deterministic broadcast channels, two theorems are introduced in the present paper for noisy two-user broadcast channels. The theorems establish polar code constructions for two important ...

2013

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

Polarization and Spatial Coupling

Seyed Hamed Hassani

During the last two decades we have witnessed considerable activity in building bridges between the fields of information theory/communications, computer science, and statistical physics. This is due to the realization that many fundamental concepts and no ...

EPFL2013

Polarization Theorems for Arbitrary DMCs

Emre Telatar, Rajai Nasser

A polarization phenomenon in a special sense is shown for an arbitrary discrete memoryless channel (DMC) by imposing a quasigroup structure on the input alphabet. The same technique is used to derive a polarization theorem for an arbitrary multiple access ...

IEEE2013

Rate-Dependent Analysis of the Asymptotic Behavior of Channel Polarization

Rüdiger Urbanke, Seyed Hamed Hassani

We consider the asymptotic behavior of the polarization process in the large block-length regime when transmission takes place over a binary-input memoryless symmetric channel W. In particular, we study the asymptotics of the cumulative distribution, P(Z(n ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Secure Network Coding with Erasures and Feedback

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

Secure network coding assumes that the underlying network links are lossless, thus it can be applied over lossy networks after channel error correction. Yet it is well known that channel losses, such as packet erasures, can be constructively used for secre ...

2013

On the Convergence Speed of Spatially Coupled LDPC Ensembles

Vahid Aref

Spatially coupled low-density parity-check codes show an outstanding performance under the low-complexity belief propagation (BP) decoding algorithm. They exhibit a peculiar convergence phenomenon above the BP threshold of the underlying non-coupled ensemb ...

2013

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

Comments on "Iterative channel decoding of FEC-based multiple-description codes"

Nikolaos Thomos

In their recent paper, Chang et al. presented a method for iterative decoding of FEC-based multiple description codes in image transmission. In this correspondence we clarify that an outer interleaver used in the above work was previously proposed for the ...

Institute of Electrical and Electronics Engineers2013

New Bounds for Random Constraint Satisfaction Problems via Spatial Coupling

Rüdiger Urbanke, Nicolas Macris, Seyed Hamed Hassani

This paper is about a novel technique called spatial coupling and its application in the analysis of random constraint satisfaction problems (CSP). Spatial Coupling was recently invented in the area of error correcting codes where it has resulted in effici ...

2013