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

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How to prove the Maxwell conjecture via spatial coupling — A proof of concept

Rüdiger Urbanke, Nicolas Macris, Andrei Giurgiu

Investigations on spatially coupled codes have lead to the conjecture that, in the infinite size limit, the average input-output conditional entropy for spatially coupled low-density parity-check ensembles, over binary memoryless symmetric channels, equals ...

2012

How to Prove the Maxwell Conjecture Via Spatial Coupling - A Proof of Concept

Rüdiger Urbanke, Nicolas Macris, Andrei Giurgiu

Ieee2012

Decay of correlations for sparse graph error correcting codes

Nicolas Macris, Shrinivas Kudekar

The subject of this paper is transmission over a general class of binary-input memoryless symmetric channels using error correcting codes based on sparse graphs, namely, low-density generator-matrix and low-density parity-check codes. The optimal (or ideal ...

2011

Threshold Saturation via Spatial Coupling: Why Convolutional LDPC Ensembles Perform So Well over the BEC

Rüdiger Urbanke, Shrinivas Kudekar

Convolutional low-density parity-check (LDPC) ensembles, introduced by Felstrom and Zigangirov, have excellent thresholds and these thresholds are rapidly increasing functions of the average degree. Several variations on the basic theme have been proposed ...

2011

Efficient Implementation of Linear Programming Decoding

Mohammad Amin Shokrollahi

While linear programming (LP) decoding provides more flexibility for finite-length performance analysis than iterative message-passing (IMP) decoding, it is computationally more complex to implement in its original form, due to both the large size of the r ...

2011

Raptor Codes

Mohammad Amin Shokrollahi

This monograph describes the theory behind Raptor codes, and elucidates elements of the processes behind the design of two of the most prominent members of this class of codes: R10 and RaptorQ (RQ). R10 has already been adopted by a number of standards' bo ...

2011

Universal Rateless Codes From Coupled LT Codes

Rüdiger Urbanke, Vahid Aref

It was recently shown that spatial coupling of individual low-density parity-check codes improves the belief-propagation threshold of the coupled ensemble essentially to the maximum a posteriori threshold of the underlying ensemble. We study the performanc ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2011

Block copolymers and uses thereof

Jeffrey Alan Hubbell, Melody Swartz, Conlin O'Neil

An encoding/decoding apparatus and method using a low-density parity-check code (LDPC code) is disclosed. Basic column group information, serving as a set of information regarding positions of rows with weight 1, is extracted from a reference column in eac ...

2010

Symmetric LDPC codes are not necessarily locally testable

Ghid Maatouk

Locally testable codes, i.e., codes where membership in the code is testable with a constant number of queries, have played a central role in complexity theory. It is well known that a code must be a "low-density parity check" (LDPC) code for it to be loca ...

2010

Forward error-correcting (FEC) coding and streaming

Mohammad Amin Shokrollahi

In a data decoder for decoding data from received symbols received over a channel from an encoder, a method for decoding data wherein the received data includes erasures and includes source symbols and repair symbols organized into one or more source block ...

2010