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Scaling Exponent of List Decoders With Applications to Polar Codes

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A Scaling Law to Predict the Finite-Length Performance of Spatially-Coupled LDPC Codes

Rüdiger Urbanke

Spatially-coupled low-density parity-check (SC-LDPC) codes are known to have excellent asymptotic properties. Much less is known regarding their finite-length performance. We propose a scaling law to predict the error probability of finite-length spatially ...

Institute of Electrical and Electronics Engineers2015

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

Finite-Length Scaling for Polar Codes

Rüdiger Urbanke, Seyed Hamed Hassani

Consider a binary-input memoryless output-symmetric channel W. Such a channel has a capacity, call it I (W), and for any R < I (W) and strictly positive constant P-e we know that we can construct a coding scheme that allows transmission at rate R with an e ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Scaling Exponent of List Decoders with Applications to Polar Codes

Rüdiger Urbanke, Seyed Hamed Hassani, Marco Mondelli

Motivated by the significant performance gains which polar codes experience when they are decoded with successive cancellation list decoders, we study how the scaling exponent changes as a function of the list size L. In particular, we fix the block error ...

Ieee2013

Polar Codes: Finite Length Implementation, Error Correlations and Multilevel Modulation

Shannon, in his seminal work, formalized the transmission of data over a communication channel and determined its fundamental limits. He characterized the relation between communication rate and error probability and showed that as long as the communicatio ...

2012

Universal bounds on the scaling behavior of polar codes

Rüdiger Urbanke, Seyed Hamed Hassani, Ali Goli

We consider the problem of determining the tradeoff between the rate and the block-length of polar codes for a given block error probability when we use the successive cancellation decoder. We take the sum of the Bhattacharyya parameters as a proxy for the ...

2012

Array-Code Ensembles -or- Two-Dimensional LDPC Codes

Mohammad Amin Shokrollahi, Yuval Cassuto

Probabilistic construction of codes on two-dimensional arrays is proposed and analyzed. Instead of a pure combinatorial erasure model used in traditional array codes, we propose a mixed combinatorial-probabilistic model of limiting the number of column fai ...

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

Polar Coding Theorems for Discrete Systems

Eren Sasoglu

Polar coding is a recently invented technique for communication over binary-input memoryless channels. This technique allows one to transmit data at rates close to the symmetric-capacity of such channels with arbitrarily high reliability, using low-complex ...

EPFL2011

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

On the scaling of polar codes: II. The behavior of un-polarized channels

Rüdiger Urbanke, Seyed Hamed Hassani

We provide upper and lower bounds on the escape rate of the Bhattacharyya process corresponding to polar codes where transmission takes place over the the binary erasure channel. More precisely, we bound the exponent of the number of sub-channels whose Bha ...

IEEE2010