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A Revisitation of Low-Rate Bounds on the Reliability Function of Discrete Memoryless Channels for List Decoding

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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

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

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

A Lower Bound on Achievable Rates by Polar Codes with Mismatch Polar Decoding

Mine Alsan

In this paper we show that mismatched polar codes over symmetric B-DMCs symmetrized under the same permutation can achieve rates of at least I (W, V) bits whenever I (W, V) > 0, where W denotes the communication channel, V the mismatched channel used in th ...

Ieee2013

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

List-Decoding for the Arbitrarily Varying Channel Under State Constraints

Michael Christoph Gastpar

List-decoding for arbitrarily varying channels (AVCs) under state constraints is investigated. It is shown that rates within of the randomized coding capacity of AVCs with input-dependent state can be achieved under maximal error with list-decoding using l ...

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

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

Rateless Codes for AVC Models

Michael Christoph Gastpar

The arbitrarily varying channel (AVC) is a channel model whose state is selected maliciously by an adversary. Fixed-blocklength coding assumes a worst-case bound on the adversary's capabilities, which leads to pessimistic results. This paper defines a vari ...

2010