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Near-Optimal Finite-Length Scaling for Polar Codes Over Large Alphabets

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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

Polarity-Balanced Codes

Balanced bipolar codes consist of sequences in which the symbols ‘−1’ and ‘+1’ appear equally often. Several generalizations to larger alphabets have been considered in literature. For example, for the q-ary alphabet {−q+1,−q+3, . . . , q−1}, known concept ...

2013

Generalized Codes on Graphs and Applications in Content Distribution

Masoud Alipour Babaei

The contribution of this thesis is twofold. In the first part, we generalize and analyze two classes of error correcting codes: LDPC codes and product codes. We generalize graphical codes by considering checks being arbitrary codes instead of single pariti ...

EPFL2013

Irregular Product Codes

Mohammad Amin Shokrollahi, Ghid Maatouk, Seyed Omid Etesami, Masoud Alipour Babaei

We introduce irregular product codes, a class of codes where each codeword is represented by a matrix and the entries in each row (column) of the matrix come from a component row (column) code. As opposed to standard product codes, we do not require that a ...

Ieee2012

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

Polar Codes: Characterization of Exponent, Bounds, and Constructions

Rüdiger Urbanke, Satish Babu Korada, Eren Sasoglu

Polar codes were recently introduced by Arikan. They achieve the capacity of arbitrary symmetric binary-input discrete memoryless channels under a low complexity successive cancellation decoding strategy. The original polar code construction is closely rel ...

2010

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

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

Polar codes for channel and source coding

Satish Babu Korada

The two central topics of information theory are the compression and the transmission of data. Shannon, in his seminal work, formalized both these problems and determined their fundamental limits. Since then the main goal of coding theory has been to find ...

EPFL2009

Polar Codes: Characterization of Exponent, Bounds, and Constructions

Rüdiger Urbanke, Satish Babu Korada, Eren Sasoglu

Polarization codes were recently introduced by Ar\i kan. They are explicit code constructions which achieve the capacity of arbitrary symmetric binary-input discrete memoryless channels (and even extensions thereof) under a low complexity successive decodi ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2009