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Concentration of Magnetization for Linear Block Codes

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Polar coding for arbitrary DMCs

Emre Telatar, Rajai Nasser

Polar codes are constructed for arbitrary channels by imposing an arbitrary quasigroup structure on the input alphabet. The block error probability under successive cancellation decoding decays exponentially with the square root of the block length. It is ...

2013

Extended Polar Codes Perform Better in Terms of Compound Rate and Scaling Behavior

Seyed Hamed Hassani

Polar codes provably achieve the capacity of a wide array of channels under successive decoding. However, in terms of some practical aspects, these codes do not perform optimally and need further improvement. In this paper, we consider two such aspects: un ...

Ieee2013

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

Multiuser Broadcast Erasure Channel With Feedback-Capacity and Algorithms

We consider the N-user broadcast erasure channel with unicast sessions (one for each user) where receiver feedback is regularly sent to the transmitter in the form of ACK/NACK messages. We first provide a generic outer bound to the capacity of this system; ...

Institute of Electrical and Electronics Engineers2013

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

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 ...

2012

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

Invertible Extractors and Wiretap Protocols

Mohammad Amin Shokrollahi, Mahdi Cheraghchi Bashi Astaneh

A wiretap protocol is a pair of randomized encoding and decoding functions such that knowledge of a bounded fraction of the encoding of a message reveals essentially no information about the message, while knowledge of the entire encoding reveals the messa ...

2012

Broadcasting Nested Message Sets

Suhas Diggavi, Vinod Malathidevi Prabhakaran, Shirin Saeedi Bidokhti

In this paper, we take a deterministic approach to the problem of broadcasting nested message sets. We mainly consider the scenario where a common message and a private message are to be encoded into a signal and transmitted over a broadcast channel toward ...

2012