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Re-proving Channel Polarization Theorems

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A Class of Generalized RS-Codes with Faster Encoding and Decoding Algorithms

Mohammad Amin Shokrollahi

In this paper we study a particular class of generalized Reed-Solomon codes and introduce encoding and decoding algorithms for such codes that speed up current hardware implementations by a factor p wherein p can be any divisor of the size of the multiplic ...

Ieee2013

New Bounds for Random Constraint Satisfaction Problems via Spatial Coupling

Rüdiger Urbanke, Nicolas Macris, Seyed Hamed Hassani

This paper is about a novel technique called spatial coupling and its application in the analysis of random constraint satisfaction problems (CSP). Spatial Coupling was recently invented in the area of error correcting codes where it has resulted in effici ...

2013

Distributed sensor failure detection in sensor networks

Pascal Frossard, Nikolaos Thomos, Tamara Tosic

We investigate the problem of distributed sensors' failure detection in networks with a small number of defective sensors, whose measurements differ significantly from neighbouring sensor measurements. We build on the sparse nature of the binary sensor fai ...

Elsevier Science Bv2013

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

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

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

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

Layered Detection and Decoding in MIMO Wireless Systems

Andreas Peter Burg, Nicholas Alexander Preyss, Christoph Studer

Iterative detection and decoding (IDD) in multiple-input multiple-output (MIMO) wireless systems is known to achieve near channel capacity. The high computational complexity of IDD, however, poses signiﬁcant challenges for practical implementations (in ter ...

2012

Polar Codes for the m-User Multiple Access Channel

Emre Telatar, Emmanuel Abbé

In this paper, polar codes for the m-user multiple access channel (MAC) with binary inputs are constructed. It is shown that Arikan's polarization technique applied individually to each user transforms independent uses of an m-user binary input MAC into su ...

Institute of Electrical and Electronics Engineers2012