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Zhang W.,University of Notre Dame | Lentmaier M.,University of Notre Dame | Lentmaier M.,Vodafone | Zigangirov K.Sh.,University of Notre Dame | And 3 more authors.
IEEE Transactions on Information Theory | Year: 2010

We present a new class of iteratively decodable turbo-like codes, called braided convolutional codes. Constructions and encoding procedures for tightly and sparsely braided convolutional codes are introduced. Sparsely braided codes exhibit good convergence behavior with iterative decoding, and a statistical analysis using Markov permutors shows that the free distance of these codes grows linearly with constraint length, i.e., they are asymptotically good. © 2009 IEEE. Source


Mazumdar A.,University of Maryland University College | Mazumdar A.,Massachusetts Institute of Technology | Barg A.,University of Maryland University College | Barg A.,Institute for Problems of Information Transmission | Kashyap N.,Indian Institute of Science
IEEE Transactions on Information Theory | Year: 2011

In terabit-density magnetic recording, several bits of data can be replaced by the values of their neighbors in the storage medium. As a result, errors in the medium are dependent on each other and also on the data written. We consider a simple 1-D combinatorial model of this medium. In our model, we assume a setting where binary data is sequentially written on the medium and a bit can erroneously change to the immediately preceding value. We derive several properties of codes that correct this type of errors, focusing on bounds on their cardinality. We also define a probabilistic finite-state channel model of the storage medium, and derive lower and upper estimates of its capacity. A lower bound is derived by evaluating the symmetric capacity of the channel, i.e., the maximum transmission rate under the assumption of the uniform input distribution of the channel. An upper bound is found by showing that the original channel is a stochastic degradation of another, related channel model whose capacity we can compute explicitly. © 2011 IEEE. Source


Lentmaier M.,TU Dresden | Sridharan A.,Seagate Technologies | Costello Jr. D.J.,University of Notre Dame | Zigangirov K.S.,University of Notre Dame | And 2 more authors.
IEEE Transactions on Information Theory | Year: 2010

An iterative decoding threshold analysis for terminated regular LDPC convolutional (LDPCC) codes is presented. Using density evolution techniques, the convergence behavior of an iterative belief propagation decoder is analyzed for the binary erasure channel and the AWGN channel with binary inputs. It is shown that for a terminated LDPCC code ensemble, the thresholds are better than for corresponding regular and irregular LDPC block codes. © 2010 IEEE. Source


Barg A.,University of Maryland University College | Barg A.,Institute for Problems of Information Transmission | Mazumdar A.,University of Maryland University College
IEEE Transactions on Information Theory | Year: 2011

We study ensembles of codes on graphs (generalized low-density parity-check, or LDPC codes) constructed from random graphs and fixed local constrained codes, and their extension to codes on hypergraphs. It is known that the average minimum distance of codes in these ensembles grows linearly with the code length. We show that these codes can correct a linearly growing number of errors under simple iterative decoding algorithms. In particular, we show that this property extends to codes constructed by parallel concatenation of Hamming codes and other codes with small minimum distance. Previously known results that proved this property for graph codes relied on graph expansion and required the choice of local codes with large distance relative to their length. © 2006 IEEE. Source


Barg A.,University of Maryland University College | Barg A.,Institute for Problems of Information Transmission | Mazumdar A.,University of Maryland University College
IEEE Transactions on Information Theory | Year: 2010

Codes for rank modulation have been recently proposed as a means of protecting flash memory devices from errors. We study basic coding theoretic problems for such codes, representing them as subsets of the set of permutations of n elements equipped with the Kendall tau distance. We derive several lower and upper bounds on the size of codes. These bounds enable us to establish the exact scaling of the size of optimal codes for large values of n. We also show the existence of codes whose size is within a constant factor of the sphere packing bound for any fixed number of errors. © 2006 IEEE. Source

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