Hessam Mahdavifar

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Suppose that Alice wishes to send messages to Bob through a communication channel C<sub>1</sub>, but her transmissions also reach an eavesdropper Eve through another channel C<sub>2</sub>. This is the wiretap channel model introduced by Wyner in 1975. The goal is to design a coding scheme that makes it possible for Alice to communicate both reliably and(More)
Flash memory is a non-volatile computer memory comprised of blocks of cells, wherein each cell can take on q different values or levels. While increasing the cell level is easy, reducing the level of a cell can be accomplished only by erasing an entire block. Since block erasures are highly undesirable, coding schemes&#x2014;known as floating codes or flash(More)
The operator channel was introduced by Koetter and Kschischang as a model of errors and erasures for randomized network coding, in the case where network topology is unknown (the noncoherent case). The input and output of the operator channel are vector subspaces of the ambient space; thus error-correcting codes for this channel are collections of such(More)
Subspace codes and rank-metric codes can be used to correct errors and erasures in network, with linear network coding. Both types of codes have been extensively studied in the past five years. Subspace codes were introduced by Koetter and Kschischang to correct errors and erasures in networks where topology is unknown (the non-coherent case). In this(More)
A scheme for concatenating the recently invented polar codes with non-binary MDS codes, as Reed-Solomon codes, is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation scheme captures the capacity-achieving property of polar codes, while having a significantly better error-decay rate.(More)
The problem of constructing error correcting codes for defective memories, where some of the cells are defected and unable to switch their states, is considered. This is a classical problem in coding theory which has recently received renewed attention due to application to new technologies for non-volatile memories such as phase change memories. We show(More)
A capacity-achieving scheme based on polar codes is proposed for reliable communication over multi-channels which can be directly applied to bit-interleaved coded modulation schemes. We start by reviewing the ground-breaking work of polar codes and then discuss our proposed scheme. Instead of encoding separately across the individual underlying channels,(More)
Designing polar codes for transmission over two-user multiple access channels is considered. In the proposed scheme, both users encode their messages using a polar encoder, while a joint successive cancellation decoder is deployed at the receiver. The encoding is done separately, while the codes are constructed jointly. This is done by treating the whole(More)
Subspace codes are collections of subspaces of a certain ambient vector space over a finite field. Koetter and Kschischang introduced subspace codes in order to correct errors and erasures in noncoherent (random) linear network coding. They have also studied a remarkable family of subspace codes obtained by evaluating certain linearized polynomials. The(More)