Publications by Ghid Maatouk | EPFL Graph Search

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Affine-invariant properties are an abstract class of properties that generalize some central algebraic ones, such as linearity and low-degree-ness, that have been studied extensively in the context of property testing. Affine invariant properties consider ...

We analyze the second moment of the ripple size during the LT decoding process and prove that the standard deviation of the ripple size for an LT-code with length k is of the order of root k. Together with a result by Karp et. al (2004) stating that the ex ...

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 ...

In this paper, the second moment of the ripple size during the Luby transform (LT) decoding process is analyzed. Combined with a result by Karp et al. (2004) stating that the expectation of the ripple size is of the order of k, our study gives bounds on th ...

Locally testable codes, i.e., codes where membership in the code is testable with a constant number of queries, have played a central role in complexity theory. It is well known that a code must be a "low-density parity check" (LDPC) code for it to be loca ...

In networks that perform linear network coding, an intermediate network node may receive a much larger number of linear equations of the source symbols than the number of messages it needs to send. For networks constructed by untrusted nodes, we propose a ...

Ghid Maatouk

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On Sums of Locally Testable Affine Invariant Properties

Analysis of the Second Moment of the LT Decoder

Irregular Product Codes

Analysis of the Second Moment of the LT Decoder

Symmetric LDPC codes are not necessarily locally testable

Untrusting network coding

Graph-based Codes and Generalized Product Constructions