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Locally correctable codes (LCCs) are error correcting codes C : \Sigmak \rightarrow \Sigman which admit local algorithms that correct any individual symbol of a corrupted codeword via a minuscule number of queries. For systematic codes, this notion is stro ...
The beginning of 21st century provided us with many answers about how to reach the channel capacity. Polarization and spatial coupling are two techniques for achieving the capacity of binary memoryless symmetric channels under low-complexity decoding algor ...
In his landmark paper "A Mathematical Theory of Communication," the founding father of information theory and coding theory, Claude E. Shannon, established the largest rate at which reliable communication is possible and he revealed that the key to this re ...
The concepts of pseudocodeword and pseudoweight play a fundamental role in the finite-length analysis of LDPC codes. The pseudoredundancy of a binary linear code is defined as the minimum number of rows in a parity-check matrix such that the corresponding ...
This thesis is concerned with a number of novel uses of spatial coupling, applied to a class of probabilistic graphical models. These models include error correcting codes, random constraint satisfaction problems (CSPs) and statistical physics models calle ...
In cloud storage systems, hot data is usually replicated over multiple disks/servers in order to accommodate simultaneous access by multiple users as well as increase the fault tolerance of the system. Recent cloud storage research has proposed using avail ...
Applications of the RApid Plasma Transport simulatOR (RAPTOR) for the simulation of the plasma tokamak parameters evolution are presented. The RAPTOR transport model has been extended by time varying terms and verified via comparisons with ASTRA simulation ...
We analyze the performance of quantized min-sum decoding of low-density parity-check codes under unreliable message storage. To this end, we introduce a simple bit-level error model and show that decoder symmetry is preserved under this model. Subsequently ...
Institute of Electrical and Electronics Engineers2014
We consider the dynamics of message passing for spatially coupled codes and, in particular, the set of density evolution equations that tracks the profile of decoding errors along the spatial direction of coupling. It is known that, for suitable boundary c ...
An online fountain code is defined as a fountain code for which an optimal encoding strategy can be found efficiently given any instantaneous decoding state. This property is important for data distribution in practical networks. In this paper, we formaliz ...
Institute of Electrical and Electronics Engineers2015
