How to prove the Maxwell conjecture via spatial coupling — A proof of concept
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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 aim of this paper is to show that spatial coupling can be viewed not only as a means to build better graphical models, but also as a tool to better understand uncoupled models. The starting point is the observation that some asymptotic properties of gr ...
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 ...
An important class of modern channel codes is the capacity-achieving sequences of low-density parity-check block codes. Such sequences are usually designed for the binary erasure channel and are decoded by iterative message-passing algorithms. In this pape ...
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 ...
We study the stability of low-density parity-check codes under blockwise or bitwise maximum a posteriori decoding, where transmission takes place over a binary-input memoryless output-symmetric channel. Our study stems from the consideration of constructin ...
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
The general subject considered in this thesis is a recently discovered coding technique, polar coding, which is used to construct a class of error correction codes with unique properties. In his ground-breaking work, Arikan proved that this class of codes, ...
The main objective of this paper is to explore the precise relationship between the Bethe free energy (or entropy) and the Shannon conditional entropy of graphical error correcting codes. The main result shows that the Bethe free energy associated with a l ...
We present a digital baseband ASIC for 60 GHz single-carrier (SC) transmission that is optimized for communication scenarios in which most of the energy is concentrated in the first few channel taps. Such scenarios occur for example in office environments ...