Capacity Achieving Codes from Randomness Conductors
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The two central topics of information theory are the compression and the transmission of data. Shannon, in his seminal work, formalized both these problems and determined their fundamental limits. Since then the main goal of coding theory has been to find ...
We consider ensembles of binary linear error correcting codes, obtained by sampling each column of the generator matrix G or parity check matrix H independently from the set of all binary vectors of weight d (of appropriate dimension). We investigate the c ...
Shannon in his seminal work \cite{paper:shannon} formalized the framework on the problem of digital communication of information and storage. He quantified the fundamental limits of compression and transmission rates. The quantity \textit{channel capacity} ...
The arbitrarily varying channel (AVC) is a channel model whose state is selected maliciously by an adversary. Fixed-blocklength coding assumes a worst-case bound on the adversary's capabilities, which leads to pessimistic results. This paper defines a vari ...
The utility of limited feedback for coding over an individual sequence of discrete memoryless channels is investigated. This study complements recent results showing how limited or noisy feedback can boost the reliability of communication. A strategy with ...
We provide upper and lower bounds on the escape rate of the Bhattacharyya process corresponding to polar codes where transmission takes place over the the binary erasure channel. More precisely, we bound the exponent of the number of sub-channels whose Bha ...
Convolutional LDPC ensembles, introduced by Felstrom and Zigangirov, have excellent thresholds and these thresholds are rapidly increasing as a function of the average degree. Several variations on the basic theme have been proposed to date, all of which s ...
This thesis deals with the asymptotic analysis of coding systems based on sparse graph codes. The goal of this work is to analyze the decoder performance when transmitting over a general binary-input memoryless symmetric-output (BMS) channel. We consider t ...
Randomized techniques play a fundamental role in theoretical computer science and discrete mathematics, in particular for the design of efficient algorithms and construction of combinatorial objects. The basic goal in derandomization theory is to eliminate ...
We consider a wireless relay network with no channel information, which implements differential distributed space-time coding. We propose a coding strategy based on Cayley codes, which yields high data rate codes available for an arbitrary number of relay ...
