An entropy inequality for q-ary random variables and its application to channel polarization
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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} ...
Convolutional low-density parity-check (LDPC) ensembles, introduced by Felstrom and Zigangirov, have excellent thresholds and these thresholds are rapidly increasing functions of the average degree. Several variations on the basic theme have been proposed ...
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 ...
In the first part of this thesis we are interested in the asymptotic performance analysis of Non-Binary Low-Density Parity-Check (NBLDPC) codes over the Binary Erasure Channel (BEC) decoded via the suboptimal Belief Propagation (BP) decoder as well as the ...
Consider communication over a binary-input memoryless output-symmetric channel with low-density parity-check (LDPC) codes and maximum a posteriori (MAP) decoding. The replica method of spin glass theory allows to conjecture an analytic formula for the aver ...
We consider communication over a binary erasure channel with low density parity check codes and optimal maximum a posteriori decoding. It is known that the problem of computing the average conditional entropy, over such code ensembles, in the asymptotic li ...
Minimum distance is an important parameter of a linear error correcting code. For improved performance of binary Low Density Parity Check (LDPC) codes, we need to have the minimum distance grow fast with n, the codelength. However, the best we can hope for ...
Consider communication over a binary-input memoryless output-symmetric channel with low density parity check (LDPC) codes and maximum a posteriori (MAP) decoding. The replica method of spin glass theory allows to conjecture an analytic formula for the aver ...
Decoding that uses an extended Hamming code in one of the primary stages of static encoding uses a calculation of the r+1 Hamming redundant symbols for k input symbols from which Hamming redundant symbols are calculated, where r satisfies 2.sup.r-1-r.ltore ...
Claude Elwood Shannon in 1948, then of the Bell Labs, published one of the ground breaking papers in the history of engineering [1]. This paper (”A Mathematical Theory of Communication”, Bell System Tech. Journal, Vol. 27, July and October 1948, pp. 379 - ...