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We consider the problem of determining the tradeoff between the rate and the block-length of polar codes for a given block error probability when we use the successive cancellation decoder. We take the sum of the Bhattacharyya parameters as a proxy for the ...
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 ...
The invention of Fountain codes is a major advance in the field of error correcting codes. The goal of this work is to study and develop algorithms for source and channel coding using a family of Fountain codes known as Raptor codes. From an asymptotic poi ...
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 ...
Coding and diversity are very effective techniques for improving transmission reliability in a mobile wireless environ- ment. The use of diversity is particularly important for multimedia communications over fading channels. In this work, we study the tran ...
Institute of Electrical and Electronics Engineers2009
We consider communication over the binary erasure and the binary additive white gaussian noise channels using fixed linear block codes and also appropriate ensembles of such codes. We show concentration of the magnetization over the channel realizations an ...
In this paper we consider the finite-length performance of Repeat-Accumulate codes in the waterfall region assuming the transmission on the binary erasure channel. We extend the finite-length scaling law of LDPC codes [1] to this ensemble and we derive the ...
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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} ...
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 ...
Fountain codes are currently employed for reliable and efficient transmission of information via erasure channels with unknown erasure rates. This correspondence introduces the notion of fountain capacity for arbitrary channels. In contrast to the conventi ...