Polar Codes for Q-ary Source Coding

Emre Telatar, Mohammad Karzand
2010
Article de conférence

Résumé

Polar coding is a recent channel coding technique invented by Arikan to achieve the 'symmetric capacity' of binary-input memoryless channels. Subsequently it was observed by Korada and Urbanke that such codes are also good for lossy channel coding, achieving the 'symmetric rate distortion' bound, when the representation alphabet is binary. In this note we extend this result to the case when the representation alphabet is q-ary, for q a prime number.

Source officielle

https://infoscience.epfl.ch/record/172015?ln=fr

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A new elementary proof of the Prime Number Theorem

Florian Karl Richter

Let

\Omega(n)

denote the number of prime factors of

n

. We show that for any bounded

f\colon\mathbb{N}\to\mathbb{C}

one has [ \frac{1}{N}\sum_{n=1}^N, f(\Omega(n)+1)=\frac{1}{N}\sum_{n=1}^N, f(\Omega(n))+\mathrm{o}_{N\to\infty}(1). ] This yields a ...

2021

Polar Codes for Q-ary Source Coding

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A new elementary proof of the Prime Number Theorem