• Corpus ID: 56475951

Polar-like Codes and Asymptotic Tradeoff among Block Length, Code Rate, and Error Probability

  title={Polar-like Codes and Asymptotic Tradeoff among Block Length, Code Rate, and Error Probability},
  author={Hsin-Po Wang and Iwan M. Duursma},
A general framework is proposed that includes polar codes over arbitrary channels with arbitrary kernels. The asymptotic tradeoff among block length $N$, code rate $R$, and error probability $P$ is analyzed. Given a tradeoff between $N,P$ and a tradeoff between $N,R$, we return an interpolating tradeoff among $N,R,P$ (Theorem 5). $\def\Capacity{\text{Capacity}}$Quantitatively, if $P=\exp(-N^{\beta^*})$ is possible for some $\beta^*$ and if $R=\Capacity-N^{1/\mu^*}$ is possible for some $1/\mu… 

Log-Logarithmic Time Pruned Polar Coding

A pruned variant of polar coding is proposed for binary erasure channel (BEC) and has the lowest per-bit time complexity among all capacity-achieving codes known to date.

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A constructive version of Shannon’s theorem with near-optimal convergence to capacity as a function of the block length is resolved, which resolves a central theoretical challenge associated with the attainment of Shannon capacity.



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This paper studies the performance of binary polar codes that are obtained from non-binary algebraic geometry codes using concatenation and finds that for each binary kernels of a given length $n$ there is an optimal choice.

Relaxed Polar Codes

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A unified framework to characterize the relationship between R, N, P<sub>e</sub>, and W is developed and it is proved that polar codes are not affected by error floors.

Polar Code Moderate Deviation: Recovering the Scaling Exponent

It is shown that polar coding is able to produce a series of codes that achieve capacity on symmetric binary-input memoryless channels and the latest result in the moderate deviation regime does not imply the scaling exponent regime as a special case.

Polar Codes with Exponentially Small Error at Finite Block Length

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Scaling Exponent of List Decoders With Applications to Polar Codes

It is shown that under MAP decoding, although the introduction of a list can significantly improve the involved constants, the scaling exponent itself, i.e., the speed at which capacity is approached, stays unaffected for any finite list size.

Near-optimal finite-length scaling for polar codes over large alphabets

  • H. PfisterR. Urbanke
  • Computer Science
    2016 IEEE International Symposium on Information Theory (ISIT)
  • 2016
The primary result is that, for any γ > 0 and δ > 0, there is a q<sub>0</sub> such that the fraction of effective channels with erasure rate at most N<sup>-γ</sup> is at least 1 - ε - O(N<Sup>-1/2+δ</sup>.

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A polar code-based concatenated scheme to be used in Optical Transport Networks (OTNs) is proposed and it is shown that the proposed scheme outperforms the existing methods by closing the gap to the capacity while avoiding error floor, and maintaining a low complexity at the same time.