# Polar Codes’ Simplicity, Random Codes’ Durability

@article{Wang2021PolarCS,
title={Polar Codes’ Simplicity, Random Codes’ Durability},
author={Hsin-Po Wang and Iwan M. Duursma},
journal={IEEE Transactions on Information Theory},
year={2021},
volume={67},
pages={1478-1508}
}
• Published 19 December 2019
• Computer Science
• IEEE Transactions on Information Theory
Over any discrete memoryless channel, we offer error correction codes such that: for one, their block error probabilities and code rates scale like random codes’; and for two, their encoding and decoding complexities scale like polar codes’. Quantitatively, for any constants <inline-formula> <tex-math notation="LaTeX">$\pi,\rho >0$ </tex-math></inline-formula> such that <inline-formula> <tex-math notation="LaTeX">$\pi +2\rho < 1$ </tex-math></inline-formula>, we construct a sequence of block…
6 Citations

## Figures and Tables from this paper

Arikan meets Shannon: Polar codes with near-optimal convergence to channel capacity
• Computer Science
STOC
• 2020
The converse theorem shows extreme unpredictability of even a single message bit for random coding at rates slightly above capacity for binary-input memoryless symmetric channels with Shannon capacity I(W) resolving a central theoretical challenge associated with the attainment of Shannon capacity.
An Optimized Successive Cancellation List Decoder for Polar Codes Combined with Critical Set
IWCMC
• 2022
This paper combines the SCL decoder and the critical set to form a new decoder, which can stably reduce the number of operations by 65% $\sim$ 70% and maintain similar decoding performance to SCLDecoder.
Accelerating Polarization via Alphabet Extension
• Computer Science
ArXiv
• 2022
The main contribution is showing that the dynamic of TECs converges to an almost– one-parameter family of channels, which then leads to an upper bound of 3 .
Sub-4.7 Scaling Exponent of Polar Codes
• Computer Science
ArXiv
• 2022
Polar code visibly approaches channel capacity in practice and is thereby a constituent code of the 5G standard, however, the per- formance of short-length polar code has rooms for improvement that could hinder its adoption by a wider class of applications.
Parallelism versus Latency in Simplified Successive-Cancellation Decoding of Polar Codes
• Computer Science
2021 IEEE International Symposium on Information Theory (ISIT)
• 2021
The tightness of the bound on SSC decoding latency and the applicability of the foregoing results is validated through extensive simulations.
Log-Logarithmic Time Pruned Polar Coding
• Computer Science
IEEE Transactions on Information Theory
• 2021
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.

## References

SHOWING 1-10 OF 117 REFERENCES
Binary Linear Codes with Optimal Scaling: Polar Codes with Large Kernels
• Computer Science
2018 IEEE Information Theory Workshop (ITW)
• 2018
We prove that, at least for the binary erasure channel, the polar-coding paradigm gives rise to codes that not only approach the Shannon limit but, in fact, do so under the best possible scaling of
Polar codes for discrete alphabets
• Eren Sasoglu
• Computer Science
2012 IEEE International Symposium on Information Theory Proceedings
• 2012
This paper answers the question in the affirmative by giving a method to polarize all discrete memoryless channels and sources and yields codes that retain the low encoding and decoding complexity of binary polar codes.
Performance of polar codes for channel and source coding
• Computer Science
2009 IEEE International Symposium on Information Theory
• 2009
Polar codes, introduced recently by Arıkan, are the first family of codes known to achieve capacity of symmetric channels using a low complexity successive cancellation decoder, and several techniques to improve their finite-length performance are discussed.
Construction of polar codes for channels with memory
• Computer Science
2015 IEEE Information Theory Workshop - Fall (ITW)
• 2015
A generalization of successive cancellation algorithm for channels with memory where the complexity is polynomial in the number of states is proposed and two polar coding scheme are proposed to generate codewords following non-i.i.d. process required to achieve the capacity.
Extremes of random coding error exponents
• Computer Science
2011 IEEE International Symposium on Information Theory Proceedings
• 2011
We show that Gallager's random coding error exponent of an arbitrary binary-input memoryless symmetric channel is upper-bounded by that of the binary erasure channel and lower-bounded by that of the
Multilevel polarization of polar codes over arbitrary discrete memoryless channels
• Computer Science
2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
• 2011
It is shown that perfect transmission of certain information letters over partially perfect channels is possible and it is also shown through an example that polar codes do not achieve the capacity of coset codes over arbitrary channels.
Universal bounds on the scaling behavior of polar codes
• Computer Science
2012 IEEE International Symposium on Information Theory Proceedings
• 2012
There exists a universal parameter μ such that for any binary memoryless symmetric channel W with capacity W, reliable communication requires rates that satisfy R <; I(W) - αN-1/μ, where α is a positive constant and N is the block-length.
Polar codes for q-ary source coding
• Computer Science
2010 IEEE International Symposium on Information Theory
• 2010
This note extends the result of Korada and Urbanke on polar coding to the case when the representation alphabet is q-ary, for q a prime number.
Binary Linear Codes with Optimal Scaling and Quasi-Linear Complexity
• Computer Science
ArXiv
• 2017
This work presents the first family of binary codes that attains optimal scaling and quasi-linear complexity, at least for the binary erasure channel (BEC), and proves that there exist $\ell\times\ell$ binary kernels, such that polar codes constructed from these kernels achieve scaling exponent that tends to the optimal value of $2$ as $\ell$ grows.
Finite-Level Quantization Procedures for Construction and Decoding of Polar Codes
• Computer Science
2020 IEEE International Symposium on Information Theory (ISIT)
• 2020
It is proved that certain D-level quantization schemes polarize and give a lower bound on achievable rates and it is shown that a broad class of quantization procedures result in a weaker form of the polarization phenomenon.