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

@article{Wang2018PolarlikeCA, title={Polar-like Codes and Asymptotic Tradeoff among Block Length, Code Rate, and Error Probability}, author={Hsin-Po Wang and Iwan M. Duursma}, journal={ArXiv}, year={2018}, volume={abs/1812.08112} }

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…

## 3 Citations

### Log-Logarithmic Time Pruned Polar Coding

- Computer ScienceIEEE 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.

### Polar Codes’ Simplicity, Random Codes’ Durability

- Computer ScienceIEEE Transactions on Information Theory
- 2021

The core theme is to incorporate polar coding with large, random, dynamic kernels (which boosts the performance to random’s realm), and the putative codes are optimal in the following manner.

### Arikan meets Shannon: Polar codes with near-optimal convergence to channel capacity

- Computer ScienceIEEE Transactions on Information Theory
- 2022

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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