Polar Coding for Non-Stationary Channels

DOI10.1109/TIT.2020.3020929zbMATH Open1453.94044arXiv1611.04203OpenAlexW3082374076MaRDI QIDQ5138867

Hessam Mahdavifar

Publication date: 4 December 2020

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Abstract: The problem of polar coding for an arbitrary sequence of independent binary-input memoryless symmetric (BMS) channels $left{W_{i}ight}_{i=1}^N$ is considered. The sequence of channels is assumed to be completely known to both the transmitter and the receiver (a coherent scenario). Also, at each code block transmission, each of the channels is used only once. In other words, a codeword of length $N$ is constructed and then the $i$-th encoded bit is transmitted over $W_i$. The goal is to operate at a rate $R$ close to the average of the symmetric capacities of $W_i$'s, denoted by $overline{I}_N$. To this end, we construct a polar coding scheme using Arikan's channel polarization transform in combination with certain permutations at each polarization level and certain skipped operations. In particular, given a non-stationary sequence of BMS channels $left{W_{i}ight}_{i=1}^N$ and $P_e$, where $0<P_e<1$, we construct a polar code of length $N$ and rate $R$ guaranteeing a block error probability of at most $P_e$ for transmission over $left{W_{i}ight}_{i=1}^N$ such that ${\displaystyle }$ N leq frac{kappa}{(overline{I}_N - R)^{mu}}, ${\displaystyle }$ where $mu$ is a constant and $kappa$ is a constant depending on $P_e$ and $mu$. We further show a numerical upper bound on $mu$ that is: $muleq7.34$ for non-stationary binary erasure channels and $muleq8.54$ for general non-stationary BMS channels. The encoding and decoding complexities of the constructed polar code preserve $O(NlogN)$ complexity of Arikan's polar codes. In an asymptotic sense, when coded bits are transmitted over a non-stationary sequence of BMS channels $left{W_{i}ight}_{i=1}^{infty}$, our proposed scheme achieves the average symmetric capacity ${\displaystyle }$ overline{I}(left{W_i ight}_{i=1}^{infty}) := lim_{N ightarrow infty} frac{1}{N}sum_{i=1}^N I(W_i), ${\displaystyle }$ assuming that the limit exists.

Full work available at URL: https://arxiv.org/abs/1611.04203

zbMATH Keywords

polar codingindependent binary-input memoryless symmetric (BMS) channels

Mathematics Subject Classification ID

Channel models (including quantum) in information and communication theory (94A40) Source coding (94A29)

Related Items (4)

Polar Coding Without Alphabet Extension for Asymmetric Models ⋮ A Simple Proof of Polarization and Polarization for Non-Stationary Memoryless Channels ⋮ Polar Coding for the Broadcast Channel With Confidential Messages: A Random Binning Analogy ⋮ Arikan meets Shannon: polar codes with near-optimal convergence to channel capacity

Recommendations

• Title not available (Why is that?) 👍 👎
• Polarization and polar codes 👍 👎
• Polar Codes for Broadcast Channels 👍 👎
• Polar Codes for the $m$-User Multiple Access Channel 👍 👎
• Capacity-Achieving Rate-Compatible Polar Codes 👍 👎
• Polar-Coded Non-Orthogonal Multiple Access 👍 👎
• On Polar Coding for Side Information Channels 👍 👎
• Polar Coding for Channels With Deletions 👍 👎
• Polar Coding Strategies for the Interference Channel With Partial-Joint Decoding 👍 👎
• Polar Codes for the Two-User Multiple-Access Channel 👍 👎

This page was built for publication: Polar Coding for Non-Stationary Channels

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q5138867)