What is recorded here?
Arıkan introduced channel polarization and polar codes that achieve the symmetric capacity of binary-input discrete memoryless channels, with encoding and successive cancellation decoding costs of O(N log N) under the stated operation model. A noisy communication link cannot reliably carry arbitrary amounts of information. Shannon had identified its capacity; the remaining challenge was to exhibit code families with provable performance and manageable encoding and decoding. Arıkan recursively combined independent copies of a binary-input channel, then split the result into channels seen by a successive decoder. Most resulting channels become either nearly perfect or nearly useless. Sending information through the good channels and freezing the other inputs gives polar codes. The 2009 paper proves asymptotic symmetric-capacity achievability and O(N log N) encoding and decoding; its initial error bound is polynomial in block length. Symmetric capacity uses equally likely input symbols and need not equal unrestricted capacity for an asymmetric channel. The original paper also says exact general code construction lacks an efficient algorithm and that its basic successive decoder may require impractically long blocks. It proposes approximations and stronger decoders for further study. Reed–Muller coding, Plotkin constructions and Shannon’s framework remain separately credited. The stronger error-rate result credited to Arıkan and Telatar is a separate contribution, not exclusively assigned to this sole-author paper.
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Scientific scope
The capacity result concerns independent uses of a binary-input discrete memoryless channel, block lengths N=2^n and fixed rate below symmetric mutual information. This equals unrestricted capacity for symmetric channels. The original successive-cancellation error rate and operation count are asymptotic; general code construction, finite-block optimality and physical implementation costs remain separate. Frozen-bit averaging in general channels differs from the symmetric-channel bound. Later sharper rates, list decoding and 5G implementations are not credited to this paper alone.
Read the original work
- Arıkan,ChannelPolarization,IEEETransactionsInformationTheory55(7),3051-3073(2009),originaljournal
- AuthorarXiv0807.3917v5 metadata,abstract andversionhistory
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People and systems
Erdal Arıkan
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English catalogue narrative
Arıkan: polar codes approach a channel’s symmetric capacity
Arıkan introduced channel polarization and polar codes that achieve the symmetric capacity of binary-input discrete memoryless channels, with encoding and successive cancellation decoding costs of O(N log N) under the stated operation model.
A noisy communication link cannot reliably carry arbitrary amounts of information. Shannon had identified its capacity; the remaining challenge was to exhibit code families with provable performance and manageable encoding and decoding. Arıkan recursively combined independent copies of a binary-input channel, then split the result into channels seen by a successive decoder. Most resulting channels become either nearly perfect or nearly useless. Sending information through the good channels and freezing the other inputs gives polar codes. The 2009 paper proves asymptotic symmetric-capacity achievability and O(N log N) encoding and decoding; its initial error bound is polynomial in block length. Symmetric capacity uses equally likely input symbols and need not equal unrestricted capacity for an asymmetric channel. The original paper also says exact general code construction lacks an efficient algorithm and that its basic successive decoder may require impractically long blocks. It proposes approximations and stronger decoders for further study. Reed–Muller coding, Plotkin constructions and Shannon’s framework remain separately credited. The stronger error-rate result credited to Arıkan and Telatar is a separate contribution, not exclusively assigned to this sole-author paper.
Scientific scope
The capacity result concerns independent uses of a binary-input discrete memoryless channel, block lengths N=2^n and fixed rate below symmetric mutual information. This equals unrestricted capacity for symmetric channels. The original successive-cancellation error rate and operation count are asymptotic; general code construction, finite-block optimality and physical implementation costs remain separate. Frozen-bit averaging in general channels differs from the symmetric-channel bound. Later sharper rates, list decoding and 5G implementations are not credited to this paper alone.
People and systems
Erdal Arıkan