Systematic polar coding

Cataloged from PDF version of article.Polar codes were originally introduced as a class of non-systematic linear block codes. This paper gives encoding and decoding methods for systematic polar coding that preserve the low-complexity nature of non-systematic polar coding while guaranteeing the same frame error rate. Simulation results are given to show that systematic polar coding offers significant advantages in terms of bit error rate performance

Polar codes for the two-user multiple-access channel

Arikan's polar coding method is extended to two-user multiple-access channels. It is shown that if the two users of the channel use the Arikan construction, the resulting channels will polarize to one of five possible extremals, on each of which uncoded transmission is optimal. The sum rate achieved by this coding technique is the one that correponds to uniform input distributions. The encoding and decoding complexities and the error performance of these codes are as in the single-user case: $O(n\log n)$ for encoding and decoding, and $o(\exp(-n^{1/2-\epsilon}))$ for block error probability, where $n$ is the block length.Comment: 12 pages. Submitted to the IEEE Transactions on Information Theor

Improved Successive Cancellation Decoding of Polar Codes

As improved versions of successive cancellation (SC) decoding algorithm, successive cancellation list (SCL) decoding and successive cancellation stack (SCS) decoding are used to improve the finite-length performance of polar codes. Unified descriptions of SC, SCL and SCS decoding algorithms are given as path searching procedures on the code tree of polar codes. Combining the ideas of SCL and SCS, a new decoding algorithm named successive cancellation hybrid (SCH) is proposed, which can achieve a better trade-off between computational complexity and space complexity. Further, to reduce the complexity, a pruning technique is proposed to avoid unnecessary path searching operations. Performance and complexity analysis based on simulations show that, with proper configurations, all the three improved successive cancellation (ISC) decoding algorithms can have a performance very close to that of maximum-likelihood (ML) decoding with acceptable complexity. Moreover, with the help of the proposed pruning technique, the complexities of ISC decoders can be very close to that of SC decoder in the moderate and high signal-to-noise ratio (SNR) regime.Comment: This paper is modified and submitted to IEEE Transactions on Communication

Polar coding for the Slepian-Wolf problem based on monotone chain rules

We give a polar coding scheme that achieves the full admissible rate region in the Slepian-Wolf problem without time-sharing. The method is based on a source polarization result using monotone chain rule expansions. © 2012 IEEE

Polar codes for the m-user multiple access channels

Polar codes are constructed for m-user multiple access channels (MAC) whose input alphabet size is a prime number. The block error probability under successive cancelation decoding decays exponentially with the square root of the block length. Although the sum capacity is achieved by this coding scheme, some points in the symmetric capacity region may not be achieved. In the case where the channel is a combination of linear channels, we provide a necessary and sufficient condition characterizing the channels whose symmetric capacity region is preserved upon the polarization process. We also provide a sufficient condition for having a total loss in the dominant face.Comment: 21 page

Challenges and Some New Directions in Channel Coding

Three areas of ongoing research in channel coding are surveyed, and recent developments are presented in each area: spatially coupled Low-Density Parity-Check (LDPC) codes, nonbinary LDPC codes, and polar coding.This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/JCN.2015.00006

Challenges and some new directions in channel coding

Three areas of ongoing research in channel coding are surveyed, and recent developments are presented in each area: Spatially coupled low-density parity-check (LDPC) codes, nonbinary LDPC codes, and polar coding. © 2015 KICS