Channel Upgradation for Non-Binary Input Alphabets and MACs

@article{Pereg2017ChannelUF,
  title={Channel Upgradation for Non-Binary Input Alphabets and MACs},
  author={Uzi Pereg and Ido Tal},
  journal={IEEE Transactions on Information Theory},
  year={2017},
  volume={63},
  pages={1410-1424}
}
  • Uzi Pereg, I. Tal
  • Published 27 August 2013
  • Mathematics, Computer Science
  • IEEE Transactions on Information Theory
Consider a single-user or multiple-access channel with a large output alphabet. A method to approximate the channel by an upgraded version having a smaller output alphabet is presented and analyzed. The original channel is not necessarily symmetric and does not necessarily have a binary input alphabet. Also, the input distribution is not necessarily uniform. The approximation method is instrumental when constructing capacity achieving polar codes for an asymmetric channel with a non-binary… 
Non-Binary Polar Coded System for the Two-User Multiple-Access Channel
  • Guan-Chen Liu, Qi-Yue Yu
  • Computer Science, Mathematics
    ArXiv
  • 2021
TLDR
Simulation results show that the choice of the kernel factors has a significant impact on the block error rate (BLER) performance; moreover, the non-binary polar codes provide a better BLER performance than their binary counterpart in the two-user MAC.
On the Construction of Polar Codes for Channels With Moderate Input Alphabet Sizes
  • I. Tal
  • Computer Science, Mathematics
    IEEE Transactions on Information Theory
  • 2017
TLDR
It is shown that any construction algorithm for channels with moderate input alphabet size, which follows the paradigm of “degrading after each polarization step,” will inherently be impractical with respect to a certain “hard” underlying channel.
On the Construction of Polar Codes for Channels With Moderate Input Alphabet Sizes
  • I. Tal
  • Mathematics, Computer Science
    IEEE Trans. Inf. Theory
  • 2017
TLDR
It is shown that any construction algorithm for channels with moderate input alphabet size, which follows the paradigm of “degrading after each polarization step,” will inherently be impractical with respect to a certain “hard” underlying channel.
Greedy-merge degrading has optimal power-law
  • Assaf Kartowsky, I. Tal
  • Mathematics, Computer Science
    2017 IEEE International Symposium on Information Theory (ISIT)
  • 2017
TLDR
It is established that greedy-merge is optimal in the power-law sense for fixed input alphabet size and variable L, and the upper bound is within a constant factor of an algorithm-independent lower bound.
An Upgrading Algorithm with Optimal Power Law
Consider a channel W along with a given input distribution PX . In certain settings, such as in the construction of polar codes, the output alphabet of W is ‘too large’, and hence we replace W by a
An Upgrading Algorithm with Optimal Power Law
Consider a channel W along with a given input distribution PX . In certain settings, such as in the construction of polar codes, the output alphabet of W is ‘too large’, and hence we replace W by a
Secure Polar Coding for the Two-Way Wiretap Channel
TLDR
This paper designs a low complexity polar coded cooperative jamming scheme that achieves the whole secrecy rate region of the general two-way wiretap channel under the strong secrecy criterion.
Construction of polar codes for arbitrary discrete memoryless channels
TLDR
If the polarizing operation relies on modulo-q addition, it is possible to merge subsets of output symbols without any loss in subchannel capacity, and it is shown that a similar speed-up can be attained for polar codes over finite field alphabets.
Polar Coding Strategies for the Interference Channel With Partial-Joint Decoding
TLDR
It is proved that fully joint decoding in the Han–Kobayashi strategy can be simplified to two types of partial-joint decoding, which are friendly to polar coding with practical decoding algorithms and extended to interference networks to show that partial-Joint decoding is a general method for designing heterogeneous superposition polar coding schemes in interference networks.
Design and Analysis of Communication Schemes via Polar Coding
TLDR
It is shown that secrecy capacity of the wiretap channel under a “strong secrecy constraint” can be achieved using an explicit scheme based on polar codes, and a construction algorithm for polar codes with arbitrarily-sized input alphabets is proposed and studied.
...
1
2
...

References

SHOWING 1-10 OF 39 REFERENCES
Channel Upgradation for Non-Binary Input Alphabets and MACs
TLDR
The approximation method is instrumental when constructing capacity achieving polar codes for an asymmetric channel with a non-binary input alphabet and the wiretap setting as well as the lossy source coding setting.
Constructing polar codes for non-binary alphabets and MACs
  • I. Tal, A. Sharov, A. Vardy
  • Mathematics, Computer Science
    2012 IEEE International Symposium on Information Theory Proceedings
  • 2012
TLDR
The approximation method is used to construct polar codes for both single-user and multiple-access channels with prime input alphabet sizes by approximating them by a degraded version of it having a smaller output alphabet size.
Upgraded Approximation of Non-Binary Alphabets for Polar Code Construction
TLDR
An algorithm is presented for approximating a single-user channel with a primeinput alphabet size and it is shown that this algorithm can be used to reduce the output alphabet size to the input alphabet size in most cases.
Polar coding without alphabet extension for asymmetric channels
  • J. Honda, Hirosuke Yamamoto
  • Mathematics, Computer Science
    2012 IEEE International Symposium on Information Theory Proceedings
  • 2012
TLDR
This work proposes another polar coding scheme for asymmetric channels, which realizes the optimal nonuniform input distribution by randomizing symbols in the frozen bits with an appropriate probability distribution.
Polarization for arbitrary discrete memoryless channels
Channel polarization, originally proposed for binary-input channels, is generalized to arbitrary discrete memoryless channels. Specifically, it is shown that when the input alphabet size is a prime
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 Arikan's construction, the resulting channels will polarize to one
Polar Codes for the $m$-User Multiple Access Channel
  • E. Abbe, E. Telatar
  • Mathematics, Computer Science
    IEEE Transactions on Information Theory
  • 2012
TLDR
It is shown that Arikan's polarization technique applied individually to each user transforms independent uses of an m-user binary input MAC into successive uses of extremal MACs, which have uniform rate regions that are not only polymatroids but matroids and are easy to communicate over.
On the Construction of Polar Codes for Channels With Moderate Input Alphabet Sizes
  • I. Tal
  • Computer Science, Mathematics
    IEEE Transactions on Information Theory
  • 2017
TLDR
It is shown that any construction algorithm for channels with moderate input alphabet size, which follows the paradigm of “degrading after each polarization step,” will inherently be impractical with respect to a certain “hard” underlying channel.
Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels
  • E. Arıkan
  • Mathematics, Computer Science
    IEEE Transactions on Information Theory
  • 2009
TLDR
The paper proves that, given any B-DMC W with I(W) > 0 and any target rate R< I( W) there exists a sequence of polar codes {Cfrn;nges1} such that Cfrn has block-length N=2n, rate ges R, and probability of block error under successive cancellation decoding bounded as Pe(N,R) les O(N-1/4) independently of the code rate.
Performance and construction of polar codes on symmetric binary-input memoryless channels
TLDR
A new construction method for arbitrary symmetric binary memoryless channel (B-MC) with linear complexity in the blocklength is proposed and new upper bound and lower bound of the block error probability of polar codes are derived for the BEC and arbitrary asymmetric B-MC.
...
1
2
3
4
...