# 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} }

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…

## 13 Citations

Non-Binary Polar Coded System for the Two-User Multiple-Access Channel

- Computer Science, MathematicsArXiv
- 2021

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

- Computer Science, MathematicsIEEE Transactions on Information Theory
- 2017

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

- Mathematics, Computer ScienceIEEE Trans. Inf. Theory
- 2017

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

- Mathematics, Computer Science2017 IEEE International Symposium on Information Theory (ISIT)
- 2017

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

- 2020

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

- 2021

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

- Computer Science, MathematicsIEEE Access
- 2018

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

- Mathematics, Computer Science2016 IEEE International Symposium on Information Theory (ISIT)
- 2016

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

- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 2019

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

- Computer Science
- 2015

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.

## References

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Channel Upgradation for Non-Binary Input Alphabets and MACs

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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.

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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.

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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.

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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…

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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…

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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

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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.

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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.

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