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 Trans. Inf. Theory},
  year={2017},
  volume={63},
  pages={1410-1424}
}
  • Uzi Pereg, I. Tal
  • Published 1 March 2017
  • Computer Science
  • IEEE Trans. Inf. 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… 
Channel Upgradation for Non-Binary Input Alphabets and MACs
  • Uzi Pereg, I. Tal
  • Mathematics, Computer Science
    IEEE Transactions on Information Theory
  • 2017
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.
Low-complexity quantization of discrete memoryless channels
  • J. Zhang, B. Kurkoski
  • Computer Science, Mathematics
    2016 International Symposium on Information Theory and Its Applications (ISITA)
  • 2016
TLDR
While the KL means algorithm is suboptimal, it produces quantizer designs which have higher mutual information than greedy combining, particularly when the number of quantizer outputs is small, as shown by numerical evaluations.
Universal Polarization for Processes with Memory
  • Boaz Shuval, I. Tal
  • Computer Science, Mathematics
    2019 IEEE International Symposium on Information Theory (ISIT)
  • 2019
TLDR
A transform that is universally polarizing over a set of channels with memory is presented, established under two key properties: memory in the form of an underlying hidden Markov state sequence that is aperiodic and irreducible and a new property: forgetfulness.
Construction of Polar Codes for Arbitrary Discrete Memoryless Channels
TLDR
The construction problem for the general case is addressed, and an algorithm based on successive reduction of the output alphabet size of the subchannels in each recursion step is analyzed, showing that a similar acceleration can be attained for polar codes over finite field alphabets.
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.
Greedy–Merge Degrading has Optimal Power-Law
TLDR
It is established that greedy–merge is optimal in the power-law sense (i.e. the power of <inline-formula> <tex-math notation="LaTeX">$L$ </tex-Math></inline- formula>).
A Fast Two-Phase Monte Carlo Method for Constructing Polar Codes With Arbitrary Binary Kernel
TLDR
Simulation results show that the TPMC method can fix 3200 bits as frozen bits in the second phase without error performance loss, which reduces the computation cost by approximately 92.6% over the MC method.
New results on information theoretic clustering
TLDR
The first polynomial time algorithm for Entropy impurity based clustering with approximation guarantee independent of the number of vectors is given and it is shown that the problem of clustering based on entropy impurity does not admit a PTAS.
Binary Partitions with Approximate Minimum Impurity
TLDR
This work proposes two new splitting procedures that provably achieve nearoptimal impurity and reports experiments that provide evidence that the proposed methods are interesting candidates to be employed in splitting nominal attributes with many values during decision tree/random forest induction.
Approximation Algorithms for Clustering via Weighted Impurity Measures
TLDR
This work presents the first polynomial time algorithm with approximation guarantee independent of the number of points/vector and not relying on any restriction on the components of the vectors for producing clusterings with minimum entropy.

References

SHOWING 1-10 OF 26 REFERENCES
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
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.
Secrecy-Achieving Polar-Coding for Binary-Input Memoryless Symmetric Wire-Tap Channels
A polar coding scheme is introduced in this paper for the wire-tap channel. It is shown that the provided scheme achieves the entire rate-equivocation region for the case of symmetric and degraded
Polar Codes for the m-User MAC
In this paper, polar codes for the $m$-user multiple access channel (MAC) with binary inputs are constructed. It is shown that Ar{\i}kan's polarization technique applied individually to each user
...
1
2
3
...