Polar Codes for Channels with Insertions, Deletions, and Substitutions

  title={Polar Codes for Channels with Insertions, Deletions, and Substitutions},
  author={Henry D. Pfister and Ido Tal},
  journal={2021 IEEE International Symposium on Information Theory (ISIT)},
  • H. Pfister, I. Tal
  • Published 2021
  • Computer Science, Mathematics
  • 2021 IEEE International Symposium on Information Theory (ISIT)
This paper presents a coding scheme for an insertion deletion substitution channel. We extend a previous scheme for the deletion channel where polar codes are modified by adding “guard bands” between segments. In the new scheme, each guard band is comprised of a middle segment of ‘1’ symbols, and left and right segments of ‘0’ symbols. Our coding scheme allows for a regular hidden-Markov input distribution, and achieves the information rate between the input and corresponding output of such a… Expand


Reliable communication over channels with insertions, deletions, and substitutions
A new block code is introduced which is capable of correcting multiple insertion, deletion, and substitution errors. The code consists of nonlinear inner codes, which we call "watermark"" codes,Expand
Polar Codes for the Deletion Channel: Weak and Strong Polarization
This paper presents the first proof of polarization for the deletion channel with a constant deletion rate and a regular hidden-Markov input distribution, and proves a weak polarization theorem for standard polar codes on the delete channel. Expand
Polar Coding for Deletion Channels: Theory and Implementation
This paper presents an implementation of low-complexity polar SC decoder for deletion channels, and proves polarization theorems for the polar bit-channels in presence of deletions when $d$ = o(n), which implies that the coding scheme is capable of achieving the symmetric information rate for this concatenated scheme with diminishing error probabilities as $n$ becomes large. Expand
Polar codes for channels with deletions
The proposed algorithm is based on the recursive structure of polar codes and it directly adopts the outputs of deletion channel to perform decoding without any preprocessing, and it is no longer required to check all (Nd) possible locations of the deletions. Expand
On the Capacity of Channels With Deletions and States
  • Yonglong Li, V. Tan
  • Computer Science, Mathematics
  • IEEE Transactions on Information Theory
  • 2021
It is shown that the polar coding scheme proposed by Tal, Pfister, Fazeli, and Vardy achieves the capacity of the binary deletion channel and that the stationary capacity can be approached by a sequence of Markov processes with increasing Markovian orders. Expand
Successive Cancellation Decoding of Polar Codes for Insertion/Deletion Error Correction
Simulation results show that the presented SC list decoding gives lower block error rates compared to existing IDS error correction coding based on LDPC code and synchronization marker. Expand
Construction of polar codes for channels with memory
A generalization of successive cancellation algorithm for channels with memory where the complexity is polynomial in the number of states is proposed and two polar coding scheme are proposed to generate codewords following non-i.i.d. process required to achieve the capacity. Expand
A Survey of Results for Deletion Channels and Related Synchronization Channels
Through the development and analysis of low-density parity-check codes and related families of codes, the authors understand how to achieve near-capacity performance for such channels extremely efficiently. Expand
Optimal Coding for the Binary Deletion Channel With Small Deletion Probability
A new systematic approach is developed to demonstrate that capacity can be computed in a series expansion for small deletion probability, and that the optimal input distribution is obtained by smoothly perturbing the iid Bernoulli (1/2) process. Expand
Upper Bounds on the Capacity of Deletion Channels Using Channel Fragmentation
  • M. Rahmati, T. Duman
  • Mathematics, Computer Science
  • IEEE Transactions on Information Theory
  • 2015
It is proved certain inequality relations among the capacities of the original channels and those of the introduced subch channels prove useful in deriving tighter capacity upper bounds for: 1) independent identically distributed (i.i.d.) deletion channels when the deletion probability exceeds 0.65 and nonbinary deletion channels. Expand