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This paper introduces a neural polar decoder (NPD) for deletion channels with a constant deletion rate. Existing polar decoders for deletion channels exhibit high computational complexity of O(N4), where N is the block length. This limits the application of polar codes for deletion channels to short-to-moderate block lengths. In this work, we demonstrate that employing NPDs for deletion channels can reduce the computational complexity. First, we extend the architecture of the NPD to support deletion channels. Specifically, the NPD architecture consists of four neural networks (NNs), each replicating fundamental successive cancellation (SC) decoder operations. To support deletion channels, we change the architecture of only one. The computational complexity of the NPD is O(ANlogN), where the parameter A represents a computational budget determined by the user and is independent of the channel. We evaluate the new extended NPD for deletion channels with deletion rates δ∈{0.01,0.1} and we verify the NPD with the ground truth given by the trellis decoder by Tal et al. We further show that due to the reduced complexity of the NPD, we are able to incorporate list decoding and further improve performance. We believe that the extended NPD presented here could have applications in future technologies like DNA storage.
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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. A key part of this work involves representing the deletion channel using a trellis and describing the plus and minus polar-decoding operations on this trellis. In particular, the plus and minus operations can be seen as combining adjacent trellis stages to yield a new trellis with half as many stages. Using this viewpoint, we prove a weak polarization theorem for standard polar codes on the deletion channel. To achieve strong polarization, we modify this scheme by adding guard bands of repeated zeros between various parts of the codeword. Using this approach, we obtain a scheme whose rate approaches the mutual information and whose probability of error decays exponentially in the cube-root of the block length.
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- PAR ID:
- 10173122
- Date Published:
- Journal Name:
- 2019 IEEE International Symposium on Information Theory (ISIT)
- Page Range / eLocation ID:
- 1362 to 1366
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ISIT.2019.8849705
