A Family of Capacity-Achieving Abelian Codes for the Binary Erasure Channel

Natarajan, Lakshmi Prasad and Krishnan, Prasad (2022) A Family of Capacity-Achieving Abelian Codes for the Binary Erasure Channel. In: 27th National Conference on Communications, NCC 2022, 24 May 2022 through 27 May 2022, Virtual, Online.

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Abstract

We identify a large family of abelian codes that achieve the capacity of the binary erasure channel (BEC) under bit-MAP decoding. The codes in this family have rich automorphism groups, their lengths are odd integers, and they can asymptotically (in the block length) achieve any code rate. This family contains codes of prime power block lengths that were originally identified by Berman (1967) and later inves-tigated by Blackmore and Norton (2001), and also contains their generalization to any odd block length. We use Rajan and Siddiqi's (1992) characterization of abelian codes using discrete Fourier transform (DFT) to identify our code family and study their automorphism groups. We then use a result of Kumar, Calderbank and Pfister (2016) that relates the automorphism group of a code to its performance in the BEC to show that this code family achieves BEC capacity. The full version of this paper including the proofs of all claims and simulation results is available online [1] © 2022 IEEE.

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IITH Creators:
IITH CreatorsORCiD
Natarajan, Lakshmi Prasadhttp://orcid.org/0000-0003-1552-5240
Item Type: Conference or Workshop Item (Paper)
Uncontrolled Keywords: Abelian codes; Automorphism groups; Binary erasure channel; Block lengths; Code rates; Generalisation; MAP decoding; Odd integers; Pfister; Power
Subjects: Electrical Engineering
Divisions: Department of Electrical Engineering
Depositing User: . LibTrainee 2021
Date Deposited: 02 Aug 2022 12:01
Last Modified: 02 Aug 2022 12:01
URI: http://raiith.iith.ac.in/id/eprint/10068
Publisher URL: http://doi.org/10.1109/NCC55593.2022.9806780
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