Summary
2020
Session Number:B03
Session:
Number:B03-1
On the dependency between the code symmetries and the decoding efficiency
Kirill Ivanov, Ruediger Urbanke,
pp.195-199
Publication Date:2020/10/18
Online ISSN:2188-5079
DOI:10.34385/proc.65.B03-1
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Summary:
A framework of monomial codes is considered, which includes linear codes generated by the evaluation of certain monomials. Polar and Reed-Muller codes are the two best-known representatives of such codes and can be considered as two extreme cases. Reed-Muller codes have a large automorphism group but their low-complexity maximum likelihood decoding still remains an open problem. On the other hand, polar codes have much less symmetries but admit the efficient near-ML decoding.
We study the dependency between the code symmetries and the decoding efficiency. We introduce a new family of codes, partially symmetric monomial codes. These codes have a smaller group of symmetries than the Reed-Muller codes and are in this sense "between" RM and polar codes. A lower bound on their parameters is introduced along with the explicit construction which achieves it. Structural properties of these codes are demonstrated and it is shown that they often have a recursive structure.