3 research outputs found
Polar Codes with Mixed-Kernels
A generalization of the polar coding scheme called mixed-kernels is
introduced. This generalization exploits several homogeneous kernels over
alphabets of different sizes. An asymptotic analysis of the proposed scheme
shows that its polarization properties are strongly related to the ones of the
constituent kernels. Simulation of finite length instances of the scheme
indicate their advantages both in error correction performance and complexity
compared to the known polar coding structures
Recursive Descriptions of Polar Codes
Polar codes are recursive general concatenated codes. This property motivates
a recursive formalization of the known decoding algorithms: Successive
Cancellation, Successive Cancellation with Lists and Belief Propagation. Using
such description allows an easy development of these algorithms for arbitrary
polarizing kernels. Hardware architectures for these decoding algorithms are
also described in a recursive way, both for Arikan's standard polar codes and
for arbitrary polarizing kernels
Polar Codes and Their Quantum-Domain Counterparts
Arikan's polar codes are capable of achieving the Shannon's capacity at a low
encoding and decoding complexity, while inherently supporting rate adaptation.
By virtue of these attractive features, polar codes have provided fierce
competition to both the turbo as well as the Low Density Parity Check (LDPC)
codes, making its way into the 5G New Radio (NR). Realizing the significance of
polar codes, in this paper we provide a comprehensive survey of polar codes,
highlighting the major milestones achieved in the last decade. Furthermore, we
also provide tutorial insights into the polar encoder, decoders as well as the
code construction methods. We also extend our discussions to quantum polar
codes with an emphasis on the underlying quantum-to-classical isomorphism and
the syndrome-based quantum polar codes.Comment: 35 pages, accepted for publication in IEEE Communications Surveys and
Tutorial