4 research outputs found
On Distance Properties of Convolutional Polar Codes
A lower bound on minimum distance of convolutional polar codes is provided.
The bound is obtained from the minimum weight of generalized cosets of the
codes generated by bottom rows of the polarizing matrix. Moreover, a
construction of convolutional polar subcodes is proposed, which provides
improved performance under successive cancellation list decoding. For
sufficiently large list size, the decoding complexity of convolutional polar
subcodes appears to be lower compared to Arikan polar subcodes with the same
performance. The error probability of successive cancellation list decoding of
convolutional polar subcodes is lower than that of Arikan polar subcodes with
the same list size.Comment: 8 pages, 5 figures, submitted to IEEE Transactions on Communication
Convolutional Polar Codes on Channels with Memory using Tensor Networks
Arikan's recursive code construction is designed to polarize a collection of
memoryless channels into a set of good and a set of bad channels, and it can be
efficiently decoded using successive cancellation. It was recently shown that
the same construction also polarizes channels with memory, and a generalization
of successive cancellation decoder was proposed with a complexity that scales
like the third power of the channel's memory size. In another line of work, the
polar code construction was extended by replacing the block polarization kernel
by a convoluted kernel. Here, we present an efficient decoding algorithm for
finite-state memory channels that can be applied to polar codes and
convolutional polar codes. This generalization is most effectively described
using the tensor network formalism, and the manuscript presents a
self-contained description of the required basic concepts. We use numerical
simulations to study the performance of these algorithms for practically
relevant code sizes and find that the convolutional structure outperforms the
standard polar codes on a variety of channels with memory
Efficient List Decoding of Convolutional Polar Codes
An efficient implementation of min-sum SC/list decoding of convolutional
polar codes is proposed. The complexity of the proposed implementation of SC
decoding is more than two times smaller than the straightforward
implementation. Moreover, the proposed list decoding algorithm does not require
to copy any LLRs during decoding.Comment: 10 pages, 6 figure
Convolutional Polar Kernels
A family of polarizing kernels is presented together with
polynomial-complexity algorithm for computing scaling exponent. The proposed
convolutional polar kernels are based on convolutional polar codes, also known
as b-MERA codes. For these kernels, a polynomial-complexity algorithm is
proposed to find weight spectrum of unrecoverable erasure patterns, needed for
computing scaling exponent. As a result, we obtain scaling exponent and
polarization rate for convolutional polar kernels of size up to 1024.Comment: 10 pages, 3 figures. Submitted to IEEE TCO