8,636 research outputs found
A Multi-Kernel Multi-Code Polar Decoder Architecture
Polar codes have received increasing attention in the past decade, and have
been selected for the next generation of wireless communication standard. Most
research on polar codes has focused on codes constructed from a
polarization matrix, called binary kernel: codes constructed from binary
kernels have code lengths that are bound to powers of . A few recent works
have proposed construction methods based on multiple kernels of different
dimensions, not only binary ones, allowing code lengths different from powers
of . In this work, we design and implement the first multi-kernel successive
cancellation polar code decoder in literature. It can decode any code
constructed with binary and ternary kernels: the architecture, sized for a
maximum code length , is fully flexible in terms of code length, code
rate and kernel sequence. The decoder can achieve frequency of more than
GHz in nm CMOS technology, and a throughput of Mb/s. The area
occupation ranges between mm for and mm for
. Implementation results show an unprecedented degree of
flexibility: with , up to code lengths can be decoded with
the same hardware, along with any kernel sequence and code rate
Magic state distillation with punctured polar codes
We present a scheme for magic state distillation using punctured polar codes.
Our results build on some recent work by Bardet et al. (ISIT, 2016) who
discovered that polar codes can be described algebraically as decreasing
monomial codes. Using this powerful framework, we construct tri-orthogonal
quantum codes (Bravyi et al., PRA, 2012) that can be used to distill magic
states for the gate. An advantage of these codes is that they permit the
use of the successive cancellation decoder whose time complexity scales as
. We supplement this with numerical simulations for the erasure
channel and dephasing channel. We obtain estimates for the dimensions and error
rates for the resulting codes for block sizes up to for the erasure
channel and for the dephasing channel. The dimension of the
triply-even codes we obtain is shown to scale like for the binary
erasure channel at noise rate and for the dephasing
channel at noise rate . The corresponding bit error rates drop to
roughly for the erasure channel and for
the dephasing channel respectively.Comment: 18 pages, 4 figure
Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey
This paper provides a comprehensive review of the domain of physical layer
security in multiuser wireless networks. The essential premise of
physical-layer security is to enable the exchange of confidential messages over
a wireless medium in the presence of unauthorized eavesdroppers without relying
on higher-layer encryption. This can be achieved primarily in two ways: without
the need for a secret key by intelligently designing transmit coding
strategies, or by exploiting the wireless communication medium to develop
secret keys over public channels. The survey begins with an overview of the
foundations dating back to the pioneering work of Shannon and Wyner on
information-theoretic security. We then describe the evolution of secure
transmission strategies from point-to-point channels to multiple-antenna
systems, followed by generalizations to multiuser broadcast, multiple-access,
interference, and relay networks. Secret-key generation and establishment
protocols based on physical layer mechanisms are subsequently covered.
Approaches for secrecy based on channel coding design are then examined, along
with a description of inter-disciplinary approaches based on game theory and
stochastic geometry. The associated problem of physical-layer message
authentication is also introduced briefly. The survey concludes with
observations on potential research directions in this area.Comment: 23 pages, 10 figures, 303 refs. arXiv admin note: text overlap with
arXiv:1303.1609 by other authors. IEEE Communications Surveys and Tutorials,
201
Error Coefficient-reduced Polar/PAC Codes
Polar codes are normally designed based on the reliability of the
sub-channels in the polarized vector channel. There are various methods with
diverse complexity and accuracy to evaluate the reliability of the
sub-channels. However, designing polar codes solely based on the sub-channel
reliability may result in poor Hamming distance properties. In this work, we
propose a different approach to design the information set for polar codes and
PAC codes where the objective is to reduce the number of codewords with minimum
weight (a.k.a. error coefficient) of a code designed for maximum reliability.
This approach is based on the coset-wise characterization of the rows of polar
transform involved in the formation of the minimum-weight
codewords. Our analysis capitalizes on the properties of the polar transform
based on its row and column indices. The numerical results show that the
designed codes outperform PAC codes and CRC-Polar codes at the practical block
error rate of . Furthermore, a by-product of the combinatorial
properties analyzed in this paper is an alternative enumeration method of the
minimum-weight codewords.Comment: 19 pages, 10 figures, 4 tables, 2 listing
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