92 research outputs found
Construction of Capacity-Achieving Lattice Codes: Polar Lattices
In this paper, we propose a new class of lattices constructed from polar
codes, namely polar lattices, to achieve the capacity \frac{1}{2}\log(1+\SNR)
of the additive white Gaussian-noise (AWGN) channel. Our construction follows
the multilevel approach of Forney \textit{et al.}, where we construct a
capacity-achieving polar code on each level. The component polar codes are
shown to be naturally nested, thereby fulfilling the requirement of the
multilevel lattice construction. We prove that polar lattices are
\emph{AWGN-good}. Furthermore, using the technique of source polarization, we
propose discrete Gaussian shaping over the polar lattice to satisfy the power
constraint. Both the construction and shaping are explicit, and the overall
complexity of encoding and decoding is for any fixed target error
probability.Comment: full version of the paper to appear in IEEE Trans. Communication
Artificial-Noise-Aided Physical Layer Phase Challenge-Response Authentication for Practical OFDM Transmission
Recently, we have developed a PHYsical layer Phase Challenge-Response
Authentication Scheme (PHY-PCRAS) for independent multicarrier transmission. In
this paper, we make a further step by proposing a novel artificial-noise-aided
PHY-PCRAS (ANA-PHY-PCRAS) for practical orthogonal frequency division
multiplexing (OFDM) transmission, where the Tikhonov-distributed artificial
noise is introduced to interfere with the phase-modulated key for resisting
potential key-recovery attacks whenever a static channel between two legitimate
users is unfortunately encountered. Then, we address various practical issues
for ANA-PHY-PCRAS with OFDM transmission, including correlation among
subchannels, imperfect carrier and timing recoveries. Among them, we show that
the effect of sampling offset is very significant and a search procedure in the
frequency domain should be incorporated for verification. With practical OFDM
transmission, the number of uncorrelated subchannels is often not sufficient.
Hence, we employ a time-separated approach for allocating enough subchannels
and a modified ANA-PHY-PCRAS is proposed to alleviate the discontinuity of
channel phase at far-separated time slots. Finally, the key equivocation is
derived for the worst case scenario. We conclude that the enhanced security of
ANA-PHY-PCRAS comes from the uncertainty of both the wireless channel and
introduced artificial noise, compared to the traditional challenge-response
authentication scheme implemented at the upper layer.Comment: 33 pages, 13 figures, submitted for possible publicatio
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