29,940 research outputs found
Peak-to-average power ratio of good codes for Gaussian channel
Consider a problem of forward error-correction for the additive white
Gaussian noise (AWGN) channel. For finite blocklength codes the backoff from
the channel capacity is inversely proportional to the square root of the
blocklength. In this paper it is shown that codes achieving this tradeoff must
necessarily have peak-to-average power ratio (PAPR) proportional to logarithm
of the blocklength. This is extended to codes approaching capacity slower, and
to PAPR measured at the output of an OFDM modulator. As a by-product the
convergence of (Smith's) amplitude-constrained AWGN capacity to Shannon's
classical formula is characterized in the regime of large amplitudes. This
converse-type result builds upon recent contributions in the study of empirical
output distributions of good channel codes
ℓp-norms of codewords from capacity- and dispersion-achieveing Gaussian codes
It is demonstrated that codewords of good codes for the additive white Gaussian noise (AWGN) channel become more and more isotropically distributed (in the sense of evaluating quadratic forms) and resemble white Gaussian noise (in the sense of ℓp norms) as the code approaches closer to the fundamental limits. In particular, it is shown that the optimal Gaussian code must necessarily have peak-to-average power ratio (PAPR) of order log n.National Science Foundation (U.S.) (Center for Science of Information Grant CCF-0939370
Polar Codes over Fading Channels with Power and Delay Constraints
The inherent nature of polar codes being channel specific makes it difficult
to use them in a setting where the communication channel changes with time. In
particular, to be able to use polar codes in a wireless scenario, varying
attenuation due to fading needs to be mitigated. To the best of our knowledge,
there has been no comprehensive work in this direction thus far. In this work,
a practical scheme involving channel inversion with the knowledge of the
channel state at the transmitter, is proposed. An additional practical
constraint on the permissible average and peak power is imposed, which in turn
makes the channel equivalent to an additive white Gaussian noise (AWGN) channel
cascaded with an erasure channel. It is shown that the constructed polar code
could be made to achieve the symmetric capacity of this channel. Further, a
means to compute the optimal design rate of the polar code for a given power
constraint is also discussed.Comment: 6 pages, 6 figure
Orthogonal Transform Multiplexing with Memoryless Nonlinearity: a Possible Alternative to Traditional Coded-Modulation Schemes
In this paper, we propose a novel joint coding-modulation technique based on
serial concatenation of orthogonal linear transform, such as discrete Fourier
transform (DFT) or Walsh-Hadamard transform (WHT), with memoryless
nonlinearity. We demonstrate that such a simple signal construction may exhibit
properties of a random code ensemble, as a result approaching channel capacity.
Our computer simulations confirm that if the decoder relies on a modified
approximate message passing algorithm, the proposed modulation technique
exhibits performance on par with state-of-the-art coded modulation schemes that
use capacity-approaching component codes. The proposed modulation scheme could
be used directly or as a pre-coder for a conventional orthogonal frequency
division multiplexing (OFDM) transmitter, resulting in a system possessing all
benefits of OFDM along with reduced peak-to-average power ratio (PAPR)
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