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)