| 1. |
- Morgenshtern, Veniamin I., et al.
(författare)
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Capacity Pre-Log of Noncoherent SIMO Channels via Hironaka’s Theorem
- 2013
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 59:7, s. 4213-4229
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Tidskriftsartikel (refereegranskat)abstract
- We find the capacity pre-log of a temporally correlatedRayleigh block-fading single-input multiple-output (SIMO)channel in the noncoherent setting. It is well known that for blocklength $L$ and rank of the channel covariance matrix equal to $Q$, the capacity pre-log in the single-input single-output (SISO) case is given by $1-Q/L$. Here, $Q/L$ can be interpreted as the pre-log penalty incurred by channel uncertainty. Our main result reveals that, by adding only one receive antenna, this penalty can be reduced to $1/L$ and can, hence, be made to vanish for the blocklength$L\to\infty$, even if $Q/L$ remains constant as $L\to\infty$. Intuitively, even though the SISO channels between the transmit antenna and the two receive antennas are statistically independent, the transmit signal induces enough statistical dependence between the corresponding receive signals for the second receive antenna to be able to resolve the uncertainty associated with the first receive antenna’s channel and thereby make the overall system appear coherent. The proof of our main theorem is based on a deep result from algebraic geometry known as Hironaka’s Theorem on the Resolution of Singularities.
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| 2. |
- Yang, Wei, 1987, et al.
(författare)
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Beta-beta bounds: Finite-blocklength analog of the golden formula
- 2018
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 64:9, s. 6236-6256
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Tidskriftsartikel (refereegranskat)abstract
- It is well known that the mutual information between two random variables can be expressed as the difference of two relative entropies that depend on an auxiliary distribution, a relation sometimes referred to as the golden formula. This paper is concerned with a finite-blocklength extension of this relation. This extension consists of two elements: 1) a finite-blocklength channel-coding converse bound by Polyanskiy and Verdú (2014), which involves the ratio of two Neyman-Pearson β functions (beta-beta converse bound); and 2) a novel beta-beta channelcoding achievability bound, expressed again as the ratio of two Neyman-Pearson β functions. To demonstrate the usefulness of this finite-blocklength extension of the golden formula, the beta-beta achievability and converse bounds are used to obtain a finite-blocklength extension of Verdú’s (2002) wideband-slope approximation. The proof parallels the derivation of the latter, with the beta-beta bounds used in place of the golden formula. The beta-beta (achievability) bound is also shown to be useful in cases where the capacity-achieving output distribution is not a product distribution due to, e.g., a cost constraint or structural constraints on the codebook, such as orthogonality or constant composition. As an example, the bound is used to characterize the channel dispersion of the additive exponentialnoise channel and to obtain a finite-blocklength achievability bound (the tightest to date) for multiple-input multiple-output Rayleigh-fading channels with perfect channel state information at the receiver.
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| 3. |
- Yang, Wei, 1987, et al.
(författare)
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Minimum Energy to Send k Bits Over Multiple-Antenna Fading Channels
- 2016
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Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448 .- 1557-9654. ; 62:12, s. 6831-6853
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Tidskriftsartikel (refereegranskat)abstract
- This paper investigates the minimum energy required to transmit k information bits with a given reliability over a multiple-antenna Rayleigh block-fading channel, with and without channel state information (CSI) at the receiver. No feedback is assumed. It is well known that the ratio between the minimum energy per bit and the noise level converges to 1.59 dB as k goes to infinity, regardless of whether CSI is available at the receiver or not. This paper shows that the lack of CSI at the receiver causes a slowdown in the speed of convergence to 1.59 dB as k -> infinity compared with the case of perfect receiver CSI. Specifically, we show that, in the no-CSI case, the gap to 1/root k dB is proportional to ((log k)/ k)(1/3), whereas when perfect CSI is available at the receiver, this gap is proportional to lksa. In both cases, the gap to -1.59 dB is independent of the number of transmit antennas and of the channel's coherence time. Numerically, we observe that, when the receiver is equipped with a single antenna, to achieve an energy per bit of 1.5 dB in the no-CSI case, one needs to transmit at least 7 x 10(7) information bits, whereas 6 x 10(4) bits suffice for the case of perfect CSI at the receiver.
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| 4. |
- Yang, Wei, 1987, et al.
(författare)
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Optimum Power Control at Finite Blocklength
- 2015
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 61:9, s. 4598-4615
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Tidskriftsartikel (refereegranskat)abstract
- This paper investigates the maximal channel coding rate achievable at a given blocklength $n$ and error probability $\epsilon$, when the codewords are subject to a long-term (i.e., averaged-over-all-codeword) power constraint. The second-order term in the large-$n$ expansion of the maximal channel coding rate is characterized both for additive white Gaussian noise (AWGN) channels and for quasi-static fading channels with perfect channel state information available at both the transmitter and the receiver. It is shown that in both cases the second-order term is proportional to $\sqrt{n^{-1}\ln n}$. For the quasi-static fading case, this second-order term is achieved by \emph{truncated channel inversion}, namely, by concatenating a dispersion-optimal code for an AWGN channel subject to a short-term power constraint, with a power controller that inverts the channel whenever the fading gain is above a certain threshold. Easy-to-evaluate approximations of the maximal channel coding rate are developed for both the AWGN and the quasi-static fading case.
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| 5. |
- Yang, Wei, 1987, et al.
(författare)
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Quasi-Static Multiple-Antenna Fading Channels at Finite Blocklength
- 2014
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 60:7, s. 4232-4265
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Tidskriftsartikel (refereegranskat)abstract
- This paper investigates the maximal achievable rate for a given blocklength and error probability over quasi-static multiple-input multiple-output (MIMO) fading channels, with and without channel state information (CSI) at the transmitter and/or the receiver. The principal finding is that outage capacity, despite being an asymptotic quantity, is a sharp proxy for the finite-blocklength fundamental limits of slow-fading channels. Specifically, the channel dispersion is shown to be zero regardless of whether the fading realizations are available at both transmitter and receiver, at only one of them, or at neither of them. These results follow from analytically tractable converse and achievability bounds. Numerical evaluation of these bounds verifies that zero dispersion may indeed imply fast convergence to the outage capacity as the blocklength increases. In the example of a particular $1\times2$ single-input multiple-output (SIMO) Rician fading channel, the blocklength required to achieve $90\%$ of capacity is about an order of magnitude smaller compared to the blocklength required for an AWGN channel with the same capacity. For this specific scenario, the coding/decoding schemes adopted in the LTE-Advanced standard are benchmarked against the finite-blocklength achievability and converse bounds.
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