Finite-Dimensional Infinite Constellations

Ingber, Amir; Zamir, Ram; Feder, Meir

doi:10.1109/tit.2012.2224145

Cited by 32 publications

(53 citation statements)

References 32 publications

(86 reference statements)

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“…2) Further analysis shows that the (38) is in fact a precise asymptotic form of the expurgation bound (here we only presented the upper bound since this contributes directly to the achievability bound). The proof for this fact follows the steps of the proof of [7,Lemma 5]. This fact shows that the analytical bound and its approximations are tight.…”

Section: B Asymptotic Formmentioning

confidence: 68%

“…for Γ[z]. Notes: 1) This bound is different from the ML bound in [7] (an explicit finite-dimensional version of the random coding bound [7]). In fact, the UUB can be viewed as the ML bound with r = ∞.…”

Section: (14)mentioning

confidence: 99%

“…The proof follows from (33), and the approximations of V n and ρ * (see [7,Eqs. (64)-(68)]). We now select α = 1 − β n since any other selection would weaken the bound by a non-constant factor.…”

Section: B Asymptotic Formmentioning

confidence: 99%

“…Recently, Poltyrev's setting was revisited with an emphasis on finite-dimensions [7], where explicit bounds (both upper and lower) on the error probability were derived. Those bounds can be used to derive refinements for the random coding and sphere packing error exponents for the setting, as well as to derive a channel dispersion result [7] [8]. The main interest and strongest results of [7] are above the critical NLD δ cr which plays the same role of the critical rate in classic channel coding [5].…”

Section: Introductionmentioning

confidence: 99%

“…Those bounds can be used to derive refinements for the random coding and sphere packing error exponents for the setting, as well as to derive a channel dispersion result [7] [8]. The main interest and strongest results of [7] are above the critical NLD δ cr which plays the same role of the critical rate in classic channel coding [5].…”

Section: Introductionmentioning

confidence: 99%

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Expurgated infinite constellations at finite dimensions

Ingber

Zamir

2012

2012 IEEE International Symposium on Information Theory Proceedings

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We revisit the setting of a Gaussian channel without power constraints, proposed by Poltyrev, where the codewords are points in Euclidean space and their density is considered instead of the communication rate. We refine the expurgation technique (proposed by Poltyrev for the derivation of the error exponent) to the finite dimensions case and obtain a finitedimensional achievability bound. While the expurgation exponent improves upon the random coding exponent only for certain rates (below a rate known as δex), we show that for finite dimensions the expurgation technique is useful for a broader range of rates. In addition, we present precise asymptotical analysis of the expurgation bound and find the sub-exponential terms, which turn out to be non-negligible.

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Section: B Asymptotic Formmentioning

confidence: 68%

Section: (14)mentioning

confidence: 99%

Section: B Asymptotic Formmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Expurgated infinite constellations at finite dimensions

Ingber

Zamir

2012

2012 IEEE International Symposium on Information Theory Proceedings

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Lattice-Based Coding to Enhance Error Performance of the Hidden Direct Sequence Spread Spectrum

Sanandaji

Falahati

2019

IETE Journal of Research

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Dispersion of infinite constellations in fast fading channels

Vituri

Feder

2012

2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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In this work we extend the setting of communication without power constraint, proposed by Poltyrev, to fast fading channels with channel state information (CSI) at the receiver. The optimal codewords density, or actually the optimal normalized log density (NLD), is considered. Poltyrev's capacity for this channel is the highest achievable NLD, at possibly large block length, that guarantees a vanishing error probability. For a given finite block length n and a fixed error probability ǫ, there is a gap between the highest achievable NLD and Poltyrev's capacity. As in other channels, this gap asymptotically vanishes as the square root of the channel dispersion V over n, multiplied by the inverse Q-function of the allowed error probability. This dispersion, derived in the paper, equals the dispersion of the power constrained fast fading channel at the high SNR regime. Connections to the error exponent of the peak power constrained fading channel are also discussed. I. INTRODUCTIONWireless communication channels are traditionally modeled as fading channels, where the transmitted signal is multiplied by a fading process and observed with additive white Gaussian noise (AWGN). In a fast fading channel the fading process is composed of fading coefficients, modeled as independent and identically distributed (i.i.d.) random variables. This is a reasonable model for many practical wireless communication systems, such as systems that use a (pseudo) random interleaver between the transmitted digital symbols (e.g. BICM techniques) over, e.g., a frequency selective wireless channel. Here we will assume that a perfect knowledge of the channel state information (the fading coefficients) is available at the receiver.Classical coding problems over the fading channels often include a peak or an average power restriction of the transmitted signal. Without power constraint the capacity of the channel is not limited, since we can choose an infinite number of codewords to be arbitrarily far apart from each other, and hence get an arbitrarily small error probability and infinite rate. Nevertheless, coded modulation methods ignore the power constraint by designing infinite constellations (IC), and then taking only a subset of codewords which are included in some "shaping region" to get a finite constellation (FC) that holds the power constraint. Hence, IC is a very convenient framework for designing codes.Poltyrev studied in [1] the IC performance over the AWGN without power constraint. He defined the density (the average number of codewords per unit volume) and the normalized log density (NLD) of the IC, in analogy to the number of codewords and the communication rate in the power constraint model, respectively. He showed that the highest achievable NLD over the unconstrained AWGN channel, with arbitrarily small error probability, is limited by a maximal NLD, sometimes termed the 'Poltyrev's capacity'. He also derived an exact term for the maximal NLD and error exponent bounds using random coding and sphere packing techniques, f...

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Finite-Dimensional Infinite Constellations

Cited by 32 publications

References 32 publications

Expurgated infinite constellations at finite dimensions

Expurgated infinite constellations at finite dimensions

Lattice-Based Coding to Enhance Error Performance of the Hidden Direct Sequence Spread Spectrum

Dispersion of infinite constellations in fast fading channels

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