Expurgated infinite constellations at finite dimensions

Ingber, Amir; Zamir, Ram

doi:10.1109/isit.2012.6283069

Cited by 5 publications

(7 citation statements)

References 9 publications

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“…On the other hand, if we let b to scale linearly with VNR as (1 − √ δ)μ c , where 0 ≤ δ ≤ 1 (see (24)), then according to the error exponent analysis, we expect that the rate of decay (slope) of the error probability 6 The asymptotic rate of decay of the error probability curve maybe defined as which indicates that the slope of the error probability is the same for any finite b. Comparison of the lattice sequential decoder's performance for various values of (fixed) bias term.…”

Section: Simulation Resultsmentioning

confidence: 99%

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On Lattice Sequential Decoding for the Unconstrained AWGN Channel

Abediseid

Alouini

2013

IEEE Trans. Commun.

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In this paper, the performance limits and the computational complexity of the lattice sequential decoder are analyzed for the unconstrained additive white Gaussian noise channel. The performance analysis available in the literature for such a channel has been studied only under the use of the minimum Euclidean distance decoder that is commonly referred to as the lattice decoder. Lattice decoders based on solutions to the NPhard closest vector problem are very complex to implement, and the search for low complexity receivers for the detection of lattice codes is considered a challenging problem. However, the low computational complexity advantage that sequential decoding promises, makes it an alternative solution to the lattice decoder. In this work, we characterize the performance and complexity tradeoff via the error exponent and the decoding complexity, respectively, of such a decoder as a function of the decoding parameter -the bias term. For the above channel, we derive the cut-off volume-to-noise ratio that is required to achieve a good error performance with low decoding complexity.

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Section: Simulation Resultsmentioning

confidence: 99%

“…where E p (µ c ) is the Poltyrev error exponent achieved by the lattice decoder which is defined in (6). Substituting ( 22) into (20) we get…”

Section: Performance Analysis: An Upper Boundmentioning

confidence: 99%

On Lattice Sequential Decoding for the Unconstrained AWGN Channel

Abediseid

Alouini

2013

IEEE Trans. Commun.

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“…Let us examine corollary 3. Assume a sequence of lattices with minimum distance λ 1 [n] = e −δ V −1/n n is available (see [19] for proof of existence). Plugging this back into (43) leads to the following necessary condition for the bound (40) to achieve the unrestricted channel error-exponent…”

Section: Error Exponents For the Awgn Channelmentioning

confidence: 99%

“…where α opt (x) is as defined in (19), σ{x ∈ Ball(z, z )} is the characteristic function of Ball(z, z ), {λ j } ∞ j=0 is the previously defined distance series of Λ 0 , and M is the maximal index j such that λ j ≤ 2r. Proof: We set g(λ) as in (24) noting that it is bounded by λ max = 2r.…”

Section: Edmhsmentioning

confidence: 99%

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Non-random coding error exponent for lattices

Domb

Feder

2012

2012 IEEE International Symposium on Information Theory Proceedings

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An upper bound on the error probability of specific lattices, based on their distance spectrum, is constructed. The derivation is accomplished using a simple alternative to the Minkowski-Hlawka mean-value theorem of the geometry of numbers. In many ways, the new bound greatly resembles the Shulman-Feder bound for linear codes. Based on the new bound, an error exponent is derived for specific lattice sequences (of increasing dimension) over the AWGN channel. Measuring the sequence's gap to capacity, using the new exponent, is demonstrated.

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Study Status and Prospect of Lattice Codes in Wireless Communication

Duan

Zhao

et al. 2015

2015 Fifth International Conference on Instrumentation and Measurement, Computer, Communication and Control (IMCCC)

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Lattice codes can achieve the capacity of additive white Gaussian noise channel with and without power construction. It is well known that lattice codes can provide a classical information theoretic way to obtain achievable rate and performance gains for point-to-point Gaussian channels. The coding scheme based on lattice codes can be used as building blocks for practical applications, such as point-topoint communication systems, Gaussian networks and MIMO communication systems etc. More importantly, lattice codes can be used to investigate new link adaptive coding and modulation schemes and design sparse code multiple access codebooks. So, lattice codes could be a potential candidate for 5G communication. This paper provides a comprehensive review of the state-of-the-art of lattice codes. It first describes the theory of lattice codes. Then, a comprehensive survey to easily understand channel capacity, error exponents and practical lattice codes is outlined. The application of nested lattice codes is also presented for lossy source coding, dirty paper channel coding and relay communication. Finally, some unresolved issues and ongoing developments related to further improvements of lattice codes are highlighted.

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Expurgated infinite constellations at finite dimensions

Cited by 5 publications

References 9 publications

On Lattice Sequential Decoding for the Unconstrained AWGN Channel

On Lattice Sequential Decoding for the Unconstrained AWGN Channel

Non-random coding error exponent for lattices

Study Status and Prospect of Lattice Codes in Wireless Communication

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