This paper studies the second-order asymptotics of codingrates for the discrete memoryless multiple-access channel (MAC) with a fixed target error probability. Using constant-composition random coding, coded time-sha...
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This paper studies the second-order asymptotics of codingrates for the discrete memoryless multiple-access channel (MAC) with a fixed target error probability. Using constant-composition random coding, coded time-sharing, and a variant of Hoeffding's combinatorial central limit theorem, an inner bound on the set of locally achievable second-order coding rates is given for each point on the boundary of the capacity region. It is shown that the inner bound for constant-composition random coding includes that recovered by independent identically distributed random coding, and that the inclusion may be strict. The inner bound is extended to the Gaussian MAC via an increasingly fine quantization of the inputs.
Motivated by the growing application of multi-access networks with stringent delay constraints, we investigate the Gaussian multiple-access channel (MAC) in the finite blocklength regime. By applying central limit the...
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Motivated by the growing application of multi-access networks with stringent delay constraints, we investigate the Gaussian multiple-access channel (MAC) in the finite blocklength regime. By applying central limit theorem (CLT) approximations to non-asymptotic information-spectrum inner bounds, we obtain second-order achievable rate regions for the Gaussian MAC with a positive average error probability and per-codeword power constraints. Our achievability results use spherical inputs uniformly distributed on the power shells, which lead to summations of dependent information random variables. However, we conduct the analysis through a convenient yet powerful form of the CLT, called the CLT for functions.
This paper studies the second-order coding rates for memoryless channels with a state sequence known non-causally at the encoder. In the case of finite alphabets, an achievability result is obtained using constant-com...
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This paper studies the second-order coding rates for memoryless channels with a state sequence known non-causally at the encoder. In the case of finite alphabets, an achievability result is obtained using constant-composition random coding, and by using a small fraction of the block to transmit the empirical distribution of the state sequence. For error probabilities less than 0.5, it is shown that the second-orderrate improves on an existing one based on independent and identically distributed random coding. In the Gaussian case (dirty paper coding) with an almost-sure power constraint, an achievability result is obtained using random coding over the surface of a sphere, and using a small fraction of the block to transmit a quantized description of the state power. It is shown that the second-order asymptotics are identical to the single-user Gaussian channel of the same input power without a state.
In this paper, second-order coding rate of channel coding is discussed for general sequence of channels. The optimum second-order transmission rate with a constant error constraint is obtained by using the information...
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In this paper, second-order coding rate of channel coding is discussed for general sequence of channels. The optimum second-order transmission rate with a constant error constraint is obtained by using the information spectrum method. We apply this result to the discrete memoryless case, the discrete memoryless case with a cost constraint, the additive Markovian case, and the Gaussian channel case with an energy constraint. We also clarify that the Gallager bound does not give the optimum evaluation in the second-order coding rate.
This paper considers the problem of channel coding with a given (possibly suboptimal) maximum-metric decoding rule. A cost-constrained random-coding ensemble with multiple auxiliary costs is introduced, and is shown t...
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This paper considers the problem of channel coding with a given (possibly suboptimal) maximum-metric decoding rule. A cost-constrained random-coding ensemble with multiple auxiliary costs is introduced, and is shown to achieve error exponents and second-order coding rates matching those of constant-composition random coding, while being directly applicable to channels with infinite or continuous alphabets. The number of auxiliary costs required to match the error exponents and second-orderrates of constant-composition coding is studied, and is shown to be at most two. For independent identically distributed random coding, asymptotic estimates of two well-known non-asymptotic bounds are given using saddlepoint approximations. Each expression is shown to characterize the asymptotic behavior of the corresponding random-coding bound at both fixed and varying rates, thus unifying the regimes characterized by error exponents, second-orderrates, and moderate deviations. For fixed rates, novel exact asymptotics expressions are obtained to within a multiplicative 1 + o(1) term. Using numerical examples, it is shown that the saddlepoint approximations are highly accurate even at short block lengths.
We present a novel achievability bound for the Wyner-Ahlswede-Korner (WAK) problem of lossless source coding with rate-limited side-information. This bound is proved using ideas from channel simulation and channel res...
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ISBN:
(纸本)9781479904464
We present a novel achievability bound for the Wyner-Ahlswede-Korner (WAK) problem of lossless source coding with rate-limited side-information. This bound is proved using ideas from channel simulation and channel resolvability. The bound improves on all previous non-asymptotic bounds on the error probability of the WAK problem. We also present achievable second-order coding rates by applying the multidimensional Berry-Esseen theorem to our new non-asymptotic bound.
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