The second-order coding rate of the multiple-input multiple-output (MIMO) quasi-static Rayleigh fading channel is studied. We tackle this problem via an information-spectrum approach and statistical bounds based on re...
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The second-order coding rate of the multiple-input multiple-output (MIMO) quasi-static Rayleigh fading channel is studied. We tackle this problem via an information-spectrum approach and statistical bounds based on recent random matrix theory techniques. We derive a central limit theorem (CLT) to analyze the information density in the regime where the block length n and the number of transmit and receive antennas K and N, respectively, grow simultaneously large. This result leads to the characterization of closed-form upper and lower bounds on the optimal average error probability when the codingrate is within Omicron(1/root nK) of the asymptotic capacity.
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 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.
The classical-input quantum-output (cq) wiretap channel is a communication model involving a classical sender X, a legitimate quantum receiver B, and a quantum eavesdropper E. The goal of a private communication proto...
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The classical-input quantum-output (cq) wiretap channel is a communication model involving a classical sender X, a legitimate quantum receiver B, and a quantum eavesdropper E. The goal of a private communication protocol that uses such a channel is for the sender X to transmit a message in such a way that the legitimate receiver B can decode it reliably, while the eavesdropper E learns essentially nothing about which message was transmitted. The epsilon-one-shot private capacity of a cq wiretap channel is equal to the maximum number of bits that can be transmitted over the channel, such that the privacy error is no larger than epsilon is an element of (0, 1). The present paper provides a lower bound on the epsilon-one-shot private classical capacity, by exploiting the recently developed techniques of Anshu, Devabathini, Jain, and Warsi, called position-based coding and convex splitting. The lower bound is equal to a difference of the hypothesis testing mutual information between X and B and the "alternate" smooth max-information between X and E. The one-shot lower bound then leads to a non-trivial lower bound on the second-order coding rate for private classical communication over a memoryless cq wiretap channel.
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.
This paper investigates the first-and second-order maximum achievable rates of codes with/without cost constraints for mixed channels whose channel law is characterized by a general mixture of (at most) uncountably ma...
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This paper investigates the first-and second-order maximum achievable rates of codes with/without cost constraints for mixed channels whose channel law is characterized by a general mixture of (at most) uncountably many stationary and memoryless discrete channels. These channels are referred to as mixed memoryless channels with general mixture and include the class of mixed memoryless channels of finitely or countably memoryless channels as a special case. For the mixed memoryless channels with general mixture, the first-ordercoding theorem which gives a formula for the e-capacity is established, and then a direct part of the second-ordercoding theorem is provided. A subclass of mixed memoryless channels whose component channels can be ordered according to their capacity is introduced, and the first-and second-ordercoding theorems are established. It is shown that the established formulas reduce to several known formulas for restricted scenarios.
In this paper, we consider single-and multi-user Gaussian channels with feedback under expected power constraints and with non-vanishing error probabilities. In the first of two contributions, we study asymptotic expa...
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In this paper, we consider single-and multi-user Gaussian channels with feedback under expected power constraints and with non-vanishing error probabilities. In the first of two contributions, we study asymptotic expansions for the additive white Gaussian noise (AWGN) channel with feedback under the average error probability formalism. By drawing ideas from Gallager and Nakiboglu's work for the direct part and the meta-converse for the converse part, we establish the e-capacity and show that it depends on epsilon in general and so the strong converse fails to hold. Furthermore, we provide bounds on the second-order term in the asymptotic expansion. We show that for any positive integer L, the second-order term is bounded between a term proportional to -ln(L)n (where ln(L)(center dot) is the L-fold nested logarithm function) and a term proportional to +(n ln n)(1/2), where n is the blocklength. The lower bound on the second-order term shows that feedback does provide an improvement in the maximal achievable rate over the case where no feedback is available. In our second contribution, we establish the e-capacity region for the AWGN multiple access channel with feedback under the expected power constraint by combining ideas from hypothesis testing, information spectrum analysis, Ozarow's coding scheme, and power control.
We introduce a novel mechanism, called timid/bold coding, by which feedback can be used to improve coding performance. For a certain class of DMCs, called compound-dispersion channels, we show that timid/bold coding a...
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We introduce a novel mechanism, called timid/bold coding, by which feedback can be used to improve coding performance. For a certain class of DMCs, called compound-dispersion channels, we show that timid/bold coding allows for an improved second-order coding rate compared with coding without feedback. For DMCs that are not compound dispersion, we show that feedback does not improve the second-order coding rate. Thus we completely determine the class of DMCs for which feedback improves the second-order coding rate. An upper bound on the second-order coding rate is provided for compound-dispersion DMCs. We also show that feedback does not improve the second-order coding rate for very noisy DMCs. The main results are obtained by relating feedback codes to certain controlled diffusions.
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.
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