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...ceding information-estimation relationships have found a number of applications, e.g., in nonlinear filtering [1], [3], in multiuser detection [4], in power allocation over parallel Gaussian channels =-=[5]-=-, [6], in the proof of Shannon’s entropy power inequality (EPI) and its generalizations [2], [7], [8], and in the treatment of the capacity region of several multiuser channels [9]–[11]. Relationships...

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...nificantly from the optimal Gaussian distributions. Thus, it is of interest to revisit the linear precoding problem under the constraint that each input follows a specified discrete constellation. In =-=[8]-=- the optimal power allocation for parallel noninteracting channels with arbitrary inputs is obtained exploiting the relation between the mutual information and the minimum mean-square error (MMSE) fou...

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...present correspondence, the evidence so far is rather convincing that using MMSE in lieu of Fisher’s information yields much crisper proofs in addition to a wide variety of new results (e.g., [5] and =-=[6]-=-). Once more, engineering intuition provides a powerful guide to get to the core of the mathematics. APPENDIX The following result can be found in [2]. We give a more concrete proof for completeness. ...

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...icient, , then there may be some elements of vector that are zero. In this case, the corresponding rows and columns of the Hessian matrix in (46) are also zero. We now generalize a result obtained in =-=[17]-=- for parallel channels were it was proved that the mutual information is concave in the power allocation for the case where the entries of the signaling vector are assumed independent (this last assum...

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...st, these fundamental relations between mutual information and MMSE have already found several applications: the mercury/waterfilling optimal power allocation over a set of parallel Gaussian channels =-=[3]-=-; the numerical optimization of linear precoders for multipleinput multiple-output (MIMO) channels [2]; a simple proof for the entropy power inequality [4]; a simple proof of the monotonicity of the n...

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...nequality [3] and of the monotonic decrease with of where are independent identically distributed (i.i.d.) [4]; for other applications and generalizations of (1), (2), and (5), see [1], [5] [2], [6], =-=[7]-=-, [9], [10], [11], and [12]. The purpose of this paper is to give a new estimation-theoretic representation for relative entropy. Since entropy, mutual information, differential entropy, and non-Gauss...

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...ability [5], [18]. Another emerging precoder design approach imbued with operational significance is based on the maximization of the mutual information between the input and the output of the system =-=[28, 34, 27, 36, 49]-=-. This novel design principle has been shown to yield considerable rate gains in a variety of communications scenarios, due to the fact that, in addition to adapting to the channel characteristics, th...

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...MMSE) for linear vector Gaussian channels put forth recently in [3], and extended to the vector case in [4], has become a fundamental tool in transmitter design beyond the Gaussian signaling case. In =-=[5]-=-, the authors derived the optimum diagonal precoder, or power allocation, in quasi-closed form, coining the term mercury/waterfilling. Their results were found for the particular case of a diagonal ch...

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...loy two well-known suboptimum BPL approaches, i.e., the margin-adaptive algorithm and the rate-adaptive algorithm, to offer the near water-filling solution and the integer number of bits/symbol [11], =-=[12]-=-. Specifically, the marginadaptive approach is to minimize the transmit power subject to the target number of bits per block and the target link performance. This approach has received considerable ap...