The paper addresses the problem of efficiently computing the mismatch capacity of a discrete memoryless channel (DMC) with oblivious relaying. The mismatch capacity is defined as the maximum achievable rate under a mismatched decoding metric, subject to a compression rate constraint at the relay.
The key contributions are:
Reformulation of the original max-min optimization problem as a consistent maximization form, by considering the dual form of the inner minimization problem (LM rate) and introducing a fixed Lagrange multiplier.
Development of an alternating maximization (AM) algorithm that provides closed-form solutions for updating the input distribution, joint distribution between the relay input/output, and the dual variables of the LM rate.
Proof of the convergence of the proposed AM algorithm.
Numerical experiments demonstrating the efficiency and accuracy of the AM algorithm, as well as providing insights into the optimized probability distributions that can inform practical quantizer design at the relay node.
The proposed AM algorithm is shown to outperform the existing MMIB algorithm in terms of computational time, especially as the alphabet size increases, while maintaining the same level of accuracy.
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by Lingyi Chen,... at arxiv.org 10-01-2024
https://arxiv.org/pdf/2409.19674.pdfDeeper Inquiries