Finding the capacity of a quantized binary-input DMC

Kurkoski, Brian M.; Yagi, Hideki

doi:10.1109/isit.2012.6284302

Cited by 9 publications

(3 citation statements)

References 10 publications

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“…A natural question is how to find the jointly optimal input distribution and channel quantizer for a given DMC. We have already considered a simple extension of the quantization algorithm which either finds the jointly optimal input distribution and channel quantizer or declares a failure [31]. However, this is a convex-concave optimization problem, a class of problems which is difficult, and finding the jointly optimal solution remains an open problem.…”

Section: Discussionmentioning

confidence: 99%

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Quantization of Binary-Input Discrete Memoryless Channels

Kurkoski

Yagi

2014

IEEE Trans. Inform. Theory

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112

126

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The quantization of the output of a binary-input discrete memoryless channel to a smaller number of levels is considered. An algorithm which finds an optimal quantizer, in the sense of maximizing mutual information between the channel input and the quantizer output is given. This result holds for arbitrary channels, in contrast to previous results for restricted channels or a restricted number of quantizer outputs. In the worst case, the algorithm complexity is cubic M 3 in the number of channel outputs M . Optimality is proved using the theorem of Burshtein, Della Pietra, Kanevsky, and Nádas for mappings which minimize average impurity for classification and regression trees.

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Section: Discussionmentioning

confidence: 99%

“…where dependence of φ on z is not needed and dropped. Note that Pr(Q −1 (z)) is identical to Pr(Z = z), and so H(X|Z) is expressed in the form of ( 30) via (31).…”

Section: Proof Of Lemmamentioning

confidence: 99%

Quantization of Binary-Input Discrete Memoryless Channels

Kurkoski

Yagi

2014

IEEE Trans. Inform. Theory

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112

126

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“…Equation (32) jointly optimizes the quantizer and input distribution. This problem, however, is known to be computationally intractable due to its nonconvex structure [35]. We use an alternate iterative optimization procedure to identify the capacity-achieving input distribution (parametrized by ρ 0 and β 0 ) and the optimal quantizer (parametrized by q 1 ).…”

Section: A Experiments Setupmentioning

confidence: 99%

On the Capacity-Achieving Input of Channels With Phase Quantization

Bernardo

Zhu

Evans

2022

IEEE Trans. Inform. Theory

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The polar receiver architecture is a receiver design that captures the envelope and phase information of the signal rather than its in-phase and quadrature components. Several studies have demonstrated the robustness of polar receivers to phase noise and other nonlinearities. Yet, the information-theoretic limits of polar receivers with finite-precision quantizers have not been investigated in the literature. The main contribution of this work is to identify the optimal signaling strategy for the additive white Gaussian noise (AWGN) channel with polar quantization at the output. More precisely, we show that the capacity-achieving modulation scheme has an amplitude phase shift keying (APSK) structure. Using this result, the capacity of the AWGN channel with polar quantization at the output is established by numerically optimizing the probability mass function of the amplitude. The capacity of the polar-quantized AWGN channel with b 1 -bit phase quantizer and optimized single-bit magnitude quantizer is also presented. Our numerical findings suggest the existence of signal-to-noise ratio (SNR) thresholds, above which the number of amplitude levels of the optimal APSK scheme and their respective probabilities change abruptly. Moreover, the manner in which the capacity-achieving input evolves with increasing SNR depends on the number of phase quantization bits.

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Trellis based node operations for LDPC decoders from the Information Bottleneck method

Lewandowsky

Bauch

2015

2015 9th International Conference on Signal Processing and Communication Systems (ICSPCS)

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Finding the capacity of a quantized binary-input DMC

Cited by 9 publications

References 10 publications

Quantization of Binary-Input Discrete Memoryless Channels

Quantization of Binary-Input Discrete Memoryless Channels

On the Capacity-Achieving Input of Channels With Phase Quantization

Trellis based node operations for LDPC decoders from the Information Bottleneck method

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