A Black Hole-Aided Deep-Helix Channel Model for DNA

In this article, we present a black-hole-aided deep-helix (bh-dh) channel model to enhance information bound and mitigate a multiple-helix directional issue in Deoxyribonucleic acid (DNA) communications. The recent observations of DNA do not match with Shannon bound due to their multiple-helix directional issue. Hence, we propose a bh-dh channel model in this paper. The proposed bh-dh channel model follows a similar fashion of DNA and enriches the earlier DNA observations as well as achieving a composite like information bound. To do successfully the proposed bh-dh channel model, we first define a black-hole-aided Bernoulli-process and then consider a symmetric bh-dh channel model. After that, the geometric and graphical insight shows the resemblance of the proposed bh-dh channel model in DNA and Galaxy layout. In our exploration, the proposed bh-dh symmetric channel geometrically sketches a deep-pair-ellipse when a deep-pair information bit or digit is distributed in the proposed channel. Furthermore, the proposed channel graphically shapes as a beautiful circulant ring. The ring contains a central-hole, which looks like a central-black-hole of a Galaxy. The coordinates of the inner-ellipses denote a deep-double helix, and the coordinates of the outer-ellipses sketch a deep-parallel strand. Finally, the proposed bh-dh symmetric channel significantly outperforms the traditional binary-symmetric channel and is verified by computer simulations in terms of Shannon entropy and capacity bound.

A Black Hole-Aided Deep-Helix Channel Model for DNA

In this article, we present a black-hole-aided deep-helix (bh-dh) channel model to enhance information bound and mitigate a multiple-helix directional issue in Deoxyribonucleic acid (DNA) communications. The recent observations of DNA do not match with Shannon bound due to their multiple-helix directional issue. Hence, we propose a bh-dh channel model in this paper. The proposed bh-dh channel model follows a similar fashion of DNA and enriches the earlier DNA observations as well as achieving a composite like information bound. To do successfully the proposed bh-dh channel model, we first define a black-hole-aided Bernoulli-process and then consider a symmetric bh-dh channel model. After that, the geometric and graphical insight shows the resemblance of the proposed bh-dh channel model in DNA and Galaxy layout. In our exploration, the proposed bh-dh symmetric channel geometrically sketches a deep-pair-ellipse when a deep-pair information bit or digit is distributed in the proposed channel. Furthermore, the proposed channel graphically shapes as a beautiful circulant ring. The ring contains a central-hole, which looks like a central-black-hole of a Galaxy. The coordinates of the inner-ellipses denote a deep-double helix, and the coordinates of the outer-ellipses sketch a deep-parallel strand. Finally, the proposed bh-dh symmetric channel significantly outperforms the traditional binary-symmetric channel and is verified by computer simulations in terms of Shannon entropy and capacity bound.

A Black Hole-Aided Deep-Helix Channel Model for DNA

In this article, we present a black-hole-aided deep-helix (bh-dh) channel model to enhance information bound and mitigate a multiple-helix directional issue in Deoxyribonucleic acid (DNA) communications. The recent observations of DNA do not match with Shannon bound due to their multiple-helix directional issue. Hence, we propose a bh-dh channel model in this paper. The proposed bh-dh channel model follows a similar fashion of DNA and enriches the earlier DNA observations as well as achieving a composite like information bound. To do successfully the proposed bh-dh channel model, we first define a black-hole-aided Bernoulli-process and then consider a symmetric bh-dh channel model. After that, the geometric and graphical insight shows the resemblance of the proposed bh-dh channel model in DNA and Galaxy layout. In our exploration, the proposed bh-dh symmetric channel geometrically sketches a deep-pair-ellipse when a deep-pair information bit or digit is distributed in the proposed channel. Furthermore, the proposed channel graphically shapes as a beautiful circulant ring. The ring contains a central-hole, which looks like a central-black-hole of a Galaxy. The coordinates of the inner-ellipses denote a deep-double helix, and the coordinates of the outer-ellipses sketch a deep-parallel strand. Finally, the proposed bh-dh symmetric channel significantly outperforms the traditional binary-symmetric channel and is verified by computer simulations in terms of Shannon entropy and capacity bound.

A modified GADIA-based upper-bound to the capacity of Gaussian general N-relay networks

In this paper, we present a general Gaussian N-relay network by allowing relays to communicate to each other and allowing a direct channel between source and destination as compared to the standard diamond network in Nazaroğlu et al. (IEEE Trans Inf Theory 60:6329–6341, 2014) at the cost of extra channel uses. Our main focus is to examine the min-cut bound capacities of the relay network. Very recently, the results in Uykan (IEEE Trans Neural Netw Learn Syst 31:3294–3304, 2020) imply that the GADIA in Babadi and Tarokh (IEEE Trans Inf Theory 56:6228–6252, 2010), a pioneering algorithm in the interference avoidance literature, actually performs max-cut of a given power-domain (nonnegative) link gain matrix in the 2-channel case. Using the results of the diamond network in Nazaroğlu et al. (2014) and the results in Uykan (2020), in this paper, we (i) turn the mutual information maximization problem in the Gaussian N-relay network into an upper bound minimization problem, (ii) propose a modified GADIA-based algorithm to find the min-cut capacity bound and (iii) present an upper and a lower bound to its min-cut capacity bound using the modified GADIA as applied to the defined “squared channel gain matrix/graph”. Some advantages of the proposed modified GADIA-based simple algorithm are as follows: (1) The Gaussian N-relay network can determine the relay clusters in a distributed fashion and (2) the presented upper bound gives an insight into whether allowing the relays to communicate to each other pays off the extra channel uses or not as far as the min-cut capacity bound is concerned. The simulation results confirm the findings. Furthermore, the min-cut upper bound found by the proposed modified-GADIA is verified by the cut-set bounds found by the spectral clustering based solutions as well.

Achievable Rates of Gaussian Interference Channel with Multi-Layer Rate-Splitting and Successive Simple Decoding

The capacity bound of the Gaussian interference channel (IC) has received extensive research interests in recent years. Since the IC model consists of multiple transmitters and multiple receivers, its exact capacity region is generally unknown. One well-known capacity achieving method in IC is Han-Kobayashi (H-K) scheme, which applies two-layer rate-splitting (RS) and simultaneous decoding (SD) as the pivotal techniques and is proven to achieve the IC capacity region within 1 bit. However, the computational complexity of SD grows exponentially with the number of independent signal layers, which is not affordable in practice. To this end, we propose a scheme which employs multi-layer RS at the transmitters and successive simple decoding (SSD) at the receivers in the two-transmitter and two-receiver IC model and then study the achievable sum capacity of this scheme. Compared with the complicated SD, SSD regards interference as noise and thus has linear complexity. We first analyze the asymptotic achievable sum capacity of IC with equal-power multi-layer RS and SSD, where the number of layers approaches to infinity. Specifically, we derive the closed-form expression of the achievable sum capacity of the proposed scheme in symmetric IC, where the proposed scheme only suffers from a little capacity loss compared with SD. We then present the achievable sum capacity with finite-layer RS and SSD. We also derive the sufficient conditions where employing finite-layer RS may even achieve larger sum capacity than that with infinite-layer RS. Finally, numerical simulations are proposed to validate that multi-layer RS and SSD are not generally weaker than SD with respect to the achievable sum capacity, at least for some certain channel gain conditions of IC.