Jar Decoding: Non-Asymptotic Converse Coding Theorems, Taylor-Type Expansion, and Optimality

Recently, a new decoding rule called jar decoding was proposed; under jar decoding, a non-asymptotic achievable tradeoff between the coding rate and word error probability was also established for any discrete input memoryless channel with discrete or continuous output (DIMC). Along the path of non-asymptotic analysis, in this paper, it is further shown that jar decoding is actually optimal up to the second order coding performance by establishing new non-asymptotic converse coding theorems, and determining the Taylor expansion of the (best) coding rate $R_n (\epsilon)$ of finite block length for any block length $n$ and word error probability $\epsilon$ up to the second order. Finally, based on the Taylor-type expansion and the new converses, two approximation formulas for $R_n (\epsilon)$ (dubbed "SO" and "NEP") are provided; they are further evaluated and compared against some of the best bounds known so far, as well as the normal approximation of $R_n (\epsilon)$ revisited recently in the literature. It turns out that while the normal approximation is all over the map, i.e. sometime below achievable bounds and sometime above converse bounds, the SO approximation is much more reliable as it is always below converses; in the meantime, the NEP approximation is the best among the three and always provides an accurate estimation for $R_n (\epsilon)$. An important implication arising from the Taylor-type expansion of $R_n (\epsilon)$ is that in the practical non-asymptotic regime, the optimal marginal codeword symbol distribution is not necessarily a capacity achieving distribution.Comment: submitted to IEEE Transaction on Information Theory in April, 201

Capacity Analysis of Linear Operator Channels over Finite Fields

Motivated by communication through a network employing linear network coding, capacities of linear operator channels (LOCs) with arbitrarily distributed transfer matrices over finite fields are studied. Both the Shannon capacity $C$ and the subspace coding capacity $C_{\text{SS}}$ are analyzed. By establishing and comparing lower bounds on $C$ and upper bounds on $C_{\text{SS}}$, various necessary conditions and sufficient conditions such that $C=C_{\text{SS}}$ are obtained. A new class of LOCs such that $C=C_{\text{SS}}$ is identified, which includes LOCs with uniform-given-rank transfer matrices as special cases. It is also demonstrated that $C_{\text{SS}}$ is strictly less than $C$ for a broad class of LOCs. In general, an optimal subspace coding scheme is difficult to find because it requires to solve the maximization of a non-concave function. However, for a LOC with a unique subspace degradation, $C_{\text{SS}}$ can be obtained by solving a convex optimization problem over rank distribution. Classes of LOCs with a unique subspace degradation are characterized. Since LOCs with uniform-given-rank transfer matrices have unique subspace degradations, some existing results on LOCs with uniform-given-rank transfer matrices are explained from a more general way.Comment: To appear in IEEE Transactions on Information Theor

On Linear Operator Channels over Finite Fields

Motivated by linear network coding, communication channels perform linear operation over finite fields, namely linear operator channels (LOCs), are studied in this paper. For such a channel, its output vector is a linear transform of its input vector, and the transformation matrix is randomly and independently generated. The transformation matrix is assumed to remain constant for every T input vectors and to be unknown to both the transmitter and the receiver. There are NO constraints on the distribution of the transformation matrix and the field size. Specifically, the optimality of subspace coding over LOCs is investigated. A lower bound on the maximum achievable rate of subspace coding is obtained and it is shown to be tight for some cases. The maximum achievable rate of constant-dimensional subspace coding is characterized and the loss of rate incurred by using constant-dimensional subspace coding is insignificant. The maximum achievable rate of channel training is close to the lower bound on the maximum achievable rate of subspace coding. Two coding approaches based on channel training are proposed and their performances are evaluated. Our first approach makes use of rank-metric codes and its optimality depends on the existence of maximum rank distance codes. Our second approach applies linear coding and it can achieve the maximum achievable rate of channel training. Our code designs require only the knowledge of the expectation of the rank of the transformation matrix. The second scheme can also be realized ratelessly without a priori knowledge of the channel statistics.Comment: 53 pages, 3 figures, submitted to IEEE Transaction on Information Theor

Experimental investigation of the transverse nonlinear vibration of an axially travelling belt

From an experimental perspective, this paper investigates the transverse vibrationpresent in an axially travelling belt undergoing uniform motion with constant travelling speed.Application of a control of the belt speed, using Matlab, a Code Composer Studio (CCS) and theavailable complementary embedded tools, a stepper motor DSP control was obtainedautomatically by using a graphical method to establish the stepper motor movement models withina Simulink environment. By changing the tension of the belt and the rotational speed of the steppermotor, the natural frequency of the travelling belt was studied. The response waveforms, spectralcontent and phase diagrams were obtained by measuring the transverse vibration displacementunder different conditions. A nonlinear model for the experimental moving belt system wasdeveloped and numerical solutions calculated. Subsequently, the nonlinear response behavior ofthis model were validated by the results of the experiment. It was shown that there were manyscenarios for which the system can exhibit periodic motion, chaotic motion and beat frequencyphenomena to be present and measured in the vibration of the axially travelling belt

DeepImageTranslator V2: Analysis of Multimodal Medical Images using Semantic Segmentation Maps Generated through Deep Learning

Introduction: Analysis of multimodal medical images often requires the selection of one or many anatomical regions of interest (ROIs) for extraction of useful statistics. This task can prove laborious when a manual approach is used. We have previously developed a user-friendly software tool for image-to-image translation using deep learning. Therefore, we present herein an update to the DeepImageTranslator V2 software with the addition of a tool for multimodal medical image segmentation analysis (hereby referred to as the MMMISA). Methods: The MMMISA was implemented using the Tkinter library; backend computations were implemented using the Pydicom, Numpy, and OpenCV libraries. We tested our software using 4188 slices from whole-body axial 2-deoxy-2-[18F]-fluoroglucose-position emission tomography/ computed tomography scans ([¹⁸F]-FDG-PET/CT) of 10 patients from the American College of Radiology Imaging Network-Head and Neck Squamous Cell Carcinoma (ACRIN-HNSCC) database. Using the deep learning software DeepImageTranslator, a model was trained with 36 randomly selected CT slices and manually labelled semantic segmentation maps. Utilizing the trained model, all the CT scans of the 10 HNSCC patients were segmented with high accuracy. Segmentation maps generated using the deep convolutional network were then used to measure organ specific [¹⁸F]-FDG uptake. We also compared measurements performed using the MMMISA and those made with manually selected ROIs. Results: The MMMISA is a tool that allows user to select ROIs based on deep learning-generated segmentation maps and to compute accurate statistics for these ROIs based on coregistered multimodal images. We found that organ-specific [¹⁸F]-FDG uptake measured using multiple manually selected ROIs is concordant with whole-tissue measurements made with segmentation maps using the MMMISA tool. Doi: 10.28991/HIJ-2022-03-03-07 Full Text: PD