Yuta Sakai

Feasible regions of symmetric capacity and Gallager's E 0 function for ternary-input discrete memoryless channels

In the refinement of a channel coding theorem, error exponents characterize the exponential convergence rates of decoding error probabilities. Error exponents are sometime called as reliability functions. In this study, we consider analyzing the reliability functions based on Gallagers E0 function. The region of the E0 function of binary-input memoryless and symmetric channels for a fixed capacity was clarified by Guillén i Fàbregas et al. in their 2013 study. More precisely, binary erasure and binary symmetric channels have maximal and minimal E0 functions, respectively, among the binary-input memoryless and symmetric channels for a fixed capacity. In this study, we extend their results from binary- to ternary-input channels that are not necessarily symmetric. First, we identify the extreme channels among the ternary-input strongly symmetric channels. Next, we identify the extreme channels among the ternary-input memoryless and symmetric channels. In addition, using channel symmetrization, we investigate whether the feasible regions of symmetric capacity and the E0 functions for discrete memoryless channels (DMCs) are identical to those for symmetric channels if the channel inputs follow a uniform distribution. We describe the feasible regions for ternary-input DMCs under a uniform input distribution. In particular, we reveal the channels with maximal E0 function among ternary-input DMCs for a fixed symmetric capacity and uniform input distribution.

Relations between conditional Shannon entropy and expectation of ℓ α -norm

The paper examines relationships between the conditional Shannon entropy and the expectation of ℓ_α-norm for joint probability distributions. More precisely, we investigate the sharp bounds of the expectation of ℓ_α-norm with a fixed conditional Shannon entropy, and vice versa. As applications of the results, we derive the sharp bounds between the conditional Shannon entropy and several information measures which are determined by the expectation of ℓ_α-norm, e.g., Arimotos conditional Rényi entropy and the conditional R-norm information. Moreover, we apply these results to discrete memoryless channels under a uniform input distribution. Then, sharp bounds are obtained for Gallagers reliability functions E₀ with a fixed mutual information under a uniform input distribution.

A generalized erasure channel in the sense of polarization for binary erasure channels

The polar transform of a binary erasure channel (BEC) can be exactly approximated by other BECs. Arikan proposed that polar codes for a BEC can be efficiently constructed by using its useful property. This study proposes a new class of arbitrary input generalized erasure channels, which can be exactly approximated the polar transform by other same channel models, as with the BEC. One of the main results is the recursive formulas of the polar transform of the proposed channel. In the study, we evaluate the polar transform by using the α-mutual information. Particularly, when the input alphabet size is a prime power, we examines the following: (i) inequalities for the average of the α-mutual information of the proposed channel after the one-step polar transform, and (ii) the exact proportion of polarizations of the α-mutual information of proposed channels in infinite number of polar transforms.

Sharp bounds on Arimoto's conditional Rényi entropies between two distinct orders

This study examines sharp bounds on Arimotos conditional Rényi entropy of order β with a fixed another one of distinct order α ≠ β. Arimoto inspired the relation between the Rényi entropy and the ℓ<inf>r</inf>-norm of probability distributions, and he introduced a conditional version of the Rényi entropy. From this perspective, we analyze the ℓ<inf>r</inf>-norms of particular distributions. As results, we identify specific probability distributions which achieve our sharp bounds on the conditional Rényi entropy. The sharp bounds derived in this study can be applicable to other information measures which are strictly monotone functions of the conditional Rényi entropy.

Optimal quantization of B-DMCs maximizing α-mutual information with monge property

This study examines quantization for outputs of binary-input discrete memoryless channels (B-DMCs) by concatenating its output with another DMC, so-called a quantizer. As an objective function of channel quantization, we employ the α-mutual information of a B-DMC, which connects to more powerful coding theorem than the ordinary mutual information. Showing a Monge property of the α-mutual information, we propose an optimal quantizer design algorithm for given B-DMC in polynomial time complexity with respect to the output alphabet size and the quantized level. Since the proposed method employs the SMAWK algorithm due to the Monge property, our algorithm is faster than a naive dynamic programming.

Frequency improvement in power system by Synchronization Inverter-based distributed generators

Owing to the growth in penetration of DGs (distributed generators), inverters installed together with the DGs have been increasing rapidly. In general, these grid-connected inverters need a dedicated synchronization unit such as a phase locked loop (PLL), which receives voltage phase, frequency, and amplitude of the grid voltage as reference from power grids. As the installation of inverters keeps growing at this rate, synchronizing power in the main power grids will become insufficient, and thus there is a possibility that the power grids will be unstable condition. This is because the inverter frequency is controlled just to follow frequency determined by the other synchronous generators. Therefore, it is necessary to improve the power grid stability considering the DGs penetration. In this paper, the authors employ an inverter named “Synchronization Inverter”, which consists of a governor function and, calculation functions of the swing equation and the power equation, to deal with massive installation of DGs. With the intention of verifying the effectiveness of a Synchronization Inverter, the authors evaluated the stability of power grid frequency in an isolated power grid simulator and compared its performance with a typical conventional inverter. Through the evaluation, we conclude that introduction of Synchronization Inverter improves the power grid stabilization even if the DGs are increased.