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BATS code is a low-complexity random linear network coding scheme that can achieve asymptotic bandwidth optimality for many types of networks with packet loss. In this paper, we propose a BATS code based network protocol and evaluate the performance by real-device experiments. Our results demonstrate significant ready-to-implement gain of network coding over forwarding in multi-hop network transmission with packet loss. We also propose an improved protocol to handle the practical issues observed in the experiments.

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A ring signature scheme allows the signer to sign on behalf of an ad hoc set of users, called a ring. The verifier can be convinced that a ring member signs, but cannot point to the exact signer. Ring signatures have become increasingly important today with their deployment in anonymous cryptocurrencies. Conventionally, it is implicitly assumed that all ring members are equally likely to be the signer. This assumption is generally false in reality, leading to various practical and devastating deanonymizing attacks in Monero, one of the largest anonymous cryptocurrencies. These attacks highlight the unsatisfactory situation that how a ring should be chosen is poorly understood. We propose an analytical model of ring samplers towards a deeper understanding of them through systematic studies. Our model helps to describe how anonymous a ring sampler is with respect to a given signer distribution as an information-theoretic measure. We show that this measure is robust – it only varies slightly when the signer distribution varies slightly. We then analyze three natural samplers – uniform, mimicking, and partitioning – under our model with respect to a family of signer distributions modeled after empirical Bitcoin data. We hope that our work paves the way towards researching ring samplers from a theoretical point of view.

The Kraft inequality gives a necessary and sufficient condition for the existence of a single channel prefix-free code. However, the multichannel Kraft inequality does not imply the existence of a multichannel prefix-free code in general. It is natural to ask whatever there exists an efficient decision procedure for the existence of multichannel prefixfree codes. In this paper, we tackle the two-channel case of the above problem by relating it to a constrained rectangle packing problem. Although a general rectangle packing problem is NP-complete, the extra imposed constraints allow us to propose an algorithm which can solve the problem efficiently.

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In recent decades, the Variational AutoEncoder (VAE) model has shown good potential and capability in image generation and dimensionality reduction. The combination of VAE and various machine learning frameworks has also worked effectively in different daily life applications, however its possible use and effectiveness in modern game design has seldom been explored nor assessed. The use of its feature extractor for data clustering has also been minimally discussed in the literature neither. This study first attempts to explore different mathematical properties of the VAE model, in particular, the theoretical framework of the encoding and decoding processes, the possible achievable lower bound and loss functions of different applications; then applies the established VAE model to generate new game levels based on two well-known game settings; and to validate the effectiveness of its data clustering mechanism with the aid of the Modified National Institute of Standards and Technology (MNIST) database. Respective statistical metrics and assessments are also utilized to evaluate the performance of the proposed VAE model in aforementioned case studies. Based on the statistical and graphical results, several potential deficiencies, for example, difficulties in handling high-dimensional and vast datasets, as well as insufficient clarity of outputs are discussed; then measures of future enhancement, such as tokenization and the combination of VAE and GAN models, are also outlined. Hopefully, this can ultimately maximize the strengths and advantages of VAE for future game design tasks and relevant industrial missions.

Batched network coding is a variation of random linear network coding which has low computational and storage costs. In order to adapt random fluctuations in the number of erasures in individual batches, it is not optimal to recode and transmit the same number of packets for all batches. Different distributed optimization models, which are called adaptive recoding schemes, were formulated for this purpose.The key component of these optimization problems is the expected value of the rank distribution of a batch at the next network node, which is also known as the expected rank. In this paper, we put forth a unified adaptive recoding framework. We show that the expected rank functions are concave when the packet loss pattern is a stationary stochastic process regardless of the field size, which covers but not limited to independent packet loss and burst packet loss. Under this concavity assumption, we show that there always exists a solution which not only can minimize the randomness on the number of recoded packets but also can tolerate rank distribution errors due to inaccurate measurements or limited precision of the machine. To obtain such an optimal solution, we propose tuning schemes that can turn any feasible solution into a desired optimal solution.