Phenylketonuria (PKU) is a genetic disorder requiring strict dietary management to prevent intellectual disability. Existing food recommendation systems struggle to address the unique needs of PKU patients, often neglecting the importance of balanced nutrition alongside protein control. This paper proposes a novel, age-based recommender system for PKU patients. The system leverages ontologies to capture knowledge about PKU-related knowledge, foods, and nutrients, ensuring safe and personalized meal recommendations. It personalizes suggestions by considering a patient's PKU diagnosis, protein tolerance level, and potentially their preferences. For infants, a rule-based system ensures safe protein consumption and suggests suitable recipes. Adults benefit from both content-based and collaborative filtering techniques. This work has the potential to empower PKU patients to effectively manage their dietary needs by providing safe, personalized, and diverse meal recommendations.

Large matrix multiplications are central to large-scale machine learning applications. These operations are often carried out on a distributed computing platform with a master server and multiple workers in the cloud operating in parallel. For such distributed platforms, it has been recently shown that coding over the input data matrices can reduce the computational delay, yielding a trade-off between recovery threshold, i.e., the number of workers required to recover the matrix product, and communication load, i.e., the total amount of data to be downloaded from the workers. In this paper, in addition to exact recovery requirements, we impose security and privacy constraints on the data matrices, and study the recovery threshold as a function of the communication load. We first assume that both matrices contain private information and that workers can collude to eavesdrop on the content of these data matrices. For this problem, we introduce a novel class of secure codes, referred to as secure generalized PolyDot (SGPD) codes, that generalize state-of-the-art non-secure codes for matrix multiplication. SGPD codes allow a flexible trade-off between recovery threshold and communication load for a fixed maximum number of colluding workers while providing perfect secrecy for the two data matrices. We then study a connection between secure matrix multiplication and private information retrieval. We specifically assume that one of the data matrices is taken from a public set known to all the workers. In this setup, the identity of the matrix of interest should be kept private from the workers. For this model, we present a variant of generalized PolyDot codes that can guarantee both secrecy of one matrix and privacy for the identity of the other matrix for the case of no colluding servers.

Tensor operations, such as matrix multiplication, are central to large-scale machine learning applications. These operations can be carried out on a distributed computing platform with a master server at the user side and multiple workers in the cloud operating in parallel. For distributed platforms, it has been recently shown that coding over the input data matrices can reduce the computational delay, yielding a tradeoff between recovery threshold and communication load. In this work, we impose an additional security constraint on the data matrices and assume that workers can collude to eavesdrop on the content of these data matrices. Specifically, we introduce a novel class of secure codes, referred to as secure generalized PolyDot codes, that generalizes previously published non-secure versions of these codes for matrix multiplication. These codes extend the state-of-the-art by allowing a flexible trade-off between recovery threshold and communication load for a fixed maximum number of colluding workers.

The uplink of a cloud radio access network architecture is studied in which decoding at the cloud takes place via network function virtualization on commercial off-the-shelf servers. In order to mitigate the impact of straggling decoders in this platform, a novel coding strategy is proposed, whereby the cloud re-encodes the received frames via a linear code before distributing them to the decoding processors. Transmission of a single frame is considered first, and upper bounds on the resulting frame unavailability probability as a function of the decoding latency are derived by assuming a binary symmetric channel for uplink communications. Then, the analysis is extended to account for random frame arrival times. In this case, the tradeoff between an average decoding latency and the frame error rate is studied for two different queuing policies, whereby the servers carry out per-frame decoding or continuous decoding, respectively. Numerical examples demonstrate that the bounds are useful tools for code design and that coding is instrumental in obtaining a desirable compromise between decoding latency and reliability.

The uplink of a cloud radio access network architecture is studied in which decoding at the cloud takes place via network function virtualization (NFV) on commercial off-the-shelf (COTS) servers. In order to mitigate the impact of straggling decoders in the cloud computing platform, a novel coding strategy is proposed, whereby the cloud re-encodes the received frames via a linear code before distributing them to the decoding processors. Upper bounds on the resulting frame unavailability probability (FUP) as a function of the decoding latency are derived by assuming a binary symmetric channel for uplink communications. The bounds leverage large deviation results for correlated variables, and depend on the properties of both the uplink linear channel code adopted at the user and the NFV linear code applied at the cloud. Numerical examples demonstrate that the bounds are useful tools for code design, and that coding is instrumental in obtaining a desirable tradeoff between FUP and decoding latency.

In this paper we present Grobner bases for lattices given in a general form, including integer and non-integer lattices. Grdot{o}bner bases for binary linear codes were introduced by Borges-Quintana et al. . We extend their work to non-binary group block codes. Then, given a lattice Λ and its associated label code L, which is a group code, we define an ideal for L. A Grobner basis is assigned to Λ as the Grobner basis of its label code L. Since the associated label code for integer and non-integer lattices are group codes, the assigned Grobner bases can be obtained for both cases. Using this Grobner basis an algebraic decoding algorithm is introduced. We provide an example of the decoding method for a lower dimension lattice. We explain that the complexity of this decoding method depends on the division algorithm and show this decoding method has polynomial time complexity. Experiments for some versions of root lattices (E_7 and E_8) show that for low SNR the performance of these lattices is near to the lower bounds given in .