Design processes, in many disciplines like architecture, civil engineering or mechanical engineering, involve navigating large, high-dimensional and heterogeneous data. While AI-driven approaches like inverse design and surrogate modeling can enhance design exploration, their adoption is hindered by complex workflows and the need for coding and machine learning expertise. To address this, we introduce AI-eXtended Design (AIXD): a low-code, open-source toolbox that integrates AI into computational design. AIXD simplifies handling of mixed data types, as well as the analysis, training, and deployment of machine learning models for inverse design, surrogate modeling, and sensitivity analysis, enabling domain experts to rapidly explore diverse solutions with minimal coding.In this paper, we show the functionalities of the toolbox, and we demonstrate AIXD’s capabilities in architectural and engineering design applications, showing how it accelerates performance evaluation, generates high-performing alternatives, and improves design understanding by delivering new insights. By bridging AI and design practice, AIXD lowers the entry barrier to data-driven methods, making AI-extended design more accessible and efficient.

Data and code working together is fundamental to machine learning (ML), but the context around datasets and interactions between datasets and code are in general captured only rudimentarily. Context such as how the dataset was prepared and created, what source data were used, what code was used in processing, how the dataset evolved, and where it has been used and reused can provide much insight, but this information is often poorly documented. That is unfortunate since it makes datasets into black-boxes with potentially hidden characteristics that have downstream consequences. We argue that making dataset preparation more accessible and dataset usage easier to record and document would have significant benefits for the ML community: it would allow for greater diversity in datasets by inviting modification to published sources, simplify use of alternative datasets and, in doing so, make results more transparent and robust, while allowing for all contributions to be adequately credited. We present a platform, Renku, designed to support and encourage such sustainable development and use of data, datasets, and code, and we demonstrate its benefits through a few illustrative projects which span the spectrum from dataset creation to dataset consumption and showcasing.

In this paper, we propose the tree-structured expectation propagation (TEP) algorithm for low-density parity-check (LDPC) decoding over the binary additive white Gaussian noise (BI-AWGN) channel. By approximating the posterior distribution by a tree-structure factorization, the TEP has been proven to improve belief propagation (BP) decoding over the binary erasure channel (BEC). We show for the AWGN channel how the TEP decoder is also able to capture additional information disregarded by the BP solution, which leads to a noticeable reduction of the error rate for finite-length codes. We show that for the range of codes of interest, the TEP gain is obtained with a slight increase in complexity over that of the BP algorithm. An efficient way of constructing the tree-like structure is also described.

We propose a decoding algorithm for LDPC codes that achieves the maximum likelihood (ML) solution over the binary erasure channel (BEC). In this channel, the tree-structured expectation propagation (TEP) decoder improves the peeling decoder (PD) by processing check nodes of degree one and two. However, it does not achieve the ML solution, as the tree structure of the TEP allows only for approximate inference. In this paper, we provide the procedure to construct the structure needed for exact inference. This algorithm, denoted as generalized tree-structured expectation propagation (GTEP), modifies the code graph by recursively eliminating any check node and merging this information in the remaining graph. The GTEP decoder upon completion either provides the unique ML solution or a tree graph in which the number of parent nodes indicates the multiplicity of the ML solution. We also explain the algorithm as a Gaussian elimination method, relating the GTEP to other ML solutions. Compared to previous approaches, it presents an equivalent complexity, it exhibits a simpler graphical message-passing procedure and, most interesting, the algorithm can be generalized to other channels.

In this paper, we put forward the tree-structured expectation propagation (TEP) algorithm for decoding block and convolutional low-density parity-check codes over any binary channel. We have already shown that TEP improves belief propagation (BP) over the binary erasure channel (BEC) by imposing marginal constraints over a set of pairs of variables that form a tree or a forest. The TEP decoder is a message-passing algorithm that sequentially builds a tree/forest of erased variables to capture additional information disregarded by the standard BP decoder, which leads to a noticeable reduction of the error rate for finite-length codes. In this paper, we show how the TEP can be extended to any channel, specifically to binary memoryless symmetric (BMS) channels. We particularly focus on how the TEP algorithm can be adapted for any channel model and, more importantly, how to choose the tree/forest to keep the gains observed for block and convolutional LDPC codes over the BEC.

In this work, we analyze the finite-length performance of low-density parity check (LDPC) ensembles decoded over the binary erasure channel (BEC) using the tree-expectation propagation (TEP) algorithm. In a previous paper, we showed that the TEP improves the BP performance for decoding regular and irregular short LDPC codes, but the perspective was mainly empirical. In this work, given the degree-distribution of an LDPC ensemble, we explain and predict the range of code lengths for which the TEP improves the BP solution. In addition, for LDPC ensembles that present a single critical point, we propose a scaling law to accurately predict the performance in the waterfall region. These results are of critical importance to design practical LDPC codes for the TEP decoder.

Spatially-coupled (SC) LDPC codes are constructed from a set of L regular sparse codes of length M. In the asymptotic limit of these parameters, SC codes present an excellent decoding threshold under belief propagation (BP) decoding, close to the maximum a posteriori (MAP) threshold of the underlying regular code. In the finite-length regime, we need both dimensions, L and M, to be sufficiently large, yielding a very large code length and decoding latency. In this paper, and for the erasure channel, we show that the finite-length performance of SC codes is improved if we consider the tree-structured expectation propagation (TEP) algorithm in the decoding stage. When applied to the decoding of SC LDPC codes, it allows using shorter codes to achieve similar error rates. We also propose a window-sliding scheme for the TEP decoder to reduce the decoding latency.

In this paper, we propose a decoding algorithm for LDPC codes that achieves the MAP solution over the BEC. This algorithm, denoted as generalized tree-structured expectation propagation (GTEP), extends the idea of our previous work, the TEP decoder. The GTEP modifies the graph by eliminating a check node of any degree and merging this information with the remaining graph. The GTEP decoder upon completion either provides the unique MAP solution or a tree graph in which the number of parent nodes indicates the multiplicity of the MAP solution. This algorithm can be easily described for the BEC, and it can be cast as a generalized peeling decoder. The GTEP naturally optimizes the complexity of the decoder, by looking for checks nodes of minimum degree to be eliminated first.

We show an application of a tree structure for approximate inference in graphical models using the expectation propagation algorithm. These approximations are typically used over graphs with short-range cycles. We demonstrate that these approximations also help in sparse graphs with long-range loops, as the ones used in coding theory to approach channel capacity. For asymptotically large sparse graph, the expectation propagation algorithm together with the tree structure yields a completely disconnected approximation to the graphical model but, for for finite-length practical sparse graphs, the tree structure approximation to the code graph provides accurate estimates for the marginal of each variable.

Low-density parity-check (LPDC) decoders assume the channel estate information (CSI) is known and they have the true a posteriori probability (APP) for each transmitted bit. But in most cases of interest, the CSI needs to be estimated with the help of a short training sequence and the LDPC decoder has to decode the received word using faulty APP estimates. In this paper, we study the uncertainty in the CSI estimate and how it affects the bit error rate (BER) output by the LDPC decoder. To improve these APP estimates, we propose a Bayesian equalizer that takes into consideration not only the uncertainty due to the noise in the channel, but also the uncertainty in the CSI estimate, reducing the BER after the LDPC decoder.