We consider the universal discrete filtering problem, where an input sequence generated by an unknown source passes through a discrete memoryless channel, and the goal is to estimate its components based on the output sequence, with limited lookahead or delay. We propose and establish the universality of a family of schemes for this setting. These schemes are induced by universal Sequential Probability Assignments (SPAs), and inherit their computational properties. We show that the schemes induced by LZ78 (a Lempel-Ziv compression algorithm) are practically implementable and well-suited for scenarios with limited computational resources and latency constraints. As a byproduct of our analysis, we obtain novel upper and lower bounds in the purely Bayesian setting using some of the intermediate results.

We consider the universal discrete filtering problem, where an input sequence generated by an unknown source passes through a discrete memoryless channel, and the goal is to estimate its components based on the output sequence, with limited lookahead or delay. We propose and establish the uni-versality of a family of schemes for this setting. These schemes are induced by universal Sequential Probability Assignments (SPAs), and inherit their computational properties. We show that the schemes induced by LZ78 are practically implementable and well-suited for scenarios with limited computational re-sources and latency constraints.