Practical Coding Schemes based on LDPC Codes for Distributed Parametric Regression

In the framework of goal-oriented communications, this paper investigates parametric regression over coded data. For this problem, information-theoretic bounds are provided in terms of rate versus regression generalization error, by considering quantize and binning achievability schemes. Alternatively, this paper focuses on practical implementations by proposing a coding scheme that combines a scalar quantizer with a non-binary LDPC code for the binning part. Given that the LDPC decoder requires prior knowledge of the regression parameters, the paper introduces a novel method to estimate these parameters directly over the LDPC-coded syndrome, without the need for prior decoding. This technique allows to both address the regression task and initialize the LDPC decoder for further data reconstruction. Monte-Carlo simulations show the efficiency of the proposed approach in terms of regression generalization error.