New Diffusion Least-Mean-Squares Algorithms With Quantization and Privacy Awareness

In this paper, we devise an enhanced diffusion LMS algorithm tailored for quantization-based communication in distributed networks. Departing from conventional diffusion approaches, the proposed algorithm, called EQ-DLMS, integrates four distinct steps: (i) weight update, (ii) quantization, (iii) modified weight combination, and (iv) moving average. Through mean-square error analysis, we show how the modified combination and moving average steps impact the steady-state error bound. Notably, without adjusting the quantizer precision, the steady-state error bound avoids the typical O(µ^-1) dependence, where µ represents the step-size. However, the EQ-DLMS introduces an additional term, O(∥w^*∥²), into the error bound, where w^* denotes the optimal network parameter vector. To mitigate this, we then develop an improved version of the algorithm, termed DEQ-DLMS, which employs differential quantization while preserving the modified weight combination and moving average steps. Furthermore, we extend the EQ-DLMS update mechanism to address privacy concerns. This leads to the development of an enhanced privacy-aware diffusion LMS algorithm, accompanied by a mean-square stability analysis under non-zero mean protection noise. Finally, simulations are conducted to demonstrate the effectiveness of the proposed approaches and corroborate our theoretical derivations. © 2026 IEEE.