Communication-Efficient Federated Learning via Quantized Compressed Sensing

Yongjeong Oh, Namyoon Lee, Yo Seb Jeon, H. Vincent Poor

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


In this paper, we present a communication-efficient federated learning framework inspired by quantized compressed sensing. The presented framework consists of gradient compression for wireless devices and gradient reconstruction for a parameter server (PS). Our strategy for gradient compression is to sequentially perform block sparsification, dimensional reduction, and quantization. By leveraging both dimension reduction and quantization, our strategy can achieve a higher compression ratio than one-bit gradient compression. For accurate aggregation of local gradients from the compressed signals, we put forth an approximate minimum mean square error (MMSE) approach for gradient reconstruction using the expectation-maximization generalized-approximate-message-passing (EM-GAMP) algorithm. Assuming Bernoulli Gaussian-mixture prior, this algorithm iteratively updates the posterior mean and variance of local gradients from the compressed signals. We also present a low-complexity approach for the gradient reconstruction. In this approach, we use the Bussgang theorem to aggregate local gradients from the compressed signals, then compute an approximate MMSE estimate of the aggregated gradient using the EM-GAMP algorithm. We also provide a convergence rate analysis of the presented framework. Using the MNIST dataset, we demonstrate that the presented framework achieves almost identical performance with the case that performs no compression, while significantly reducing communication overhead for federated learning.

Original languageEnglish (US)
Pages (from-to)1087-1100
Number of pages14
JournalIEEE Transactions on Wireless Communications
Issue number2
StatePublished - Feb 1 2023
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Applied Mathematics


  • Federated learning
  • distributed stochastic gradient descent
  • gradient compression
  • gradient reconstruction
  • quantized compressed sensing


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