In this paper, my co-author Vaishnavi Anekar and I look at over-the-air computation (OAC), a technique that exploits the natural superposition of signals on a wireless multiple-access channel to let a receiver compute a function of many nodes' data directly from the channel, rather than decoding each node's message separately.
We built on SumComp, an existing digital OAC scheme that uses the algebraic structure of Gaussian integer rings to support standard modulation while enabling sum computation with low complexity. Its limitation is that reliability is capped by the minimum distance of the constellation formed when many nodes' signals add up at the receiver, so performance degrades as the number of transmitting nodes grows.
What we did:
We proposed Coded SumComp, embedding a linear code over the integer ring Zq into the SumComp encoder and decoder to boost the effective minimum distance of the aggregated constellation, while preserving the algebraic structure needed for over-the-air sum computation.
We identified that the resulting modulo-folded channel induces Lee-type errors, and designed a syndrome-based decoder with integer lifting and ML decoding to exploit this structure.
We derived an analytical upper bound on the MSE of the recovered sum in terms of the decoder failure probability under Lee-metric decoding.
We validated the analysis through Monte Carlo simulations, showing a 2–3 dB MSE improvement over uncoded SumComp in the moderate-to-high SNR regime.
Why it matters: Over-the-air computation is emerging as a key enabler for 6G networks, where massive numbers of connected devices need to have their data aggregated efficiently without the latency and overhead of conventional orthogonal access. It is particularly attractive for federated learning at the wireless edge, where model updates from many clients must be averaged over the air rather than communicated and combined one at a time, directly easing the communication bottleneck that limits distributed learning at scale. Coded SumComp shows that classical coding-theoretic tools (linear codes, syndrome decoding, Lee-metric distance) can be layered onto ring-based digital OAC schemes without breaking the algebraic structure that makes computation-over-the-air possible, offering a concrete way to make such aggregation more reliable as the number of participating devices grows.