CKKS Decoding, Conjugate sum

Looks like you are referring to this part in OpenFHE?

The added Gaussian noise does not affect the most significant bits of the message. It only affects the noise which lives in the least significant bits of the message. Hence, the message is not significantly affected but the original noise is flooded. Subtracting (rather than summing) the conjugate from the message is to find the imaginary part, which includes the accumulated noise in the ciphertext as a result of the computation. The ciphertext noise is needed to estimate the magnitude of the flooding noise that needs to be added to the message.

More on noise flooding can be found in the resources below:

  1. Securing Approximate Homomorphic Encryption Using Differential Privacy
  2. Appropriate error parameters for the noise flooding - #5 by Nick_Genise