  This paper shows that a class of codes such as Reed-Muller (RM) codes have
vanishing bit-error probability below capacity on symmetric channels. The proof
relies on the notion of `camellia codes': a class of symmetric codes
decomposable into `camellias', i.e., set systems that differ from sunflowers by
allowing for scattered petal overlaps. The proof then follows from a boosting
argument on the camellia petals with second moment Fourier analysis. For
erasure channels, this gives a self-contained proof of the bit-error result in
Kudekar et al.'17, without relying on sharp thresholds for monotone properties
Friedgut-Kalai'96. For error channels, this gives a shortened proof of
Reeves-Pfister'23 with an exponentially tighter bound, and a proof variant of
the bit-error result in Abbe-Sandon'23. The control of the full (block) error
probability still requires Abbe-Sandon'23 for RM codes.
