Approaching Rate-Distortion Limits in Neural Compression with Lattice
  Transform Coding
Eric Lei Hamed Hassani Shirin Saeedi Bidokhti
Neural compression has brought tremendous progress in designing lossy
compressors with good rate-distortion (RD) performance at low complexity. Thus
far, neural compression design involves transforming the source to a latent
vector, which is then rounded to integers and entropy coded. While this
approach has been shown to be optimal in a one-shot sense on certain sources,
we show that it is highly sub-optimal on i.i.d. sequences, and in fact always
recovers scalar quantization of the original source sequence. We demonstrate
that the sub-optimality is due to the choice of quantization scheme in the
latent space, and not the transform design. By employing lattice quantization
instead of scalar quantization in the latent space, we demonstrate that Lattice
Transform Coding (LTC) is able to recover optimal vector quantization at
various dimensions and approach the asymptotically-achievable rate-distortion
function at reasonable complexity. On general vector sources, LTC improves upon
standard neural compressors in one-shot coding performance. LTC also enables
neural compressors that perform block coding on i.i.d. vector sources, which
yields coding gain over optimal one-shot coding.