Rateless Coding and Perfect Rate-Compatible Codes for Gaussian Channels

A rateless code, or a rate-compatible family of codes, has the property that the higher rate codes have codewords that are prefixes of those of the lower rate ones. A perfect family of such codes is one in which each of the codes in the family is capacity-achieving. We show by construction that perfect rateless codes with low-complexity decoding algorithms exist for additive white Gaussian noise channels. As an illustration of our framework, we design a practical three-rate code family. We further demonstrate that a rich set of perfect or near-perfect rateless codes may be found via numerical optimization