Rateless Coding for Gaussian Channels

— A rateless code—i.e., a rate-compatible family of codes—has the property that codewords of the higher rate codes 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. Our construction involves the use of layered encoding and successive decoding, together with a repetition and dithering technique. As an illustration of our framework, we design a practical three-rate code family. We further construct rich sets of near-perfect rateless codes within our architecture that require either significantly fewer layers or lower complexity than their perfect counterparts. Variations of the basic construction are also discussed.

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Uri Erez, Mitchell D. Trott, Gregory W. Wornell
• Keywords: Additive White Gaussian Noise, CORR 2007, Education, Lower Rate Ones, Rateless Codes