Rateless Coding for Non-Ergodic Channels with Decoder Channel State Information

Rateless coding has recently been the focus of much practical as well as theoretical research. In this paper we argue that rateless codes find a natural application in non-ergodic channels where the channel law varies unpredictably. Such unpredictability means that to guarantee reliability block-codes are limited by worst-case channel variations. However, the dynamic-decoding nature of rateless codes allows them to adapt opportunistically to the realized channel variations. If the channel state selector is not malicious, but also not predictable, decoding can occur earlier, producing a rate of communication that can be much higher than the worst case. Indeed, we argue that the application of fountain codes to the binary erasure channel can be understood as an example of these ideas – channel ergodicity is not required. Further, this sort of decoding can be usefully understood as an incremental form of erasure decoding. We show how to use ideas of erasure decoding to make significant increases in the reliability function of our scheme.