Rateless codes approaching capacity of the Gaussian channel

We study codes for the AWGN channel. We build upon the recently proposed sparse superposition codes of Barron and Joseph, which for any constant backoff from capacity can achieve exponential error probability with polynomial decoding time as long as the block-length is greater than a fixed constant (which depends on the backoff). Our contribution is twofold: • First, we give a variant of the code that achieves qualitatively similar results, but that has a simpler decoding algorithm and much simpler proof than the original. • Second, we show how to make both codes rateless with minimal loss in the performance. In a rateless code, the transmitter is unaware of the channel capacity, and the receiver decodes from the appropriate length prefix of the code.