Rateless Coding for Gaussian Channels

Abstract

Abstract-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 repetition using time-varying layer weights. 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 developed, including one for timevarying channels in which there is no a priori stochastic model.

Rateless spinal codes

“…The top most curve shows the Shannon capacity bound. Somewhat surprisingly, spinal codes achieve rates very close to the Shannon capacity Spinal, m =24, B =16 LDPC, rate= 1 2 , BPSK LDPC, rate= 1 2 , QAM-4 LDPC, rate= 3 4 , QAM-4 LDPC, rate= 1 2 , QAM-16 LDPC, rate= 3 4 , QAM-16 LDPC, rate= 2 3 , QAM-64 LDPC, rate= 3 4 , QAM-64 LDPC, rate= 5 6 , QAM-64…”

“…A very different and promising approach to design of capacity achieving rateless codes for AWGN channel was put forth by Erez, Trott, and Wornell [3]. Their "layered approach" uses existing base codes and combines them to produce transmission symbols in a rateless way.…”

“…An alternative approach to these problems is to use a rateless code between the sender and receiver, as previous work has noted [3,5]. Ideally, with such a code, the sender encodes and transmits the coded data at a rate higher than what the channel can currently sustain, and keeps going until the receiver determines that it has correctly decoded all the data and informs the sender to move to the next packet.…”

A super-nyquist architecture for reliable underwater acoustic communication

“…The front end of each receive element consists of matched filtering (i.e., ideal low-pass filtering for sinc modulation), followed by sampling at the SNQ rate W L. The discretetime signals are given by (8). Taking into account the dithered transmission as given is (10), we have…”

“…The VR coding architecture developed in this paper is related to the family of IR redundancy codes developed for the AWGN channel in [7] [8] in that it is based on layering (superposition), dithering, and successive interference cancellation. Indeed, in one respect, this paper represents the extension of such methods to ISI channels.…”