Delete-and-Conquer: Rateless coding with constrained feedback

Abstract

Traditional rateless codes were designed without the use of a feedback channel, though one is available in many applica tions. In this work, we build upon recent interest in rateless coding with feedback to produce a novel approach, dubbed Delete-and Conquer coding, for rateless coding with very little feedback. In our scheme, the feedback used is a measure of distance between a received word and the symbols already decoded at the receiver.This distance, in turn, permits a transmitter to deduce which symbols have been decoded and exclude them from subsequent transmissions. Our approach can be tuned to the specific transmis sion properties of a given feedback channel, and we empirically show that a very small amount of feedback from receiver back to the transmitter can significantly reduce coding overhead and encoding/decoding complexity. We also provide some analytically backed intuition for this improvement. I. INTRODUC TIONReliable communication over erasure channels has emerged as a key technology for various Internet applications (e.g., digital video broadcasting). In applications where there exists a high-throughput feedback channel, automatic repeat request (ARQ) protocols can achieve capacity over erasure-based links. However, when such feedback channels are not available, rate less codes, such as the capacity achieving Luby-Transform (LT) [1] and Raptor codes [2], can often provide reliable com munication for sufficiently long block lengths.There have been several methods proposed in the literature for exploiting a feedback channel to improve coding perfor mance on short and intermediate block lengths, where LT codes are less efficient. The authors in [3] propose real-time oblivious erasure codes, which utilize feedback messages to send the number of decoded symbols to the broadcaster. Shifted LT codes [4] utilize a similar approach by shifting the LT codes' Robust Solution distribution [1] according to the number of decoded symbols noted through the receiver's feedback channel. The authors in [5] use more informative feedback messages to notify the transmitter of which input symbols have been decoded, and this information is then applied to modify the degree distribution. Typical performance criteria for such feedback-based schemes include:• coding overhead: number of encoded symbols needed to decode all input symbols with a high probability;• computation cost: the amount of arithmetic operations needed in the encoder and decoder;• utilization of feedback channel: the amount of feedback transmitted through the back channel. We propose a novel coding scheme, dubbed Delete-and Conquer, that optimizes for these same metrics by using a different type of feedback message. Our feedback contains in formation on the distance between a received encoding symbol and the set of already decoded symbols at the receiver. The encoder uses this feedback to infer which symbols are known to the decoder, and those symbols are excluded from future transmissions.For applications with constrained feedback channels, a Delete-a...

Fountain Codes With Nonuniform Selection Distributions Through Feedback

“…In this case, the decoder allocates a single bit of 0 as the feedback message. On the other hand, if the calculated ratio is smaller than 1 2 , it shows that majority of neighbors have been decoded and feedback message would be 1. To limit the number of feedback transmissions, the receiver bundles the 1-bit feedback messages together for every interval of s received encoding symbols, and sends the s-bit messages back to the encoder.…”

CDP

“…The number of ACK messages in this scheme is equal to the number of input packets, whereas our protocol potentially sends fewer ACKs. Indeed, the type of ACK messages in our protocol is based on the distance feedback initially introduced in (Hashemi et al 2013) and (Hashemi and Trachtenberg 2014). Our decoder occasionally sends a light-weight feedback (one bit per feedback message) to the encoder, from which the encoder infers which symbols have been recovered at the decoder side and can be discarded from the encoding queue.…”