Trading off coding complexity and feedback requirements for the packet erasure channel

Abstract

We study the tradeoffs in employing two different approaches -coding and feedback -for reliable communication over packet erasure channels. Results are shown for a scheme that combines both approaches. Inspired by this scheme, we use rate distortion results to characterize the best achievable tradeoffs for a class of joint coding-and-feedback schemes.

Coding versus feedback: Hybrid ARQ protocols for the packet erasure channel

“…We have introduced new hybrid ARQ protocols for erasure channels that allow for tradeoffs between coding complexity for erasure correction and the amount of feedback needed for re-transmission requests. The new protocols improve upon schemes proposed in [6], and their performance is substantially superior to time-sharing between coding-only and feedbackonly when the erasure probability is smaller than 0.2 or bigger than 0.9.…”

“…Thus, the above strategy amounts to feeding back a lossy compressed version of a Bernoulli sequence of length n, such that, in the reconstructed sequence, no 1 → 0 substitutions occur and the number of 0 → 1 substitutions is at most nD. The number of bits required for this compression is given by nR(D), where R (D) is the appropriate rate-distortion function [6], given bỹ…”

“…This is a straightforward extension of the hybrid scheme in [6]. A Tornado code of rate R = 1 − δ/(1 − ) is used to communicate the message, as in the coding-only protocol; however, the encoding/decoding complexity is reduced with the aid of limited feedback.…”

“…This process is repeated until all k message bits are received at d. It is easily shown that this requires an average of k · h(δ)/(1 − δ) bits to be sent on the feedback channel [6], where h(·) is the binary entropy function.…”

“…In particular, we develop and analyze a class of hybrid protocols that allow one to trade off coding complexity at the expense of utilization of the feedback channel. In doing so, we build on prior work in [6], in which complexity-feedback tradeoffs for some simple hybrid schemes were presented; this paper presents some extensions and generalizations, leading to improved tradeoffs.…”