Zero-Rate Feedback Can Achieve the Empirical Capacity

Abstract

TitleZero-rate feedback can achieve the empirical capacity

A little feedback can simplify sensor network cooperation

“…Proposition 2 tells us that the distortion scales faster than max{ M , M We again condition on the value of S 0 , which gives the the same success probabilities as (29) and (31). Therefore the distortion with this one bit of feedback is also O(M −1/3 ).…”

“…It can sometimes increase capacity in networks or channels with uncertainty or memory [19]- [31]. In a sense, the method in this paper is a way of using zero-rate feedback to combat uncertainty in the observation model.…”

Rateless Codes for AVC Models

“…Specifically, suppose that during the th chunk of channel uses the channel inputs were and the state was . Under the maximal error criterion, we define the average channel under during the th chunk by Under the nosy noise criterion we define the average channel under and by (12) A receiver with full side information would learn the channel explicitly. We consider instead the case where the receiver is given a set after the -th chunk, where is a subset of channels such that .…”

“…Their proofs are given in Sections V-A-1 and V-C. To state our results in a way that makes the tradeoff between error probability and blocklength clearer, we will assume (28) (29) For maximum and minimum rates and the number of messages is and . there exists a rateless code whose decoding time satisfies where is the average channel in (12). The nosy maximal error at this decoding time satisfies for , state sequences and -consistent side information given by (16).…”

“…In our model, the partial state information takes the form of estimates of the average channel induced by the channel state over "chunks" of size . In practice this channel information may come from exogenous measurements or from training information in the forward link, as in [12].…”