Adversarial Channels with O(1)-Bit Partial Feedback

05/23/2023
by   Eric Ruzomberka, et al.
0

We consider point-to-point communication over q-ary adversarial channels with partial noiseless feedback. In this setting, a sender Alice transmits n symbols from a q-ary alphabet over a noisy forward channel to a receiver Bob, while Bob sends feedback to Alice over a noiseless reverse channel. In the forward channel, an adversary can inject both symbol errors and erasures up to an error fraction p ∈ [0,1] and erasure fraction r ∈ [0,1], respectively. In the reverse channel, Bob's feedback is partial such that he can send at most B(n) ≥ 0 bits during the communication session. As a case study on minimal partial feedback, we initiate the study of the O(1)-bit feedback setting in which B is O(1) in n. As our main result, we provide a tight characterization of zero-error capacity under O(1)-bit feedback for all q ≥ 2, p ∈ [0,1] and r ∈ [0,1], which we prove this result via novel achievability and converse schemes inspired by recent studies of causal adversarial channels without feedback. Perhaps surprisingly, we show that O(1)-bits of feedback are sufficient to achieve the zero-error capacity of the q-ary adversarial error channel with full feedback when the error fraction p is sufficiently small.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/15/2021

Stochastic-Adversarial Channels : Online Adversaries With Feedback Snooping

The growing need for reliable communication over untrusted networks has ...
research
12/12/2022

Binary Error-Correcting Codes with Minimal Noiseless Feedback

In the setting of error-correcting codes with feedback, Alice wishes to ...
research
02/07/2022

Channel Capacity for Adversaries with Computationally Bounded Observations

We study reliable communication over point-to-point adversarial channels...
research
07/15/2020

How to apply the rubber method for channels with feedback

We give an overview of applications of the rubber method. The rubber met...
research
11/16/2021

On Reverse Elastic Channels and the Asymmetry of Commitment Capacity under Channel Elasticity

Commitment is an important cryptographic primitive. It is well known tha...
research
08/18/2020

Deepcode and Modulo-SK are Designed for Different Settings

We respond to [1] which claimed that "Modulo-SK scheme outperforms Deepc...
research
02/21/2020

Sequential decomposition of discrete memoryless channel with noisy feedback

In this paper, we consider a discrete memoryless point to point channel ...

Please sign up or login with your details

Forgot password? Click here to reset