The Capacity of Anonymous Communications

TL;DR

This paper determines the maximum rate of anonymous communication over a parallel channel with multiple transmitters, showing that the capacity is inversely proportional to the number of transmitters and establishing randomness requirements.

Contribution

It derives the capacity of anonymous communication in a parallel channel setting and specifies the necessary correlated randomness at transmitters, a novel theoretical result.

Findings

Capacity of anonymous communication is 1/K.

Each transmitter needs at least 1 bit of correlated randomness per message bit.

Total randomness at all transmitters must be at least (K-1) bits per message bit.

Abstract

We consider the communication scenario where K transmitters are each connected to a common receiver with an orthogonal noiseless link. One of the transmitters has a message for the receiver, who is prohibited from learning anything in the information theoretic sense about which transmitter sends the message (transmitter anonymity is guaranteed). The capacity of anonymous communications is the maximum number of bits of desired information that can be anonymously communicated per bit of total communication. For this anonymous communication problem over a parallel channel with K transmitters and 1 receiver, we show that the capacity is 1/K, i.e., to communicate 1 bit anonymously, each transmitter must send a 1 bit signal. Further, it is required that each transmitter has at least 1 bit correlated randomness (that is independent of the messages) per message bit and the size of correlated randomness at all K transmitters is at least K-1 bits per message bit.