If the warden Willie attempting to detect the transmission knows the statistics of his receiver noise, Alice can transmit no more than O(√n) covert bits reliably to Bob in n channel uses of an AWGN channel. However, if Willie does not know his noise statistics exactly, Alice can covertly transmit O(n) bits. In this letter, Willie lacks knowledge of his channel statistics but observes T(n) length-n codeword slots, where some number may be used by Alice to attempt covert transmission. We show that Willie can often limit Alice to the same performance scaling as when he knows his channel statistics.
If the warden Willie attempting to detect the transmission knows the statistics of his receiver noise, Alice can transmit no more than O(√n) covert bits reliably to Bob in n channel uses of an AWGN channel. However, if Willie does not know his noise statistics exactly, Alice can covertly transmit O(n) bits. In this letter, Willie lacks knowledge of his channel statistics but observes T(n) length-n codeword slots, where some number may be used by Alice to attempt covert transmission. We show that Willie can often limit Alice to the same performance scaling as when he knows his channel statistics.
Recent work has established that when transmitter Alice wishes to communicate reliably to recipient Bob without detection by warden Willie, with additive white Gaussian noise (AWGN) channels between all parties, communication is limited to O(√n) bits in n channel uses. However, this assumes that Willie has an accurate statistical characterization of the channel. When Willie has uncertainty about such and his receiver is limited to a threshold test on the received power, Alice can transmit covertly with a power that does not decrease with n, thus conveying O(n) bits covertly and reliably in n uses of an AWGN channel. Here, we consider covert communication of O(n) bits in n channel uses while generalizing the environment and removing any restrictions on Willie's receiver. We assume that an uninformed “jammer” is present to help Alice, and we consider AWGN and block fading channels. In some scenarios, Willie's optimal detector is a threshold test on the received power. When the channel between the jammer and Willie has multiple fading blocks per codeword, a threshold test on the received power is not optimal. However, we establish that Alice can remain covert with a transmit power that does not decrease with n even when Willie employs an optimal detector.
Recent work has established that when transmitter Alice wishes to communicate reliably to recipient Bob without detection by warden Willie, with additive white Gaussian noise (AWGN) channels between all parties, communication is limited to O(n) bits in n channel uses. However, this assumes Willie has an accurate statistical characterization of the channel. When Willie has uncertainty about such and his receiver is limited to a threshold test on the received power, Alice can transmit covertly with a power that does not decrease with n, thus conveying O(n) bits covertly and reliably in n uses of an AWGN channel. Here, we consider covert communication of O(n) bits in n channel uses while generalizing the environment and removing any restrictions on Willie's receiver. We assume an uninformed "jammer" is present to help Alice, and we consider AWGN and block fading channels. In some scenarios, Willie's optimal detector is a threshold test on the received power. When the channel between the jammer and Willie has multiple fading blocks per codeword, a threshold test on the received power is not optimal. However, we establish that Alice can remain covert with a transmit power that does not decrease with n even when Willie employs an optimal detector.
Recent work has established that when transmitter Alice wishes to communicate reliably to recipient Bob without detection by warden Willie, with additive white Gaussian noise (AWGN) channels between all parties, communication is limited to O(√n) bits in n channel uses. However, this result is predicated on Willie having an accurate statistical characterization of the background noise. When Willie has uncertainty about his noise characteristics and his receiver is limited to a power detector, O(n) bits can be covertly delivered. Here, we establish covert communication of O(n) bits in n channel uses while: (i) generalizing the environment; and (ii) removing any restrictions on Willie's receiver. We consider the case where an additional node, called the "jammer", is present to help Alice and Bob communicate covertly. This jammer is termed "uninformed", as it does not know the content or timing of Alice's transmission. We consider both AWGN channels and a scenario with a block faded jammer with a single fade per codeword. In these scenarios, we are able to establish the optimality of the power detector for Willie, from which the achievability of reliable and covert communication at a positive rate follows.
Consider a channel where authorized transmitter Jack sends packets to authorized receiver Steve according to a Poisson process with rate λ packets per second for a time period T. Suppose that covert transmitter Alice wishes to communicate information to covert receiver Bob on the same channel without being detected by a watchful adversary Willie. We consider two scenarios. In the first scenario, we assume that warden Willie cannot look at packet contents but rather can only observe packet timings, and Alice must send information by inserting her own packets into the channel. We show that the number of packets that Alice can covertly transmit to Bob is on the order of the square root of the number of packets that Jack transmits to Steve; conversely, if Alice transmits more than that, she will be detected by Willie with high probability. In the second scenario, we assume that Willie can look at packet contents but that Alice can communicate across an M/M/1 queue to Bob by altering the timings of the packets going from Jack to Steve. First, Alice builds a codebook, with each codeword consisting of a sequence of packet timings to be employed for conveying the information associated with that codeword. However, to successfully employ this codebook, Alice must always have a packet to send at the appropriate time. Hence, leveraging our result from the first scenario, we propose a construction where Alice covertly slows down the packet stream so as to buffer packets to use during a succeeding codeword transmission phase. Using this approach, Alice can covertly and reliably transmit O(λT) covert bits to Bob in time period T over an M/M/1 queue with service rate μ > e · λ.
Recent works have considered the ability of transmitter Alice to communicate reliably to receiver Bob without being detected by warden Willie. These works generally assume a standard discrete-time model. But the assumption of a discrete-time model in standard communication scenarios is often predicated on its equivalence to a continuous-time model, which has not been established for the covert communications problem. Here, we consider the continuous-time channel directly and study if efficient covert communication can still be achieved. We assume that an uninformed jammer is present to assist Alice, and we consider additive white Gaussian noise (AWGN) channels between all parties. For a channel with approximate bandwidth W, we establish constructions such that O(WT) information bits can be transmitted covertly and reliably from Alice to Bob in T seconds for two separate scenarios: 1) when the path-loss between Alice and Willie is known; and 2) when the path-loss between Alice and Willie is unknown.
The recent square root law (SRL) for covert communication demonstrates that Alice can reliably transmit O(√n) bits to Bob in n uses of an additive white Gaussian noise (AWGN) channel while keeping ineffective any detector employed by the adversary; conversely, exceeding this limit either results in detection by the adversary with high probability or nonzero decoding error probability at Bob. This SRL is under the assumption that the adversary knows when Alice transmits (if she transmits); however, in many operational scenarios, he does not know this. Hence, here, we study the impact of the adversary's ignorance of the time of the communication attempt. We employ a slotted AWGN channel model with T(n) slots each containing n symbol periods, where Alice may use a single slot out of T(n). Provided that Alice's slot selection is secret, the adversary needs to monitor all T(n) slots for possible transmission. We show that this allows Alice to reliably transmit O(min{(n log T(n))1/2, n}) bits to Bob (but no more) while keeping the adversary's detector ineffective. To achieve this gain over SRL, Bob does not have to know the time of transmission provided T(n)cTn, cT= O(1).