Stochastic network codes for consensus testing (CT) via a relay are proposed, where each of two or more parties knows a message and can find out if all these messages are equal, e.g. as an integrity check in a decentralized storage system or the control of mobile autonomous robots. The proposed codes achieve the CT capacity for memoryless uplinks channels when common randomness (CR) is available and no local randomness is used. With only local randomness at the edge nodes, upper and lower bounds for the capacity are given. The lower bound is achieved by CR generation via decode-and-forward transmission, and then using a common-randomness (CR)-assisted code. The upper bound is imposed by the CT over the uplink, when this consists of independent parallel channels to the relay. A recent derandomization result for encoders shows that, unlike deterministic encoding and CR shared between both encoders, the use of local randomness prevents the relay from successfully testing consensus. Therefore, in the proposed coding scheme, the relay recodes only to transmit random seeds and message hashes generated with these seeds. This scheme relies on an underlying CT code based on almost-universal hashing, where hashing is done with random seeds.

The understanding of achievable rates for quantum identification is far behind that of quantum transmission, as well as classical identification and transmission. Notably, in the classical case, common randomness shared between Alice and Bob before communication begins can greatly enhance the identification capacity. In the quantum regime, pre-shared entanglement may have an even more profound impact on the quantum identification (ID) capacity. This paper presents a regularized expression for the quantum ID capacity with entanglement assistance and demonstrates how it grows with the entanglement rate. Additionally, we provide deeper insights into the nature of quantum ID capacity. Interestingly, while the classical ID capacity becomes unbounded with unlimited common randomness, we find that the quantum ID capacity remains bounded even with unlimited entanglement assistance. Additionally, we find that entanglement plays the same role as an additional noiseless channel that is amortized, i.e., only used to make the rate positive.

This paper investigates secure communication over a broadcast channel in the presence of an unreliable cooperation link between the two decoders. Two messages are sent over the channel. One receiver aims to decode both messages while ensuring that the second message remains confidential from the other receiver. The second receiver is only interested in the first message, decoding either a part of it when the cooperation link fails or the entire message when the link is operational. A communication scheme is proposed that ensures reliability, confidentiality, and robustness against potential link failures. The capacity regions are characterized for both the discrete memoryless and the Gaussian version of the channel. Additionally, several notable special cases of the problem are examined.

We introduce the concept of locally homomorphic channels (LHCs) as a framework for analyzing the composition and decomposition of channels that simulate functions. We establish an equivalence between a specific class of LHCs and function computation codes for noisy channels. Further, we show for LHCs composed of multiple parts, e.g., an encoder, a noisy channel, and a decoder, that each component is independently locally homomorphic. A key implication is that stochastic decoding offers only very limited improvements in reliability. In scenarios where two messages from a large set are encoded independently, such as in K-identification, we prove that, in general, at most one of the encoders can compress the messages to logarithmic size. This result has significant consequences: for instance, it implies that consensus testing (CT) over discrete memoryless multiple-access channels becomes impossible when the message set has double-exponential size. In contrast, independent encoders can be reliable in such a setting, when the number of messages is only exponential. We demonstrate this for the example of deterministic consensus testing over a pair of binary symmetric channels.

Physical-layer network codes for consensus-testing (CT) via a relay are proposed, where each of two parties knows a message and can find out if all messages are equal, e.g. as an integrity check in a decentralized storage system or the control of mobile autonomous robots. By assumption, the encoders cannot randomize. The proposed codes achieve the CT capacity for channels with a memoryless uplink multiple-access channel that is a binary adder channel or a pair of q-ary symmetric or erasure channels. There, the capacity of noiseless uplinks can always be achieved, by using generalized deterministic identification (ID) codes for the uplink, testing consensus at the relay, and broadcasting the one-bit result using zero rate. For pairs of Gaussian channels and Gaussian adder channels, the capacity bounds equal those known for ID over certain noiseless uplinks, where the code sizes scale superexponentially in the block length. Using a recent derandomization result for decoders, it is shown that for general channels, the ID capacity of certain noiseless uplinks upper-bounds the CT capacity. In contrast, both for transmission coding for the uplink and additive linear network codes, the asymptotically achievable code sizes and necessary block lengths are shown to be suboptimal.

An upper bound to the identification capacity of discrete memoryless wiretap channels is derived under the requirement of semantic effective secrecy, combining semantic secrecy and stealth constraints. A previously established lower bound is improved by applying it to a prefix channel, formed by concatenating an auxiliary channel and the actual channel. The bounds are tight if the legitimate channel is more capable than the eavesdropper’s channel. An illustrative example is provided for a wiretap channel that is composed of a point-to-point channel, and a parallel, reversely degraded wiretap channel. A comparison with results for message transmission and for identification with only secrecy constraint is provided.

Deterministic identification over K-input multiple-access channels with average input cost constraints is considered. The capacity region for deterministic identification is determined for an average-error criterion, where arbitrarily large codes are achievable. For a maximal-error criterion, upper and lower bounds on the capacity region are derived. The bounds coincide if all average partial point-to-point channels are injective under the input constraint, i.e. all inputs at one terminal are mapped to distinct output distributions, if averaged over the inputs at all other terminals. The achievability is proved by treating the MAC as an arbitrarily varying channel with average state constraints. For injective average channels, the capacity region is a hyperrectangle. The modulo-2 and modulo-3 binary adder MAC are presented as examples of channels which are injective under suitable input constraints. The binary multiplier MAC is presented as an example of a non-injective channel, where the achievable identification rate region still includes the Shannon capacity region.

The identification capacity region of the compound broadcast channel is determined under an average error criterion, where the sender has no channel state information. We give single-letter identification capacity formulas for discrete channels and multiple-input multiple-output Gaussian channels under an average input constraint. The capacity theorems apply to general discrete memoryless broadcast channels. This is in contrast to the transmission setting, where the capacity is only known for special cases, notably the degraded broadcast channel and the multipleinput multiple-output broadcast channel with private messages. Furthermore, the identification capacity region of the compound multiple-input multiple-output broadcast channel can be larger than the transmission capacity region. This is a departure from the single-user behavior of identification, since the identification capacity of a single-user channel equals the transmission capacity.

The identification (ID) capacity region of the compound broadcast channel is determined under an average error criterion, where the sender has no channel state information. We give single-letter ID capacity formulas for discrete channels and MIMO Gaussian channels, under an average input constraint. The capacity theorems apply to general broadcast channels. This is in contrast to the transmission setting, where the capacity is only known for special cases, notably the degraded broadcast channel and the MIMO broadcast channel with private messages. Furthermore, the ID capacity region of the compound MIMO broadcast channel is in general larger than the transmission capacity region. This is a departure from the single-user behavior of ID, since the ID capacity of a single-user channel equals the transmission capacity.

In the identification problem, as opposed to the information transmission task, the decoder only identifies whether a message of his choosing was sent or not. This relaxation allows for a double-exponential code size. An achievable identification region is derived for a quantum broadcast channel, and a full characterization for the class of classical-quantum broadcast channels. The results are demonstrated for a depolarizing broadcast channel. Furthermore, the identification capacity region of the single-mode pure-loss bosonic broadcast channel is obtained as a consequence. In contrast to the single-user case, the capacity region for identification can be significantly larger than for transmission.