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IEEE Transactions on Information Theory

On identification via multiway channels with feedback

Rudolf Ahlswede, B. Verboven

Published Jan 1, 1991• 35 citations
Publisher

Abstract

For the case of complete feedback, a fairly unified theory of identification is presented. Its guiding principle is the discovery that communicators (sender and receiver) must set up a common random experiment with maximal entropy and use it as randomization for a suitable identification technique. It is shown how this can be done in a constructive manner. The proof of optimality (weak converse) is based on a novel entropy bound, which can be viewed as a substitute for Fano's lemma in the present context. The single-letter characterization of (second-order) capacity regions now rests on an entropy characterization problem, which often can be solved. This is done for the multiple-access channel with deterministic encoding strategies, and for the broadcast channel with randomized encoding strategies.>

DOI
10.1109/18.104313

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For the case of complete feedback, a fairly unified theory of identification is presented. Its guiding principle is the discovery that communicators (sender and receiver) must set up a common random experiment with maximal entropy and use it as randomization for a suitable identification technique. It is shown how this can be done in a constructive manner. The proof of optimality (weak converse) is based on a novel entropy bound, which can be viewed as a substitute for Fano's lemma in the present context. The single-letter characterization of (second-order) capacity regions now rests on an entropy characterization problem, which often can be solved. This is done for the multiple-access channel with deterministic encoding strategies, and for the broadcast channel with randomized encoding strategies.>
A study is made of the identification problem in the presence of a noiseless feedback channel, and the second-order capacity C/sub f/ (resp. C/sub F/) for deterministic (resp. randomized) encoding strategies is determined. Several important phenomena are encountered. (1) Although feedback does not increase the transmission capacity of a discrete memoryless channel (DMC), it does increase the (second-order) identification capacity; (2) noise increases C/sub f/; (3) the structure of the new capacity formulas is simpler than C.E. Shannon's (1948) familiar formula. This has the effect that proofs of converses become easier than in the authors' previous work.>
We investigate message identification over a K-sender Gaussian multiple access channel (K-GMAC). Unlike conventional Shannon transmission codes, the size of randomized identification (ID) codes experiences a doubly exponential growth in the code length. Improvements in the ID approach can be attained through additional resources such as quantum entanglement, common randomness (CR), and feedback. It has been demonstrated that an infinite capacity can be attained for a single-user Gaussian channel with noiseless feedback, irrespective of the chosen rate scaling. We establish the capacity region of both the K-sender Gaussian multiple access channel (K-GMAC) and the K-sender state-dependent Gaussian multiple access channel (K-SD-GMAC) when strictly causal noiseless feedback is available.
Studies two problems in the theory of identification via channels. The first problem concerns the identification via channels with noisy feedback. Whereas for Shannon's transmission problem the capacity of a discrete memoryless channel does not change with feedback, it is known that the identification capacity is affected by feedback. The authors study its dependence on the feedback channel. They prove both, a direct and a converse coding theorem. Although a gap exists between the upper and lower bounds provided by these two theorems, the known result for channels without feedback and the known result for channels with complete feedback, are both special cases of these two new theorems, because in these cases the bounds coincide. The second problem is the identification via wiretap channels. A secrecy identification capacity is defined for the wiretap channel. A "dichotomy theorem" is proved which says that the second-order secrecy identification capacity is the same as Shannon's capacity for the main channel as long as the secrecy transmission capacity of the wiretap channel is not zero, and zero otherwise. Equivalently, one can say that the identification capacity is not lowered by the presence of a wiretapper as long as 1 bit can be transmitted (or identified) correctly with arbitrarily small error probability. This is in strong contrast to the case of transmission.>
In contrast to Shannon transmission codes, the size of identification (ID) codes for discrete memoryless channels (DMCs) experiences doubly exponential growth with the block length when randomized encoding is used. Additional enhancements within the ID paradigm can be realized through supplementary resources such as quantum entanglement, common randomness (CR), and feedback. Joint transmission and sensing demonstrate significant benefits over separation-based methods. Inspired by the significant impact of feedback on the ID capacity, our work delves into the realm of joint ID and sensing (JIDAS) for state-dependent multiple access channels (SD-MACs) with noiseless strictly casual feedback. Here, the senders aim to convey ID messages to the receiver while simultaneously sensing the channel states. We establish a lower bound on the capacity-distortion region of the SD-MACs. An example shows that JIDAS outperforms the separation-based approach.
The concept of the wiretap channel was first proposed by Wyner. He considered the case in which data is to be transmitted reliably over a discrete memoryless main channel to a legitimate receiver. The wiretapper views the output of the main channel through another discrete memoryless channel. It is assumed that the wiretapper knows the code being used and his only handicap is the additional noise in his signal. The problem is to maximize the transmission rate R to the legitimate receiver and the equivocation d of the wiretapper. In this dissertation, the additive white Gaussian noise wiretap channel is introduced and the set of all achievable (R,d) pairs is determined explicitly through the use of certain special properties of the Gaussian channel. Some useful characterizations of a special class of wiretap channels are also explored. A model of the wiretap channel with feedback is proposed. It turns out that with the introduction of feedback, even when the main channel is inferior to the wiretapper's channel, it is still possible to reliably communicate with the legitimate receiver in complete secrecy. The binary erasure wiretap channel with feedback is examined and inner and outer bounds on the achievable (R,d) region are given. Finally, a scheme for enlarging the capacity region of multiple-access channels using feedback is analyzed. It is shown that conditions under which an enlargement is possible are fairly weak, indicating that feedback can almost increase the capacity region. (Author)
We define classical quantum multiway channels for transmission of classical information, after recent work by Allahverdyan and Saakian. Bounds on the capacity region are derived in a uniform way, which are analogous to the classically known ones, simply replacing Shannon entropy with von Neumann entropy. For the single receiver case (multiple-access channel) the exact capacity region is determined. These results are applied to the case of noisy channels, with arbitrary input signal states. A second issue of this work is the presentation of a calculus of quantum information quantities, based on the algebraic formulation of quantum theory.