Capacity of a POST Channel With and Without Feedback

Permuter, Haim H.; Asnani, Himanshu; Weissman, Tsachy

doi:10.1109/tit.2014.2343232

Cited by 30 publications

(61 citation statements)

References 23 publications

(41 reference statements)

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“…Furthermore, the state at time instance i is also the output of the receiver, Y i = S i . As pointed out in [80] such state dependent channels belong to the class of channels studied (with and without feedback) in [81,82]. Even though we have a channel with memory, the main result is that the capacity is achieved by i.i.d.…”

Section: Capacity For the Ligand-receptor Modelmentioning

confidence: 96%

Information theory of molecular communication: directions and challenges

Gohari

Mirmohseni

Nasiri-Kenari

2016

IEEE Trans. Mol. Biol. Multi-Scale Commun.

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Molecular Communication (MC) is a communication strategy that uses molecules as carriers of information, and is widely used by biological cells. As an interdisciplinary topic, it has been studied by biologists, communication theorists and a growing number of information theorists. This paper aims to specifically bring MC to the attention of information theorists. To do this, we first highlight the unique mathematical challenges of studying the capacity of molecular channels. Addressing these problems require use of known, or development of new mathematical tools. Toward this goal, we review a subjective selection of the existing literature on information theoretic aspect of molecular communication. The emphasis here is on the mathematical techniques used, rather than on the setup or modeling of a specific paper. Finally, as an example, we propose a concrete information theoretic problem that was motivated by our study of molecular communication.

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Section: Capacity For the Ligand-receptor Modelmentioning

confidence: 96%

Information theory of molecular communication: directions and challenges

Gohari

Mirmohseni

Nasiri-Kenari

2016

IEEE Trans. Mol. Biol. Multi-Scale Commun.

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“…The POST channel was introduced in [24] as an example of a channel whose previous output serves as the next channel state. The channel inputs and outputs are related as follows.…”

Section: Post Channelmentioning

confidence: 99%

“…As a result, it was possible to solve the DP problem analytically for several channels, which yielded several new feedback capacity results [11], [29]- [32]. However, while there are several more capacity results of FSCs with feedback, when feedback is absent, except for the POST channel [24], only certain FSCs with strict symmetry conditions were solved, all with an input distribution that is drawn i.i.d. [33]- [35].…”

Section: Introductionmentioning

confidence: 99%

Computable Upper Bounds for Unifilar Finite-State Channels

Huleihel

Sabag

Permuter

et al. 2019

2019 IEEE International Symposium on Information Theory (ISIT)

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The capacity of finite-state channels (FSCs) without feedback is investigated. We derive upper bounds that depend on the choice of a test distribution on the channel output process. We show that if the test distributions are structured on directed graphs, then the upper bounds are computable for two classes of FSCs. The computability of the upper bounds, subject to such test distributions, is shown via a novel dynamic programming (DP) formulation. We evaluate our bounds for several examples, including the well-known Trapdoor and Ising channels. For these channels, our bounds are analytic, simple, and strictly better than all previously reported bounds in the literature. Moreover, by studying the dicode erasure channel (DEC) we show that extending the standard Markovian test distribution to the choice of graph-based test distributions improves significantly the performance of the upper bounds.Finally, an alternative converse for the Previous Output is STate (POST) channel is shown.

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“…Remark 6.3: An extended Blahut-Arimoto algorithm is proposed in [39] to maximize the directed information for feedback channels. This algorithm can be adapted to compute the inner maximization of the directed information in (40). In fact, by [40, Lemma 1], the causal conditioning distributions form a polyhedron in R |X | N |EH | N .…”

Section: B Upper Bounds For Eh-sc2mentioning

confidence: 99%

Capacity Analysis of Discrete Energy Harvesting Channels

Mao

Hassibi

2017

IEEE Trans. Inform. Theory

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We study the channel capacity of a general discrete energy harvesting channel with a finite battery.Contrary to traditional communication systems, the transmitter of such a channel is powered by a device that harvests energy from a random exogenous energy source and has a finite-sized battery. As a consequence, at each transmission opportunity the system can only transmit a symbol whose energy is no more than the energy currently available. This new type of power supply introduces an unprecedented input constraint for the channel, which is simultaneously random, instantaneous, and influenced by the full history of the inputs and the energy harvesting process. Furthermore, naturally, in such a channel the energy information is observed causally at the transmitter. Both of these characteristics pose great challenges for the analysis of the channel capacity. In this work we use techniques developed for channels with side information and finite state channels, to obtain lower and upper bounds on the capacity of energy harvesting channels. In particular, in a general case with Markov energy harvesting processes we use stationarity and ergodicity theory to compute and optimize the achievable rates for the channels, and derive series of computable capacity upper and lower bounds. Index TermsChannel capacity, energy harvesting, causal CSIT, finite state channel, ergodicity. 23 As in the main text, the state index is increased by 1 compared to the original definition in [18]. 24 Actually from (43), (Yn, Sn+1) is also conditionally independent of the future inputs, i.e., the channel is causal. It is also implicitly assumed when computing the block conditional probability in [18] (equation (4.6.1)). This condition is indeed satisfied by the FSC models we study. (See [23] for more discussion). 25 Such an extension is always possible and unique by the Kolmogorov extension theorem if the measurable space (A, A) is standard, which is true for countable or Euclidean spaces. Interested readers may consult [41, Ch. 2,3] for details.

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Capacity of a POST Channel With and Without Feedback

Cited by 30 publications

References 23 publications

Information theory of molecular communication: directions and challenges

Information theory of molecular communication: directions and challenges

Computable Upper Bounds for Unifilar Finite-State Channels

Capacity Analysis of Discrete Energy Harvesting Channels

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