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Mukul Agarwal

Publications and source records attributed to Mukul Agarwal.

11 recordsLinked to original sources
arXiv2020

Non-existence of certain kind of finite-letter mutual information characterization for a class of time-invariant Markoff channels

We provide a rigorous definition of a certain kind of characterization for capacity regions of a family of Markoff networks which is based on optimization problems resulting out of calculating conditional mutual information from a finite number of random variables and by constraining these random variables in a certain way. This definition is partly motivated by the definition of single-letter characterizations in information theory. For a point-to-point Markoff channel, we prove that approximating the solution to these characterizations within an additive constant is a computable problem. Based on previous undecidability results concerning capacities of certain class of finite state machine channels (FSMCs), it will follow that there exists an example of family of FSMCs for which given such a characterization, this characterization cannot represent the capacity of this family of FSMCs.

cs.IT↗
arXiv2018

Source-channel separation for two-way interactive communication with fidelity criteria

Consider the channel coding problem where two users are interacting in order to communicate an i.i.d. source X1 from User 1 to User 2 with distortion D1 and an i.i.d. source X2 from User 2 to User 1 with distortion D2. X1 and X2 may be dependent. Communication occurs from User 1 to User 2 via a DMC C1 and from User 2 to User 1 over a DMC C2, where C1 and C2 act independently of each other. Communication occurs during each time slot between both users and each user can make a coding and decoding based on all past available knowledge. This interactive communication problem is formulated and it is proved that source-channel separation based architectures are optimal.

cs.IT↗
arXiv2018

Layered black-box, behavioral interconnection perspective and applications to the problem of communication with fidelity criteria, Part I: i.i.d. sources

In this paper, the problem of communication over an essentially unknown channel, which is known to be able to communicate a source to a destination to within a certain distortion level, is considered from a behavioral, interconnection view-point. Rates of reliable communication are derived and source-channel separation for communication with fidelity criteria is proved. The results are then generalized to the multi-user setting under certain assumptions. Other applications of this problem problem which follow from this perspective are discussed.

cs.IT↗
arXiv2015

A randomized covering-packing duality between source-coding and channel-coding

A randomized covering-packing duality between source and channel coding will be discussed by considering the source coding problem of coding a source with a certain distortion level and by considering a channel which communicates the source within a certain distortion level. An operational view of source-channel separation for communication with a fidelity criterion will be discussed in brief.

cs.IT↗
arXiv2013

A universal, operational theory of unicast multi-user communication with fidelity criteria

This is a three part paper. Optimality of source-channel separation for communication with a fidelity criterion when the channel is compound as defined by Csiszar and Korner in their book and general as defined by Verdu and Han, is proved in Part I. It is assumed that random codes are permitted. The word "universal" in the title of this paper refers to the fact that the channel model is compound. The proof uses a layered black-box or a layered input-output view-point. In particular, only the end-to-end description of the channel as being capable of communicating a source to within a certain distortion level is used when proving separation. This implies that the channel model does not play any role for separation to hold as long as there is a source model. Further implications of the layered black-box view-point are discussed. Optimality of source-medium separation for multi-user communication with fidelity criteria over a general, compound medium in the unicast setting is proved in Part II, thus generalizing Part I to the unicast, multi-user setting. Part III gets to an understanding of the question, "Why is a channel which is capable of communicating a source to within a certain distortion level, also capable of communicating bits at any rate less than the infimum of the rates needed to code the source to within the distortion level": this lies at the heart of why optimality of separation for communication with a fidelity criterion holds. The perspective taken to get to this understanding is a randomized covering-packing perspective, and the proof is operational.

cs.IT↗
arXiv2011

Architecture for communication with a fidelity criterion in unknown networks

We prove that in order to communicate independent sources (this is the unicast problem) between various users over an unknown medium to within various distortion levels, it is sufficient to consider source-channel separation based architectures: architectures which first compress the sources to within the corresponding distortion levels followed by reliable communication over the unknown medium. We are reducing the problem of universal rate-distortion communication of independent sources over a network to the universal reliable communication problem over networks. This is a reductionist view. We are not solving the reliable communication problem in networks.

cs.IT↗
arXiv2009

Equivalence perspectives in communication, source-channel connections and universal source-channel separation

An operational perspective is used to understand the relationship between source and channel coding. This is based on a direct reduction of one problem to another that uses random coding (and hence common randomness) but unlike all prior work, does not involve any functional computations, in particular, no mutual-information computations. This result is then used to prove a universal source-channel separation theorem in the rate-distortion context where universality is in the sense of a compound ``general channel.''

cs.IT↗
arXiv2006

Coding into a source: a direct inverse Rate-Distortion theorem

Shannon proved that if we can transmit bits reliably at rates larger than the rate distortion function $R(D)$, then we can transmit this source to within a distortion $D$. We answer the converse question ``If we can transmit a source to within a distortion $D$, can we transmit bits reliably at rates less than the rate distortion function?'' in the affirmative. This can be viewed as a direct converse of the rate distortion theorem.

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