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The Necessity and Sufficiency of Anytime Capacity for Control over a Noisy Communication Link: Parts I and II
"... We review how Shannon's classical notion of capacity is not enough to characterize a noisy communication channel if we intend to use that channel as a part of a feedback loop to stabilize an unstable linear system. While classical capacity is not enough, another parametric sense of capacity cal ..."
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Cited by 40 (6 self)
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We review how Shannon's classical notion of capacity is not enough to characterize a noisy communication channel if we intend to use that channel as a part of a feedback loop to stabilize an unstable linear system. While classical capacity is not enough, another parametric sense of capacity called "anytime capacity" is shown to be necessary for the stabilization of an unstable process. The rate required is given by the log of the system gain and the sense of reliability required comes from the sense of stability desired. A consequence of this necessity result is a sequential generalization of the Schalkwijk/Kailath scheme for communication over the AWGN channel with feedback. In cases of sufficiently...
Error Exponents of Optimum Decoding for the Interference Channel
"... Exponential error bounds for the finite–alphabet interference channel (IFC) with two transmitter–receiver pairs, are investigated under the random coding regime. Our focus is on optimum decoding, as opposed to heuristic decoding rules that have been used in previous works, like joint typicality deco ..."
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Cited by 15 (12 self)
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Exponential error bounds for the finite–alphabet interference channel (IFC) with two transmitter–receiver pairs, are investigated under the random coding regime. Our focus is on optimum decoding, as opposed to heuristic decoding rules that have been used in previous works, like joint typicality decoding, decoding based on interference cancellation, and decoding that considers the interference as additional noise. Indeed, the fact that the actual interfering signal is a codeword and not an i.i.d. noise process complicates the application of conventional techniques to the performance analysis of the optimum decoder. Using analytical tools rooted in statistical physics, we derive a single letter expression for error exponents achievable under optimum decoding and demonstrate strict improvement over error exponents obtainable using suboptimal decoding rules, but which are amenable to more conventional analysis.
A throughputdelay tradeoff in packetized systems with erasures, in
 Proc. 2005 IEEE International Symposium on Information Theory, ISIT 2005
, 2005
"... AbstractIn this paper we propose an information theoretic framework for studying coding and throughput optimization for multilayered packet transmission systems. Our approach assumes that the system is divided into two separate layers: One code word forms a packet at the physical layer and the co ..."
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Cited by 10 (4 self)
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AbstractIn this paper we propose an information theoretic framework for studying coding and throughput optimization for multilayered packet transmission systems. Our approach assumes that the system is divided into two separate layers: One code word forms a packet at the physical layer and the code at the network layer spans over these packets. At the receiver, the network layer assumes that the decoded packets arriving from the physical layer either have no errors or are marked as deleted. Thus, albeit the packet loss may be caused, for example, by decoding error, congestion or channel conditions, the network layer treats all decoding errors as erasures regardless of the cause. This allows us to view the system at the network layer as transmission over memoryless erasure channel. We study the throughput optimization and code design across the layers under a total code length constraint while taking also into account the network layer imperfections in the transmission. We use random coding error exponents to achieve results that do not depend on specific coding scheme used. The proposed scheme provides also means for investigating important physical layer phenomena, such as, channel model and lower layer error correction coding in the packet erasure models. Our approach extends to fading channels and networks of multiple nodes and by viewing the two layers of coding as a concatenated coding scheme, a comparison between layerbylayer and joint crosslayer rate optimization can be made, as outlined in this paper.
A FiniteBlocklength Perspective on Gaussian MultiAccess Channels
, 2014
"... Motivated by the growing application of wireless multiaccess networks with stringent delay constraints, we investigate the Gaussian multiple access channel (MAC) in the finite blocklength regime. Building upon information spectrum concepts, we develop several nonasymptotic inner bounds on channel ..."
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Cited by 8 (0 self)
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Motivated by the growing application of wireless multiaccess networks with stringent delay constraints, we investigate the Gaussian multiple access channel (MAC) in the finite blocklength regime. Building upon information spectrum concepts, we develop several nonasymptotic inner bounds on channel coding rates over the Gaussian MAC with a given finite blocklength, positive average error probability, and maximal power constraints. Employing Central Limit Theorem (CLT) approximations, we also obtain achievable secondorder coding rates for the Gaussian MAC based on an explicit expression for its dispersion matrix. We observe that, unlike the pentagon shape of the asymptotic capacity region, the secondorder region has a curved shape with no sharp corners. A main emphasis of the paper is to provide a new perspective on the procedure of handling input cost constraints for tight achievability proofs. Contrary to the complicated achievability techniques in the literature, we show that with a proper choice of input distribution, tight bounds can be achieved via the standard random coding argument and a modified typicality decoding. In particular, we prove that codebooks generated randomly according to independent uniform distributions on the respective “power shells ” perform far better than both independent and identically distributed (i.i.d.) Gaussian inputs and TDMA with power control. Interestingly, analogous to an error exponent result of Gallager, the resulting achievable region lies roughly halfway between that of the i.i.d. Gaussian inputs and that of a hypothetical “sumpower shell” input. However, dealing with such a noni.i.d. input requires additional analysis such as a new change of measure technique and application of a BerryEsseen CLT for functions of random variables.
Diversity gain region for mimo fading broadcast and multiple access channels
, 2005
"... In wireless communication systems, users with heterogeneous information content such as data, voice, and multimedia constrain the network by having different reliability requirements. In this paper an informationtheoretic framework is proposed to study communication systems which provide heterogen ..."
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Cited by 6 (0 self)
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In wireless communication systems, users with heterogeneous information content such as data, voice, and multimedia constrain the network by having different reliability requirements. In this paper an informationtheoretic framework is proposed to study communication systems which provide heterogeneous reliabilities for the users. This is done by defining individual probabilities of error for the users in the network and obtaining their fundamental tradeoffs. Using this framework, a system can be realized, which can provide a tradeoff of reliabilities among the users for a fixed vector of users’ rates. This adds a completely new dimension to the performance tradeoff in such networks, which is unique to multiterminal communication systems, and is beyond what is given by the conventional performance versus rate tradeoff in singleuser systems. Although this is a very general concept and can be applied to any multiterminal communication system, in this paper we consider multipleinput multipleoutput (MIMO) fading broadcast and multiple access channels. In particular, we quantify the reliability tradeoff by introducing the notion of diversity gain region (DGR), which specifies the set of diversity gain vectors that are simultaneously achievable by the users for a fixed vector of users’ multiplexing gains. We show the existence of a tradeoff among the users ’ diversity gains by deriving inner and outer bounds for the DGR.
Lossless coding for distributed streaming sources
 IEEE Trans. Inform. Theory
"... Distributed source coding is traditionally viewed in the block coding context — all the source symbols are known in advance at the encoders. This paper instead considers a streaming setting in which iid source symbol pairs are revealed to the separate encoders in real time and need to be reconstruct ..."
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Cited by 3 (2 self)
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Distributed source coding is traditionally viewed in the block coding context — all the source symbols are known in advance at the encoders. This paper instead considers a streaming setting in which iid source symbol pairs are revealed to the separate encoders in real time and need to be reconstructed at the decoder with some tolerable endtoend delay using finite rate noiseless channels. A sequential random binning argument is used to derive a lower bound on the error exponent with delay and show that both ML decoding and universal decoding achieve the same positive error exponents inside the traditional SlepianWolf rate region. The error events are different from the blockcoding error events and give rise to slightly different exponents. Because the sequential random binning scheme is also universal over delays, the resulting code eventually reconstructs every source symbol correctly with probability 1. 1
Error Exponents for Block Markov Superposition Encoding with Varying Decoding Latency
"... Abstract—Block Markov superposition encodinghas been used on a number of channels to enable transmitter cooperation, including the decodeandforward (DF) relaying scheme on the fullduplex relay channel. We analyze the error performance of DF with regular encoding and sliding window decoding as the ..."
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Abstract—Block Markov superposition encodinghas been used on a number of channels to enable transmitter cooperation, including the decodeandforward (DF) relaying scheme on the fullduplex relay channel. We analyze the error performance of DF with regular encoding and sliding window decoding as the window size of the decoder is allowed to grow. Specifically, we use Gallager’s random coding exponent to analyze the behavior of DF in the finite block length regime where the error probability cannotbemadearbitrarilysmallforafixedrateandblocklength. Although using a larger decoding window may not result in a better achievable rate in the infiniteblock length regime, doingso for finite block lengths enables a higher rate of transmission for a given error probability. In particular, these rate enhancements canleadtoalarger rangeofoperatingscenarios inwhichrelaying can outperform direct transmission. I.
Opportunistic capacity and error exponent regions for compound channel with feedback,” 2010, submitted to
 IEEE Trans. Inf. Theory. [Online]. Available: http://arxiv.org/abs/0911.2023
"... Abstract—Capacity of a compound channel without feedback is defined in a pessimistic manner as the maximum rate determined before the start of communication such that communication is reliable. In the presence of feedback, the transmission rate can adapt to the channel chosen by nature. Thus, capaci ..."
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Abstract—Capacity of a compound channel without feedback is defined in a pessimistic manner as the maximum rate determined before the start of communication such that communication is reliable. In the presence of feedback, the transmission rate can adapt to the channel chosen by nature. Thus, capacity can be defined in an opportunistic manner as the maximum rate determined at the end of communication such that communication is reliable. Under this definition, transmission rate and error exponents are regions rather than scalars. In this paper, variable length communication over a compound channel with feedback is formulated, its opportunistic capacity region is characterized, and lower bounds for its error exponent region are provided. I.
Error Exponents for Degraded Broadcast Channels with Degraded Message Sets
"... Abstract—We consider a degraded broadcast channel with maximum likelihood decoders and derive lower bounds on the error exponent of each user. Unlike earlier results, our exponents pertain to optimal decoding and include both rates. I. ..."
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Abstract—We consider a degraded broadcast channel with maximum likelihood decoders and derive lower bounds on the error exponent of each user. Unlike earlier results, our exponents pertain to optimal decoding and include both rates. I.