Related papers: The Sphere Packing Bound for DSPCs with Feedback a…
We derive a new upper bound on the reliability function for channel coding over discrete memoryless channels. Our bounding technique relies on two main elements: (i) adding an auxiliary genie-receiver that reveals to the original receiver a…
In this paper, we revisit the problem of finding the average capacity of the Gaussian feedback channel. First, we consider the problem of finding the average capacity of the analog Gaussian noise channel where the noise has an arbitrary…
We continue the study of the linear programming bounds for sphere packing introduced by Cohn and Elkies. We use theta series to give another proof of the principal theorem, and present some related results and conjectures.
This is the fifth in a series of papers giving a proof of the Kepler conjecture, which asserts that the density of a packing of congruent spheres in three dimensions is never greater than $\pi/\sqrt{18}\approx 0.74048...$. This is the…
This is the sixth in a series of papers giving a proof of the Kepler conjecture, which asserts that the density of a packing of congruent spheres in three dimensions is never greater than $\pi/\sqrt{18}\approx 0.74048...$. This is the…
We define three-point bounds for sphere packing that refine the linear programming bound, and we compute these bounds numerically using semidefinite programming by choosing a truncation radius for the three-point function. As a result, we…
In this letter, we derive the impulse response of the channel with a spherical absorbing receiver, a spherical reflecting boundary, and a point transmitter in molecular communication domain. By exploring the channel characteristics and…
The contact number of a packing of finitely many balls in Euclidean $d$-space is the number of touching pairs of balls in the packing. A prominent subfamily of sphere packings is formed by the so-called totally separable sphere packings:…
We derive upper bounds on the rate of transmission of classical information over quantum channels by block codes with a given blocklength and error probability, for both entanglement-assisted and unassisted codes, in terms of a unifying…
Feedback control actively dissipates uncertainty from a dynamical system by means of actuation. We develop a notion of "control capacity" that gives a fundamental limit (in bits) on the rate at which a controller can dissipate the…
We provide a tight asymptotic characterization of the error exponent for classical-quantum channel coding assisted by activated non-signaling correlations. Namely, we find that the optimal exponent--also called reliability function--is…
We have studied the packing of congruent disks on a spherical cap, for caps of different size and number of disks, $N$. This problem has been considered before only in the limit cases of circle packing inside a circle and on a sphere…
The concept and existence of sphere-bound-achieving and capacity-achieving lattices has been explained on AWGN channels by Forney. LDPC lattices, introduced by Sadeghi, perform very well under iterative decoding algorithm. In this work, we…
This paper considers the quantization problem on the Grassmann manifold with dimension n and p. The unique contribution is the derivation of a closed-form formula for the volume of a metric ball in the Grassmann manifold when the radius is…
This paper presents a new derivation method of converse bounds on the non-asymptotic achievable rate of discrete weakly symmetric memoryless channels. It is based on the finite blocklength statistics of the channel, where with the use of an…
We study channel simulation under common randomness assistance in the finite-blocklength regime and identify the smooth channel max-information as a linear program one-shot converse on the minimal simulation cost for fixed error tolerance.…
The cognitive interference channel is an interference channel in which one transmitter is non-causally provided with the message of the other transmitter. This channel model has been extensively studied in the past years and capacity…
We consider the discrete memoryless asymmetric broadcast channels. We prove that the error probability of decoding tends to one exponentially for rates outside the capacity region and derive an explicit lower bound of this exponent…
The capacity region of the interference channel in which one transmitter non-causally knows the message of the other, termed the cognitive interference channel, has remained open since its inception in 2005. A number of subtly differing…
We study lower bounds on the optimal error probability in classical coding over classical-quantum channels at rates below the capacity, commonly termed quantum sphere-packing bounds. Winter and Dalai have derived such bounds for…