Related papers: An Improved Sphere-Packing Bound for Finite-Length…
We recently showed in [1] the superiority of certain structured coding matrices ensembles (such as partial row-orthogonal) for sparse superposition codes when compared with purely random matrices with i.i.d. entries, both…
Establishing the sphere packing bound for block codes on the discrete stationary product channels with feedback ---which are commonly called the discrete memoryless channels with feedback--- was considered to be an open problem until…
This paper studies the third-order characteristic of nonsingular discrete memoryless channels and the Gaussian channel with a maximal-power constraint. The third-order term in our expansions employs a new quantity here called the channel…
We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds known at least for dimensions 4 through…
An upper bound on the capacity of multiple-input multiple-output (MIMO) Gaussian fading channels is derived under peak amplitude constraints. The upper bound is obtained borrowing concepts from convex geometry and it extends to MIMO…
In this paper, lower bounds on error probability in coding for discrete classical and classical-quantum channels are studied. The contribution of the paper goes in two main directions: i) extending classical bounds of Shannon, Gallager and…
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…
Sphere decoding (SD) of polar codes is an efficient method to achieve the error performance of maximum likelihood (ML) decoding. But the complexity of the conventional sphere decoder is still high, where the candidates in a target sphere…
We consider the use of the well-known dual capacity bounding technique for deriving upper bounds on the capacity of indecomposable finite-state channels (FSCs) with finite input and output alphabets. In this technique, capacity upper bounds…
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…
We investigate the classical communication over quantum channels when assisted by no-signaling (NS) and positive-partial-transpose-preserving (PPT) codes, for which both the optimal success probability of a given transmission rate and the…
We recently proved threshold saturation for spatially coupled sparse superposition codes on the additive white Gaussian noise channel. Here we generalize our analysis to a much broader setting. We show for any memoryless channel that…
Sparse Regression Codes (SPARCs) are capacity-achieving codes introduced for communication over the Additive White Gaussian Noise (AWGN) channels and were later extended to general memoryless channels. In particular it was shown via…
We study error bounds for linear programming decoding of regular LDPC codes. For memoryless binary-input output-symmetric channels, we prove bounds on the word error probability that are inverse doubly-exponential in the girth of the factor…
The Shannon upper bound places a limit on the error-free information transmission rate (capacity) of a noisy channel. It has stood for over sixty years, and underlies both theoretical and practical work in the telecommunications industry.…
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…
A judicious application of the Berry-Esseen theorem via suitable Augustin information measures is demonstrated to be sufficient for deriving the sphere packing bound with a prefactor that is…
The sphere packing bound, in the form given by Shannon, Gallager and Berlekamp, was recently extended to classical-quantum channels, and it was shown that this creates a natural setting for combining probabilistic approaches with some…
The sphere packing bound, in the form given by Shannon, Gallager and Berlekamp, was recently extended to classical-quantum channels, and it was shown that this creates a natural setting for combining probabilistic approaches with some…
A fundamental quantity of interest in Shannon theory, classical or quantum, is the error exponent of a given channel $W$ and rate $R$: the constant $E(W,R)$ which governs the exponential decay of decoding error when using ever larger…