Related papers: Supplement to: Code Spectrum and Reliability Funct…
We revise the proof of low-rate upper bounds on the reliability function of discrete memoryless channels for ordinary and list-decoding schemes, in particular Berlekamp and Blinovsky's zero-rate bound, as well as Blahut's bound for low…
The comments of Guseinov on our recent paper (Czech. J. Phys., 52 (2002)1297) have been analyzed critically. It is shown that his comments are irrelevant and also unjust. In contrast to his comment, it is proved that the presented formulae…
We establish a new simple explicit description of combinatorial wall-crossing for the rational Cherednik algebra applied to the trivial representation. In this way we recover a theorem of P. Dimakis and G. Yue. We also present two…
A very simple but useful almost sure convergence theorem of probability is given.
Transmission of information reliably and efficiently across channels is one of the fundamental goals of coding and information theory. In this respect, efficiently decodable deterministic coding schemes which achieve capacity provably have…
In this paper, we study the symmetry of polar codes on symmetric binary-input discrete memoryless channels (B-DMC). The symmetry property of polar codes is originally pointed out in Arikan's work for general B-DMC channels. With the…
We define, answering a question of Sarnak in his letter to Bombieri, a symplectic pairing on the spectral interpretation (due to Connes and Meyer) of the zeroes of Riemann's zeta function. This pairing gives a purely spectral formulation of…
Coding theorems and (strong) converses for memoryless quantum communication channels and quantum sources are proved: for the quantum source the coding theorem is reviewed, and the strong converse proven. For classical information…
Random coding arguments are the backbone of most channel capacity achievability proofs. In this paper, we show that in their standard form, such arguments are insufficient for proving some network capacity theorems: structured coding…
Recently we have obtained two simple proofs of Sharkovsky's theorem, one with directed graphs [7] and the other without [8]. In this note, we present yet more simple proofs of Sharkovsky's theorem.
In this paper, by treating Reed-Muller (RM) codes as a special class of low-density parity-check (LDPC) codes and assuming that sub-blocks of the parity-check matrix are randomly interleaved to each other as Gallager's codes, we present a…
Achieving security against adversaries with unlimited computational power is of great interest in a communication scenario. Since polar codes are capacity achieving codes with low encoding-decoding complexity and they can approach perfect…
It is shown that polar coding schemes achieve the known achievable rate regions for several multi-terminal communications problems including lossy distributed source coding, multiple access channels and multiple descriptions coding. The…
We extend a low-rate improvement of the random coding bound on the reliability of a classical discrete memoryless channel to its quantum counterpart. The key observation that we make is that the problem of bounding below the error exponent…
In information theory the reliability function and its bounds, describing the exponential behavior of the error probability, are the most important quantitative characteristics of the channel performance. From a general point of view, these…
We prove the Courtade-Kumar conjecture, for several classes of n-dimensional Boolean functions, for all $n \geq 2$ and for all values of the error probability of the binary symmetric channel, $0 \leq p \leq 1/2$. This conjecture states that…
New channel coding converse and achievability bounds are derived for a single use of an arbitrary channel. Both bounds are expressed using a quantity called the "smooth 0-divergence", which is a generalization of Renyi's divergence of order…
The question of whether Reed-Muller (RM) codes achieve capacity on binary memoryless symmetric (BMS) channels has drawn attention since it was resolved positively for the binary erasure channel by Kudekar et al. in 2016. In 2021, Reeves and…
Let $W$ be a binary-input memoryless symmetric (BMS) channel with Shannon capacity $I(W)$ and fix any $\alpha > 0$. We construct, for any sufficiently small $\delta > 0$, binary linear codes of block length $O(1/\delta^{2+\alpha})$ and rate…
In this paper, we design explicit codes for strong coordination in two-node networks. Specifically, we consider a two-node network in which the action imposed by nature is binary and uniform, and the action to coordinate is obtained via a…