Related papers: The theoretical capacity of the Parity Source Code…
The quantum capacity of a memoryless channel is often used as a single figure of merit to characterize its ability to transmit quantum information coherently. The capacity determines the maximal rate at which we can code reliably over…
An ensemble of LDPC convolutional codes with parity-check matrices composed of permutation matrices is considered. The convergence of the iterative belief propagation based decoder for terminated convolutional codes in the ensemble is…
The problem of performing similarity queries on compressed data is considered. We focus on the quadratic similarity measure, and study the fundamental tradeoff between compression rate, sequence length, and reliability of queries performed…
We present a new information-theoretic definition and associated results, based on list decoding in a source coding setting. We begin by presenting list-source codes, which naturally map a key length (entropy) to list size. We then show…
A major open problem in understanding shallow quantum circuits (QAC$^0$) is whether they can compute Parity. We show that this question is solely about the Fourier spectrum of QAC$^0$: any QAC$^0$ circuit with non-negligible high-level…
An upper limit is given to the amount of quantum information that can be transmitted reliably down a noisy, decoherent quantum channel. A class of quantum error-correcting codes is presented that allow the information transmitted to attain…
Network coding theory studies the transmission of information in networks whose vertices may perform nontrivial encoding and decoding operations on data as it passes through the network. The main approach to deciding the feasibility of…
A rateless coding scheme transmits incrementally more and more coded bits over an unknown channel until all the information bits are decoded reliably by the receiver. We propose a new rateless coding scheme based on polar codes, and we show…
Shannon's channel coding theorem characterizes the maximal rate of information that can be reliably transmitted over a communication channel when optimal encoding and decoding strategies are used. In many scenarios, however, practical…
The more than thirty years old issue of the information capacity of quantum communication channels was dramatically clarified during the last period, when a number of direct quantum coding theorems was discovered. To considerable extent…
We investigate the potential of scale-free networks as error-correcting codes. We find that irregular low-density parity-check codes with highest performance known to date have degree distributions well fitted by a power-law function…
A central challenge in quantum error correction is identifying powerful quantum codes tailored to specific hardware and determining their error thresholds above which quantum information is unprotected. This problem is hard because we…
We study the following semi-deterministic setting of the joint source-channel coding problem: a deterministic source sequence (a.k.a. individual sequence) is transmitted via a memoryless channel, using delay-limited encoder and decoder,…
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…
Ar{\i}kan's polar coding, is by now a well studied technique that allows achieving the symmetric capacity of binary input memoryless channels with low complexity encoding and decoding, provided that the polar decoding architecture is used…
We consider transmission of two independent and separately encoded sources over a two-user binary-input Gaussian multiple-access channel. The channel gains are assumed to be unknown at the transmitter and the goal is to design an…
The paper presents bounds on the achievable rates and the decoding complexity of low-density parity-check (LDPC) codes. It is assumed that the communication of these codes takes place over statistically independent parallel channels where…
According to Kolmogorov complexity, every finite binary string is compressible to a shortest code -- its information content -- from which it is effectively recoverable. We investigate the extent to which this holds for infinite binary…
Arikan's polar codes are capable of achieving the Shannon's capacity at a low encoding and decoding complexity, while inherently supporting rate adaptation. By virtue of these attractive features, polar codes have provided fierce…
We study correlations in the prepare-and-measure scenario when quantum communication is constrained by photon-number statistics. Such constraints are natural and practical control parameters for semi-device-independent certification in…