Related papers: Gallager error correcting codes for binary asymmet…
In this paper, we consider quantum error correction over depolarizing channels with non-binary low-density parity-check codes defined over Galois field of size $2^p$ . The proposed quantum error correcting codes are based on the binary…
To model printing noise a binary noisy channel and a set of controlled gates are introduced. The channel input is an image created by a halftoning algorithm and its output is the printed picture. Using this channel robustness to noise…
This paper proposes a method for designing error correction codes by combining a known coding scheme with an autoencoder. Specifically, we integrate an LDPC code with a trained autoencoder to develop an error correction code for intractable…
Due to process variation in nanoscale manufacturing, there may be permanently missing connections in information processing hardware. Due to timing errors in circuits, there may be missed messages in intra-chip communications, equivalent to…
Fundamental limits on communication rates over quantum channels are given by mathematical expressions involving entropic formulas. Often, it is unclear if these expressions are computable. This thesis describes contributions to the study of…
This paper determines the range of feasible values of standard error exponents for binary-input memoryless symmetric channels of fixed capacity $C$ and shows that extremes are attained by the binary symmetric and the binary erasure channel.…
Polar codes are introduced for discrete memoryless broadcast channels. For $m$-user deterministic broadcast channels, polarization is applied to map uniformly random message bits from $m$ independent messages to one codeword while…
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…
While the channel capacity reflects a theoretical upper bound on the achievable information transmission rate in the limit of infinitely many bits, it does not characterise the information transfer of a given encoding routine with finitely…
We describe certain extremalities for Gallager's $E_0$ function evaluated under the uniform input distribution for binary input discrete memoryless channels. The results characterize the extremality of the $E_0(\rho)$ curves of the binary…
We study encodings that give the best known thresholds for the non-zero capacity of quantum channels, i.e., the upper bound for correctable noise, using an entropic approach to calculation of the threshold values. Our results show that…
Estimates of noise channels for quantum gates are required for most error mitigation techniques and are desirable for informing quantum error correction decoders. These estimates can be obtained by resource-intensive off-line…
Polar coding is a method for communication over noisy classical channels which is provably capacity-achieving and has an efficient encoding and decoding. Recently, this method has been generalized to the realm of quantum information…
An algorithm is proposed to encode low-density parity-check (LDPC) codes into codewords with a non-uniform distribution. This enables power-efficient signalling for asymmetric channels. We show gains of 0.9 dB for additive white Gaussian…
Optical communication channels are ultimately quantum-mechanical in nature, and we must therefore look beyond classical information theory to determine their communication capacity as well as to find efficient encoding and decoding schemes…
We study error correction type protocols in which a quantum channel encodes logical information into an enlarged Hilbert space. Specifically, we consider channels realized by one dimensional random noisy quantum circuits with spatially…
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…
Second-order coding rate of channel coding is discussed for general sequence of channels. The optimum second-order transmission rate with a constant error constraint $\epsilon$ is obtained by using the information spectrum method. We apply…
We develop practical coding schemes for the cognitive overlay radios as modeled by the cognitive interference channel, a variation of the classical two user interference channel where one of the transmitters has knowledge of both messages.…
Low-density parity-check (LDPC) codes are specified by graphs, and are the error correction technique of choice in many communications and data storage contexts. Message passing decoders diffuse information carried by parity bits into the…