Related papers: Equidistant Polarizing Transforms
A lower bound on minimum distance of convolutional polar codes is provided. The bound is obtained from the minimum weight of generalized cosets of the codes generated by bottom rows of the polarizing matrix. Moreover, a construction of…
The Quantum Key Distribution protocol can encode a single quantum state and implements an information-theoretically secure key distribution protocol in communication. In the actual QKD experimental system, there are usually two encoding…
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…
This paper presents, for the first time, the concept of polarforming for wireless communications. Polarforming refers to a novel technique that enables the polarization of an antenna to shape into a desired polarization state for aligning…
We study the performance of common quantum stabilizer codes in the presence of asymmetric and correlated errors. Specifically, we consider the depolarizing noisy quantum memory channel and perform quantum error correction via the five and…
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…
Enabling ultra fast systems has been widely investigated during recent decades. Although polarization has been deployed from the beginning in satellite communications, nowadays it is being exploited to increase the throughput of satellite…
Polar codes, introduced by Arikan, achieve symmetric capacity of any discrete memoryless channels under low encoding and decoding complexity. Recently, non-binary polar codes have been investigated. In this paper, we calculate error…
Polar codes that approach capacity at a near-optimal speed, namely with scaling exponents close to $2$, have been shown possible for $q$-ary erasure channels (Pfister and Urbanke), the BEC (Fazeli, Hassani, Mondelli, and Vardy), all BMS…
For short-packet, low-latency communications over random access channels, piloting overhead significantly reduces spectral efficiency. Therefore, pilotless systems recently gained attraction. While blind phase estimation algorithms such as…
We provide a generalization of quantum polar codes to quantum channels with qudit-input, achieving the symmetric coherent information of the channel. Our scheme relies on a channel combining and splitting construction, where a two-qudit…
Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some…
In this paper, we study the lossless analog compression for i.i.d. nonsingular signals via the polarization-based framework. We prove that for nonsingular source, the error probability of maximum a posteriori (MAP) estimation polarizes…
We consider finite-level, symmetric quantization procedures for construction and decoding of polar codes. Whether polarization occurs in the presence of quantization is not known in general. Hassani and Urbanke have shown that a simple…
Reed Muller (RM) codes are known for their good minimum distance. One can use their structure to construct polar-like codes with good distance properties by choosing the information set as the rows of the polarization matrix with the…
In practical satellite-based quantum key distribution (QKD) systems, the preparation and transmission of polarization-encoding photons suffer from complex environmental effects and high channel-loss. Consequently, the hinge to enhancing the…
Arikan's polar coding method is extended to two-user multiple-access channels. It is shown that if the two users of the channel use the Arikan construction, the resulting channels will polarize to one of five possible extremals, on each of…
In this paper, we propose a new class of nonbinary polar codes with two-stage polarization for ultra-reliable and low-latency communications (URLLC), where the outer (symbol-level) polarization is achieved by using a 2X2 q-ary matrix [1 0;…
Scalar quantization and probabilistic shaping are applied to the distributed source coding of Gaussian sources, with mean-square error distortion. A coding scheme with a modulo interval, dithering, and truncated Gaussian shaping is shown to…
Characterizing the ultimate rates of entanglement distribution is essential for both foundational research and the practical deployment of quantum technologies. To investigate these limits, we introduce an erasure-Pauli channel model…