Related papers: Interpolation of Quantum Polar Codes and Quantum R…
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…
Unrolling a decoding algorithm allows to achieve extremely high throughput at the cost of increased area. Look-up tables (LUTs) can be used to replace functions otherwise implemented as circuits. In this work, we show the impact of…
Polar codes are a new family of error correction codes for which efficient hardware architectures have to be defined for the encoder and the decoder. Polar codes are decoded using the successive cancellation decoding algorithm that includes…
Designing quantum error correcting codes that promise a high error threshold, low resource overhead and efficient decoding algorithms is crucial to achieve large-scale fault-tolerant quantum computation. The concatenated quantum Hamming…
This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…
By solving a problem regarding polynomials in a quotient ring, we obtain the relative hull and the Hermitian hull of projective Reed-Muller codes over the projective plane. The dimension of the hull determines the minimum number of…
It is known that polar codes can be efficiently constructed for binary-input channels. At the same time, existing algorithms for general input alphabets are less practical because of high complexity. We address the construction problem for…
Reed-Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an…
Code decompositions (a.k.a code nestings) are used to design good binary polar code kernels. The proposed kernels are in general non-linear and show a better rate of polarization under successive cancelation decoding, than the ones…
Despite the promise that fault-tolerant quantum computers can efficiently solve classically intractable problems, it remains a major challenge to find quantum algorithms that may reach computational advantage in the present era of noisy,…
The challenge of building a scalable quantum processor requires consolidation of the conflicting requirements of achieving coherent control and preservation of quantum coherence in a large scale quantum system. Moreover, the system should…
In this work, we present a family of architectures for polar decoders using a reduced-complexity successive-cancellation decoding algorithm that employs unrolling to achieve extremely high throughput values while retaining moderate…
Recently, a purely quantum version of polar codes has been proposed in [1] based on a quantum channel combining and splitting procedure, where a randomly chosen two-qubit Clifford unitary acts as channel combining operation. Here, we…
This work is on fast encoding and decoding of polar codes. We propose and detail 8-bit and 16-bit parallel decoders that can be used to reduce the decoding latency of the successive-cancellation decoder. These decoders are universal and can…
Polar codes are constructed for m-user multiple access channels (MAC) whose input alphabet size is a prime number. The block error probability under successive cancelation decoding decays exponentially with the square root of the block…
We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However,…
Here we concerned with quantum key distribution - a way to establish common cryptographic key between several parties. The work proposes a combination between quantum key distribution and systematic polar coding (an error correction…
Polar codes are of great interest since they are the first provably capacity-achieving forward error correction codes. To improve throughput and to reduce decoding latency of polar decoders, maximum likelihood (ML) decoding units are used…
Universal fault-tolerant quantum computation will require real-time decoding algorithms capable of quickly extracting logical outcomes from the stream of data generated by noisy quantum hardware. We propose modular decoding, an approach…
The training complexity of deep learning-based channel decoders scales exponentially with the codebook size and therefore with the number of information bits. Thus, neural network decoding (NND) is currently only feasible for very short…