Related papers: Quantum Speedup for Polar Maximum Likelihood Decod…
Long polar codes can achieve the symmetric capacity of arbitrary binary-input discrete memoryless channels under a low complexity successive cancelation (SC) decoding algorithm. However, for polar codes with short and moderate code length,…
Polar codes under cyclic redundancy check aided successive cancellation list (CA-SCL) decoding can outperform the turbo codes and the LDPC codes when code lengths are configured to be several kilobits. In order to reduce the decoding…
A framework is proposed that allows for a joint description and optimization of both binary polar coding and $2^m$-ary digital pulse-amplitude modulation (PAM) schemes such as multilevel coding (MLC) and bit-interleaved coded modulation…
A quantum error correcting protocol can be substantially improved by taking into account features of the physical noise process. We present an efficient decoder for the surface code which can account for general noise features, including…
As large language models (LLMs) demonstrate outstanding performance across various tasks, attention-driven models have profoundly transformed the field of machine learning. Since attention computations account for the primary computational…
Polar codes are widely used in modern communication systems due to their capacity-achieving properties. This paper investigates the importance of coded bits in the decoding process of polar codes and aims to determine which bits contribute…
This paper proposes a method to optimize communication code rates via the application of neural polar decoders (NPDs). Employing this approach enables simultaneous optimization of code rates over input distributions while providing a…
The performance of maximum-likelihood (ML) decoding on the binary erasure channel for finite-length low-density parity-check (LDPC) codes from two random ensembles is studied. The theoretical average spectrum of the Gallager ensemble is…
Mixed-integer linear programming problems are extensively used in industry for a wide range of optimization tasks. However, as they get larger, they present computational challenges for classical solvers within practical time limits.…
Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes…
Permutation decoding gained recent interest as it can exploit the symmetries of a code in a parallel fashion. Moreover, it has been shown that by viewing permuted polar codes as polar subcodes, the set of usable permutations in permutation…
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…
We propose a novel optimization-based decoding algorithm for LDPC-coded massive MIMO channels. The proposed decoding algorithm is based on a proximal gradient method for solving an approximate maximum a posteriori (MAP) decoding problem.…
Polar encoding, described by Arikan in IEEE Transactions on Information Theory, Vol. 55, No. 7, July 2009, was a milestone for telecommunications. A Polar code distributes information among high and low-capacity channels, showing the…
Previous work showed that polar codes can be decoded using off-the-shelf LDPC decoders by imposing special constraints on the LDPC code structure, which, however, resulted in some performance degradation. In this paper we show that this…
For polar codes, successive cancellation list (SCL) decoding algorithm significantly improves finite-length performance compared to SC decoding. SCL-flip decoding can further enhance the performance but the gain diminishes as code length…
We study the use of polar codes for both discrete and continuous variables Quantum Key Distribution (QKD). Although very large blocks must be used to obtain the efficiency required by quantum key distribution, and especially continuous…
Decoding error-correctiong codes by methods of mathematical optimization, most importantly linear programming, has become an important alternative approach to both algebraic and iterative decoding methods since its introduction by Feldman…
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,…
A framework is proposed that allows for a joint description and optimization of both binary polar coding and the multilevel coding (MLC) approach for $2^m$-ary digital pulse-amplitude modulation (PAM). The conceptual equivalence of polar…