Related papers: Efficient Algorithms for Maximum Likelihood Decodi…
We formulate maximum likelihood (ML) channel decoding as a quadratic unconstraint binary optimization (QUBO) and simulate the decoding by the current commercial quantum annealing machine, D-Wave 2000Q. We prepared two implementations with…
Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold…
Quantum error-correcting codes (QECCs) are necessary for fault-tolerant quantum computation. Surface codes are a class of topological QECCs that have attracted significant attention due to their exceptional error-correcting capabilities and…
We investigate threshold-based multi-trial decoding of concatenated codes with an inner Maximum-Likelihood decoder and an outer error/erasure (L+1)/L-extended Bounded Distance decoder, i.e. a decoder which corrects e errors and t erasures…
Low-rank decomposition has emerged as an important problem in Large Language Model (LLM) fine-tuning and inference. Through Singular Value Decomposition (SVD), the weight matrix can be factorized into low-rank spaces optimally. Previously,…
In multiple-input multiple-output (MIMO) fading channels maximum likelihood (ML) detection is desirable to achieve high performance, but its complexity grows exponentially with the spectral efficiency. The current state of the art in MIMO…
We study the problem of zero-delay coding for the transmission of a Markov source over a noisy channel with feedback and present a reinforcement learning solution which is guaranteed to achieve near-optimality. To this end, we formulate the…
We propose a decoder for the correction of erasures with hypergraph product codes, which form one of the most popular families of quantum LDPC codes. Our numerical simulations show that this decoder provides a close approximation of the…
A linear time approximate maximum likelihood decoding algorithm on tail-biting trellises is prsented, that requires exactly two rounds on the trellis. This is an adaptation of an algorithm proposed earlier with the advantage that it reduces…
An algorithm for exact maximum likelihood(ML) decoding on tail-biting trellises is presented, which exhibits very good average case behavior. An approximate variant is proposed, whose simulated performance is observed to be virtually…
Spinal codes are a type of capacity-achieving rateless codes that have been proved to approach the Shannon capacity over the additive white Gaussian noise (AWGN) channel and the binary symmetric channel (BSC). In this paper, we aim to…
Surface code error correction offers a highly promising pathway to achieve scalable fault-tolerant quantum computing. When operated as stabilizer codes, surface code computations consist of a syndrome decoding step where measured stabilizer…
In this paper, we investigate symbol-level precoding (SLP) and efficient decoding techniques for downlink transmission, where we focus on scenarios where the base station (BS) transmits multiple QAM constellation streams to users equipped…
Fault-tolerant quantum computation relies on scaling up quantum error correcting codes in order to suppress the error rate on the encoded quantum states. Topological codes, such as the surface code or color codes are leading candidates for…
The high computational cost of approaching the performance of Maximum-likelihood (ML) decoding has limited its practical use for decades. Because the complexity grows exponentially with the message length, researchers have spent years…
Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum…
We propose Dijkstra's algorithm with bounded list size after QR decomposition for decreasing the computational complexity of near maximum-likelihood (ML) detection of signals over multiple-input-multiple-output (MIMO) channels. After that,…
Transversal logical gates offer the opportunity for fast and low-noise logic, particularly when interspersed by a single round of parity check measurements of the underlying code. Using such circuits for the surface code requires decoding…
We give a broad generalisation of the mapping, originally due to Dennis, Kitaev, Landahl and Preskill, from quantum error correcting codes to statistical mechanical models. We show how the mapping can be extended to arbitrary stabiliser or…
In this paper, we distinguish two guessing algorithms for decoding binary linear codes. One is the guessing noise decoding (GND) algorithm, and the other is the guessing codeword decoding (GCD) algorithm. We prove that the GCD is a maximum…