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Recently proposed orthogonal time frequency space (OTFS) modulation has been considered as a promising candidate for accommodating various emerging communication and sensing applications in high-mobility environments. In this paper, we…
In this paper we define codes over some Octonion integers. We prove that in some conditions these codes can correct up to two errors for a transmitted vector and the code rate of the codes is grater than the code rate of the codes defined…
Accurate methods of assessing the performance of quantum gates are extremely important. Quantum process tomography and randomized benchmarking are the current favored methods. Quantum process tomography gives detailed information, but…
Descriptions of quantum algorithms, communication etc. protocols assume the existence of closed quantum system. However, real life quantum systems are open and are highly sensitive to errors. Hence error correction is of utmost importance…
Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead…
Quantum computation holds the promise of solving certain complex problems exponentially faster than classical computers. However, the high prevalent noise in current quantum devices impedes the accurate execution of even basic algorithms.…
In this paper, we present error-correcting codes which are the results of our research on the sub-exceeding functions. For a short and medium distance data transmission (wifi network, bluetooth, cable, ...), we see that these codes…
Orthogonal Frequency Division Multiplexing (OFDM) has gained a lot of popularity over the years. Due to its popularity, OFDM has been adopted as a standard in cellular technology and Wireless Local Area Network (WLAN) communication systems.…
This paper introduces a new counting code. Its design was motivated by distributed video coding where, for decoding, error correction methods are applied to improve predictions. Those error corrections sometimes fail which results in…
We construct error correcting codes for jointly transmitting a finite set of independent messages to an 'informed receiver' which has prior knowledge of the values of some subset of the messages as side information. The transmitter is…
Practical quantum computation heavily relies on the ability to perform quantum error correction in a fault-tolerant manner. Fault-tolerant encoding is a critical first step, and careful consideration of the error correction cycle that…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…
Although forward error-correction (FEC) coding is an essential part of modern fiber-optic communication systems, it is impractical to implement and evaluate FEC in transmission experiments and simulations. Therefore, it is desirable to…
This work compares the overhead of quantum error correction with concatenated and topological quantum error-correcting codes. To perform a numerical analysis, we use the Quantum Resource Estimator Toolbox (QuRE) that we recently developed.…
In this work, the efficient quantum error-correction protocol against the general independent noise is constructed with the three-qubit codes. The rules of concatenation are summarized according to the error-correcting capability of the…
Quantum error correction protects fragile quantum information by encoding it into a larger quantum system. These extra degrees of freedom enable the detection and correction of errors, but also increase the operational complexity of the…
An algorithm is presented for error correction in the surface code quantum memory. This is shown to correct depolarizing noise up to a threshold error rate of 18.5%, exceeding previous results and coming close to the upper bound of 18.9%.…
Decoding via sequentially guessing the error pattern in a received noisy sequence has received attention recently, and ORBGRAND has been proposed as one such decoding algorithm that is capable of utilizing the soft information embedded in…
This report surveys quantum error-correcting codes. As Preskill claimed, 21st century would be the golden age of quantum error correction. Quantum channels behave differently from classical channels, so researchers face difficulties in…
In a recent paper ([1]=quant-ph/0606035) it is shown how the optimal recovery operation in an error correction scheme can be considered as a semidefinite program. As a possible future improvement it is noted that still better error…