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%. The time complexity of the algorithm is found to be polynomial with error suppression, allowing efficient error correction for codes of realistic sizes.

From: TM Synchronization and Channel Coding is used to protect the transfer frames against telemetry channel noise‐induced errors. Reference [3] describes the CCSDS Recommended Standard for TM Synchronization and Channel Coding, including specification of a convolutional code, a Reed‐ Solomon block‐oriented code, a concatenated coding system consisting of a convolutional inner code and a Reed‐S...

The IBM 3850 Mass Storage System (MSS) stores digital data onflexible magnetic tape media; however, it is different in many respects from the conventional multitrack tape machines. In particular, the use of a single-element rotary readwrite head imposes new demands in the areas of data encoding and error recovery. This paper presents a comprehensive scheme for error recovery for the 3850 MSS wh...

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 decoded values worse than the initial prediction. Our code exploits the fact that bit errors are relatively unlikely events: more than a few bit errors in a decode...

In order to calculate the error probability of a code it is necessary to know the distribution of the coset leaders. The enumeration of cosets of the first order Reed Muller code has been studied (i) by Berlekamp and Welch (1972) by associating with each coset a class of Boolean functions, and (ii) by Sloane and Dick (1971) by associating with each coset a class of single-error-correcting codes...

Asymmetric quantum error-correcting codes are quantum codes defined over biased quantum channels: qubitflip and phase-shift errors may have equal or different probabilities. The code construction is the Calderbank-ShorSteane construction based on two linear codes. We present families of toric surfaces, toric codes and associated asymmetric quantum error-correcting codes.

z TRW Abstract Block Cyclic Redundancy Check (CRC) codes represent a popular and powerful class of error detection techniques in modern data communication systems. Though eecient, CRC's can detect errors only after an entire block of data has been received and processed. In this work, we propose a new \continuous" error detection scheme using arithmetic coding that provides a novel tradeoo betw...

The Gottesman-Kitaev-Preskill (GKP) code is an important type of bosonic quantum error-correcting code. Since the GKP only protects against small shift errors in $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{p}$ and \^{}\fi{}}{q}$ quadratures, it necessary to concatenate with a stabilizer for larger error correction. In this paper, we consider concatenation single-mode two-dimensional (2D) color (...

In magnetic recording channels, a standard code architecture consists of an outer Reed-Solomon code in concatenation with an inner parity code. The inner parity code is used to detect and correct commonly occurring error events. Generally, a parity code with short block length performs better, as multiple error events within one block and, consequently, miscorrection are less likely. In this pa...