More Like this

1. Binary Linear Codes With Optimal Scaling: Polar Codes With Large Kernels

   https://doi.org/10.1109/TIT.2020.3038806  

   Fazeli, Arman; Hassani, Hamed; Mondelli, Marco; Vardy, Alexander (September 2021, IEEE Transactions on Information Theory)
2. Monomial-Cartesian codes and their duals, with applications to LCD codes, quantum codes, and locally recoverable codes

   https://doi.org/10.1007/s10623-020-00726-x  

   López, Hiram H.; Matthews, Gretchen L.; Soprunov, Ivan (January 2020, Designs, Codes and Cryptography)
3. Triangulation codes: a family of non-linear codes with graceful degradation

   Roozbehani, Hajir; Polyanskiy, Yury (March 2018, 2018 Conf. Inform. Sciences and Syst. (CISS))

   This paper introduces the notion of triangulation codes, a family of non-linear codes that 1) admit efficient encoding/decoding 2) their bit error rate deteriorates gracefully as the quality of the erasure channel degrades. Some coding theoretic properties of these codes are established. In the case of transmitting data over the erasure channel, it is shown that, even with sub-optimal decoding, they can achieve lower bit error rate than uncoded transmission for any number of received output symbols. 

   more » « less
4. Polar Codes with Balanced Codewords

   https://doi.org/10.1109/ISIT44484.2020.9174042  

   Gupta, Utkarsh; Kiah, Han Mao; Vardy, Alexander; Yao, Hanwen (June 2020, 2020 IEEE International Symposium on Information Theory (ISIT))

   null (Ed.)
5. Handling leakage with subsystem codes

   https://doi.org/10.1088/1367-2630/ab3372  

   Brown, Natalie C.; Newman, Michael; Brown, Kenneth R. (July 2019, New Journal of Physics)

   Abstract Leakage is a particularly damaging error that occurs when a qubit state falls out of its two-level computational subspace. Compared to independent depolarizing noise, leaked qubits may produce many more configurations of harmful correlated errors during error-correction. In this work, we investigate different local codes in the low-error regime of a leakage gate error model. When restricting to bare-ancilla extraction, we observe that subsystem codes are good candidates for handling leakage, as their locality can limit damaging correlated errors. As a case study, we compare subspace surface codes to the subsystem surface codes introduced by Bravyiet al. In contrast to depolarizing noise, subsystem surface codes outperform same-distance subspace surface codes below error rates as high as ⪅ 7.5 × 10⁻⁴while offering better per-qubit distance protection. Furthermore, we show that at low to intermediate distances, Bacon–Shor codes offer better per-qubit error protection against leakage in an ion-trap motivated error model below error rates as high as ⪅ 1.2 × 10⁻³. For restricted leakage models, this advantage can be extended to higher distances by relaxing to unverified two-qubit cat state extraction in the surface code. These results highlight an intrinsic benefit of subsystem code locality to error-corrective performance. 

   more » « less