diff --git a/codes/classical/analog/hyperbolic/hyperbolic.yml b/codes/classical/analog/hyperbolic/hyperbolic.yml new file mode 100644 index 000000000..db322ab68 --- /dev/null +++ b/codes/classical/analog/hyperbolic/hyperbolic.yml @@ -0,0 +1,39 @@ +####################################################### +## This is a code entry in the error correction zoo. ## +## https://github.com/errorcorrectionzoo ## +####################################################### + +code_id: hyperbolic +physical: reals +logical: reals + +name: 'Hyperbolic sphere packing' +introduced: '\cite{doi:10.1109/ITW.1998.706453,doi:10.1016/j.jfranklin.2005.09.001}' + +description: | + Encodes states (codewords) into coordinates in the hyperbolic plane \(\mathbb{H}^2\). + +protection: | + Designed to communicate information over channels for which a Lorentzian metric is appropriate \cite{doi:10.1137/1104038}. + Linear programming bounds exist for hyperbolic surfaces \cite{arxiv:2302.02540}. + +relations: + parents: + - code_id: analog + cousins: + - code_id: pam + detail: 'Hyperbolic PAM constellations may yield improved performance over Euclidean ones \cite{doi:10.1109/ITW.1998.706453}.' + - code_id: psk + detail: 'Hyperbolic PSK constellations may yield improved performance over Euclidean ones \cite{manual:{Silva, E. B., and R. Palazzo Jr. "M-PSK signal constellations in hyperbolic space achieving better performance than the M-PSK signal constellations in Euclidean space." 1999 IEEE Information Theory Workshop, Metsovo, Greece. 1999.}}.' + - code_id: qam + detail: 'Hyperbolic QAM constellations may yield improved performance over Euclidean ones \cite{manual:{Silva, E. B., R. Palazzo Jr, and M. Firer. "Performance analysis of QAM-like constellations in hyperbolic space." 2000 International Symposium on Information Theory and its Applications, Honolulu, USA. 2000.}}.' + + +# Begin Entry Meta Information +_meta: + # Change log - most recent first + changelog: + - user_id: VictorVAlbert + date: '2022-11-02' + - user_id: VictorVAlbert + date: '2022-02-16' diff --git a/codes/quantum/qubits/qubits_into_qubits.yml b/codes/quantum/qubits/qubits_into_qubits.yml index b2ab8d121..1fda3a4b3 100644 --- a/codes/quantum/qubits/qubits_into_qubits.yml +++ b/codes/quantum/qubits/qubits_into_qubits.yml @@ -14,9 +14,9 @@ description: | Encodes \(K\)-dimensional Hilbert space into a \(2^n\)-dimensional (i.e., \(n\)-qubit) Hilbert space. Usually denoted as \(((n,K))\) or \(((n,K,d))\), where \(d\) is the code's distance. protection: | - Corrects erasure errors on up to \(d-1\) qubits. + An \(((n,K,d))\) code corrects erasure errors on up to \(d-1\) qubits. The number of correctable errors is often called the \textit{decoding radius}, and it is upper bounded by half of the code distance. - As a result, qubit codes cannot tolerate adversarial errors on more than \((1-R)/4\) registers. + As a result, qubit codes cannot tolerate adversarial errors on more than \((1-R)/4\) registers, where \(R = \log_2 K/n\) is the code rate. A convenient and often considered error set is the \textit{Pauli error} or \textit{Pauli string} basis. For a single qubit, this set consists of products of powers of the Pauli matrices \begin{align}