hyperbolic

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'

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}