CRC

codes/classical/bits/easy/crc.yml

@@ -0,0 +1,45 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: crc
+physical: bits
+logical: bits
+
+name: 'Cyclic redundancy check (CRC) code'
+short_name: 'CRC'
+introduced: '\cite{doi:10.1109/JRPROC.1961.287814,preset:PetersonWeldon,preset:LinCostello}'
+
+alternative_names:
+  - 'Frame check sequence (FCS)'
+
+description: |
+  A generalization of the single parity-check code in which the generalization of the parity bit is the remainder of the data string (mapped into a polynomial via the \ref{topic:Cyclic-to-polynomial-correspondence}) divided by some generator polynomial.
+  A notable family of codes is referred to as \textit{CRC-}\(m-1\), where \(m\) is the length of the generator polynomial.
+
+protection: 'Detects any ''burst'' error up to the length of the generator polynomial.'
+
+realizations:
+  - 'CRC-16 and CRC-32 are used in data transmission, e.g., IEEE 802.16e, IEEE 802.3 \cite{manual:{Borrelli, Chris. "IEEE 802.3 cyclic redundancy check." application note: Virtex Series and Virtex-II Family, XAPP209 (v1. 0) (2001).}} and TCP/IP communication cite[Sec. 2.3.3]{doi:10.1007/978-0-387-68192-4_2}.'
+
+notes:
+  - 'See Ref. \cite{doi:10.1109/CICN.2015.108} and book \cite{manual:{Wells, Richard B. Applied coding and information theory for engineers. Prentice-Hall, Inc., 1998.}} for introductions to CRC codes.'
+  - 'See Refs. \cite{doi:10.1109/DSN.2002.1028931,doi:10.1109/DSN.2004.1311885} for exhaustive lists of CRC polynomials, as well as the \href{https://users.ece.cmu.edu/~koopman/crc/crc32.html}{CRC Polynomial Zoo website} by Philip Koopman.'
+
+relations:
+  parents:
+    - code_id: binary_cyclic
+  cousins:
+    - code_id: polar
+      detail: 'CRC codes concataned with polar codes yield improved performance of the SCL polar-code decoder \cite{doi:10.1109/LCOMM.2012.111612.121898,doi:10.1109/TIT.2015.2410251}.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-02-25'
+    - user_id: GageErwin
+      date: '2023-08-11'

codes/classical/bits/easy/parity_check.yml

@@ -10,7 +10,14 @@ logical: bits
 name: 'Single parity-check (SPC) code'
 short_name: 'SPC'
 
-description: 'Also known as a \textit{sum-zero}, \textit{zero-sum}, or \textit{even-weight} code. An \([n,n-1,2]\) linear binary code whose codewords consist of the message string appended with a parity-check bit such that the parity (i.e., sum over all coordinates of each codeword) is zero. If the Hamming weight of a message is odd (even), then the parity bit is one (zero). This code requires only one extra bit of overhead and is therefore inexpensive.'
+alternative_names:
+  - 'Sum-zero code'
+  - 'Zero-sum code'
+  - 'Even-weight code'
+
+description: |
+  An \([n,n-1,2]\) linear binary code whose codewords consist of the message string appended with a \textit{parity-check bit} or \textit{parity bit} such that the parity (i.e., sum over all coordinates of each codeword) is zero.
+  If the Hamming weight of a message is odd (even), then the parity bit is one (zero). This code requires only one extra bit of overhead and is therefore inexpensive.'
 
 protection: 'This code cannot protect information, it can only detect 1-bit error.'
 
@@ -26,10 +33,10 @@ realizations:
 
 relations:
   parents:
-    - code_id: binary_cyclic
-      detail: 'Since permutations preserve parity, the cyclic permutation of an SPC codeword is another codeword. The generator polynomial of the code is \(x-1\).'
-    - code_id: q-ary_parity_check
+    - code_id: crc
+      detail: 'A CRC using the divisor 11 is a single parity-check code \cite[Sec. 2.3.3]{doi:10.1007/978-0-387-68192-4_2}.'
     - code_id: reed_muller
+    - code_id: q-ary_parity_check
       detail: 'RM\((m-1,m)\) are parity-check codes.'
     - code_id: nearly_perfect
     - code_id: mds
@@ -45,6 +52,9 @@ relations:
     - code_id: ldgm
       detail: 'Concatenated SPCs are LDGM \cite{doi:10.1109/20.917609}.'
 
+# - code_id: binary_cyclic
+#   detail: 'Since permutations preserve parity, the cyclic permutation of an SPC codeword is another codeword. The generator polynomial of the code is \(x-1\).'
+
 
 # Begin Entry Meta Information
 _meta:

codes/quantum/qubits/subsystem/subsystem_product.yml

@@ -8,6 +8,7 @@ physical: qubits
 logical: qubits
 
 name: 'Subsystem product (SP) code'
+short_name: 'SP'
 introduced: '\cite{arXiv:2007.12152}'