~

Author: valbert4

codes/classical/bits/tanner/irregular/ra/ira.yml

@@ -19,12 +19,13 @@ description: |
   IRA codes can be optimized against various noise channels \cite{doi:10.1109/TIT.2004.831778}.
 
 features:
-  rate: 'IRA codes nearly achieve the Shannon capacity of the binary erasure channel using iterative decoding \cite{manual:{Jin, Hui, Aamod Khandekar, and Robert McEliece. "Irregular repeat-accumulate codes." Proc. 2nd Int. Symp. Turbo codes and related topics. 2000.}}. Puncturing ressens the decoding complexity while still allowing sequences of codes to achive capacity \cite{doi:10.1109/TIT.2005.850079}.'
+  rate: 'IRA codes nearly achieve the Shannon capacity of the binary erasure channel using iterative decoding \cite{manual:{Jin, Hui, Aamod Khandekar, and Robert McEliece. "Irregular repeat-accumulate codes." Proc. 2nd Int. Symp. Turbo codes and related topics. 2000.}}. Puncturing lessens the decoding complexity while still allowing sequences of codes to achieve capacity \cite{doi:10.1109/TIT.2005.850079}.'
   encoders:
-    - 'One linear-time encoder for a \textit{systematic} IRA code consists of first encoding into an \([n,k]\) LDGM binary linear code, applying a random permutation, and then applying an acumulator to obtain
+    - 'One linear-time encoder for a \textit{systematic} IRA code consists of first encoding into an \([n,k]\) LDGM binary linear code, applying a random permutation, and then applying an accumulator to obtain
     \begin{align}
-      (u_{1},u_{1}+u_{2},\cdots,u_{1}+\cdots+u_{3K})~.
-    \end{align}'
+      (u_{1},u_{1}+u_{2},\cdots,u_{1}+\cdots+u_{N})~,
+    \end{align}
+    where \(N\) is the length of the permuted LDGM output.'
   decoders:
     - 'Linear-time decoder \cite{manual:{Jin, Hui, Aamod Khandekar, and Robert McEliece. "Irregular repeat-accumulate codes." Proc. 2nd Int. Symp. Turbo codes and related topics. 2000.}}.'
 

codes/classical/matrices/spacetime/orthogonal/alamouti.yml

@@ -11,9 +11,9 @@ name: 'Alamouti code'
 introduced: '\cite{doi:10.1109/49.730453}'
 
 description: |
-  The simplest OSTBC, with \(n=2\) transmitting antennas, \(m=1\) receiving antennas, and \(t=2\) uses.
+  The simplest OSTBC, with \(n=2\) transmitting antennas, \(m=1\) receiving antenna, and \(t=2\) channel uses.
 
-  The unitary coding matrix is
+  The transmit matrix is
   \begin{align}
     \begin{pmatrix}c_{1} & c_{2}\\
     -c_{2}^{\star} & c_{1}^{\star}
@@ -22,7 +22,7 @@ description: |
   where \(c_i\) are complex numbers, and where \(\star\) denotes complex conjugation.
 
 features:
-  rate: 'The only OSTBC with full rate, \(k = mt = 2\).'
+  rate: 'The only complex OSTBC with full rate, i.e., one complex information symbol per channel use \cite{doi:10.1109/18.771146,doi:10.1109/TIT.2003.817426}.'
 
 realizations:
   - 'Wireless standards since: 3G, LTE, LTE-Advanced, and 5G.'

codes/classical/properties/block/distributed_storage/lrc/code_with_locality.yml

@@ -8,8 +8,8 @@ code_id: code_with_locality
 name: 'Code with locality'
 
 description: |
-  A code with \((r,\delta)\) locality is a code that encodes each codeword coordinate into an \([r+\delta-1,r,\delta]\) MDS code \cite[Sec. 31.3.4.5]{preset:HKSdist}. 
-  In other words, given a codeword \(c\) and coordinate \(c_i\), there exists a coordinate set \(S_i\) of size \(\leq r+\delta-1\) such that the restriction \(C_{|S_i}\) of the code to that set is a code with minimum distance \(\delta\). 
+  A code has \((r,\delta)\) locality if each codeword coordinate belongs to a repair group of size at most \(r+\delta-1\) whose restricted code has minimum distance at least \(\delta\) \cite[Sec. 31.3.4.5]{preset:HKSdist}.
+  Equivalently, given a codeword \(c\) and coordinate \(c_i\), there exists a coordinate set \(S_i\) of size \(\leq r+\delta-1\) containing \(i\) such that the restriction \(C_{|S_i}\) has minimum distance at least \(\delta\).
 
 protection: |
   There is a generalized Singleton minimum distance bound \cite{arxiv:1202.2414},

codes/classical/properties/block/distributed_storage/lrc/lcc.yml

@@ -17,8 +17,8 @@ short_name: 'LCC'
 
 
 description: |
-  Recall that a block code encodes a length-\(k\) message into a length-\(n\) codeword, which is then sent through a noise channel to yield an error word.
-  Informally, an LCC is a block code for which one can recover any coordinate of a codeword from at most \(r\) coordinates of the error word (assuming the error word is within some tolerated corruption rate \(\delta\)).
+  Recall that a block code encodes a length-\(k\) message into a length-\(n\) codeword, which is then sent through a noise channel to yield a received word.
+  Informally, an LCC is a block code for which one can recover any coordinate of a codeword from at most \(r\) coordinates of the received word (assuming the received word is within some tolerated corruption rate \(\delta\)).
 
   Modified versions of local correctability include \textit{relaxed local correctability} \cite{doi:10.4086/toc.2020.v016a018}.
 
@@ -33,8 +33,7 @@ notes:
 relations:
   parents:
     - code_id: locally_recoverable
-      detail: 'LRCs (LCCs) allow one to recover any coordinate of a codeword from at most \(r\) coordinates of a codeword (an error word within the decoding radius).
-      Since a codeword is a trivial error word, any LCC is also an LRC.'
+      detail: 'LRCs recover a coordinate from a small number of other coordinates of an uncorrupted codeword, while LCCs allow recovery from a corrupted received word within the decoding radius. Since an uncorrupted codeword is a special case of a received word, any LCC is also an LRC.'
   cousins:
     - code_id: ldc
       detail: 'Any family of LCCs can be converted to a family of LDCs whose rate differs by a constant \cite{arxiv:1611.06980}; see \cite[Sec. 2.4.1]{manual:{Gopi, Sivakanth. Locality in coding theory. Diss. Princeton University, 2018.}}.'

codes/classical/q-ary_digits/alternant/bch/q-ary_bch.yml

@@ -13,7 +13,7 @@ introduced: '\cite{doi:10.1137/0109020}'
 
 description: |
   Cyclic \(q\)-ary code, with \(n\) and \(q\) relatively prime, whose zeroes are consecutive powers of a primitive \(n\)th root of unity \(\alpha\). More precisely, the generator polynomial of a BCH code of \textit{designed distance} \(\delta\geq 1\) is the lowest-degree monic polynomial with zeroes \(\{\alpha^b,\alpha^{b+1},\cdots,\alpha^{b+\delta-2}\}\) for some \(b\geq 0\). BCH codes are called \textit{narrow-sense} when \(b=1\), and are called \textit{primitive} when \(n=q^r-1\) for some \(r\geq 2\).
-  More general BCH codes can be defined for zeroes are powers of the form \(\{b,b+s,b+2s,\cdots,b+(\delta-2)s\}\) where gcd\((s,n)=1\).
+  More general BCH codes can be defined for zeroes of the form \(\{b,b+s,b+2s,\cdots,b+(\delta-2)s\}\), where gcd\((s,n)=1\).
 
   The code dimension is related to the \textit{multiplicative order} of \(q\) modulo \(n\), i.e., the smallest integer \(m\) such that \(n\) divides \(q^m-1\). The dimension of a BCH code is at least \(n-m(\delta-1)\). The field \(\mathbb{F}_{q^m}\) is the smallest field containing the above root of unity \(\alpha\), and is the splitting field of the polynomial \(x^n-1\) (see \ref{topic:Cyclic-to-polynomial-correspondence}).
 

codes/classical/q-ary_digits/distributed_storage/mds.yml

@@ -21,7 +21,7 @@ description: |
   becomes an equality.
   A code is called \textit{almost MDS} (AMDS) when \(d=n-k\).
   A bound for general (i.e., nonlinear or unrestricted) \(q\)-ary codes can also be formulated; see \cite[Thm. 1.9.10]{preset:HKSbasics}.
-  A code is \textit{near MDS} (NMDS) if the code and its dual are mode AMDS.
+  A code is \textit{near MDS} (NMDS) if both the code and its dual are AMDS.
 
   The codes \( [n,1,n]_q, [n,n-1,2]_q, [n,n,1]_q \) for any \(q\) are MDS codes. These are called the \textit{trivial} MDS codes. The only binary MDS codes are the trivial ones.
   Many, but not all, \(q\)-ary MDS codes are related to RS codes and their extensions; see, e.g., \cite[Prob. 11.11]{doi:10.1017/CBO9780511808968}.

codes/classical/spherical/modulation/psk.yml

@@ -22,7 +22,7 @@ description: |
   Concatenating PSK with \(q\)-ary codes yields a natural non-binary way of digitizing the analog AWGN channel \cite{manual:{Massey, J. L. "Convolutional codes over rings." Fourth Joint Swedish-Soviet International Workshop on Information Theory. 1989.},manual:{Massey, J. L. "Ring convolutional codes for phase modulation." presented at the IEEE Int. Symp. on Information Theory, San Diego, CA, Jan. 14-19. 1990.}}.
 
 features:
-  rate: 'Nearly achieves Shannon AWGN capacity for 1D constellations in the limit of infinite signal-to-noise \cite[Fig. 11.7]{doi:10.1017/CBO9780511811401}.'
+  rate: 'As the constellation size \(q\) grows, \(q\)-PSK approaches the Shannon AWGN capacity of the corresponding two-dimensional signal set \cite[Fig. 11.7]{doi:10.1017/CBO9780511811401}.'
 
 realizations:
   - 'Telephone-line modems: 1967 Milgo 4400/48 and international standard V.27 used 8-PSK \cite{manual:{International Telecommunication Union-T, Recommendation V.27ter: 4800/2400 Bits Per Second Modem Standardized For Use in the General Switched Telephone Network, 1984}}.'

codes/classical/spherical/polytope/6-8d/hess_polytope.yml

@@ -32,7 +32,7 @@ relations:
       detail: 'The \(3_{21}\) polytope code is a sharp configuration \cite{doi:10.1515/dma.1994.4.2.143,arxiv:math/0607446}.'
   cousins:
     - code_id: spherical_design
-      detail: 'The \(3_{21}\) polytope code forms a tight spherical 5-design \cite{doi:10.1007/BF03187604,doi:10.4153/CJM-1981-038-7}\cite[Ch. 14]{doi:10.1007/978-1-4757-6568-7} that is associated with.'
+      detail: 'The \(3_{21}\) polytope code forms a tight spherical 5-design \cite{doi:10.1007/BF03187604,doi:10.4153/CJM-1981-038-7}\cite[Ch. 14]{doi:10.1007/978-1-4757-6568-7}.'
     - code_id: eseven_shell
       detail: '\(3_{21}\) polytope codewords form the minimal lattice-shell code of the \(E_7^{\perp}\) lattice \cite{doi:10.1007/978-3-642-76709-8_5}.'
     - code_id: complex_projective

scripts/checked_files.txt

@@ -462,3 +462,23 @@ codes/classical/bits/tanner/regular_tanner/regular_binary_tanner.yml
 /home/valbert/eczoo_data/codes/classical/q-ary_digits/distributed_storage/multiple_erasure_lrc/parallel_recovery.yml
 /home/valbert/eczoo_data/codes/classical/q-ary_digits/convolutional/irregular_convolutional.yml
 /home/valbert/eczoo_data/codes/classical/q-ary_digits/dual/dual.yml
+/home/valbert/eczoo_data/codes/classical/q-ary_digits/alternant/bch/q-ary_bch.yml
+/home/valbert/eczoo_data/codes/classical/bits/tanner/regular_tanner/regular_ldpc/pg_ldpc.yml
+/home/valbert/eczoo_data/codes/classical/matrices/spacetime/orthogonal/alamouti.yml
+/home/valbert/eczoo_data/codes/classical/spherical/polytope/3d/icosahedron.yml
+/home/valbert/eczoo_data/codes/classical/properties/block/distributed_storage/lrc/code_with_locality.yml
+/home/valbert/eczoo_data/codes/classical/bits/ltc/dinur.yml
+/home/valbert/eczoo_data/codes/classical/spherical/modulation/psk.yml
+/home/valbert/eczoo_data/codes/classical/spherical/polytope/infinite/hypercube.yml
+/home/valbert/eczoo_data/codes/classical/spherical/polytope/3d/rhombicuboctahedron.yml
+/home/valbert/eczoo_data/codes/classical/q-ary_digits/ag/varieties/schubert.yml
+/home/valbert/eczoo_data/codes/classical/q-ary_digits/projective/projective_two_weight/bose_qvist.yml
+/home/valbert/eczoo_data/codes/classical/bits/tanner/qc/difference_set.yml
+/home/valbert/eczoo_data/codes/classical/q-ary_digits/dual/pless_symmetry/pless_symmetry.yml
+/home/valbert/eczoo_data/codes/classical/matrices/spacetime/spacetime.yml
+/home/valbert/eczoo_data/codes/classical/q-ary_digits/distributed_storage/roth_lempel.yml
+/home/valbert/eczoo_data/codes/classical/spherical/q-ary/polyphase.yml
+/home/valbert/eczoo_data/codes/classical/q-ary_digits/weight/two_weight.yml
+/home/valbert/eczoo_data/codes/classical/bits/reed_muller/reed_muller.yml
+/home/valbert/eczoo_data/codes/classical/bits/quantum_inspired/newman_moore.yml
+/home/valbert/eczoo_data/codes/classical/properties/group_orbit.yml