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codes/classical/ecc.yml

@@ -11,6 +11,10 @@ short_name: 'ECC'
 description: |
   Code designed for transmission of classical information through classical channels in a robust way.
 
+  A code is a subset of a set or \textit{alphabet}, with each element called a \textit{codeword}. 
+  An error-correcting code consists of \(K\) codewords over an alphabet with \(N\) elements such that it is possible to recover the codewords from errors \(E\) from some error set \(\mathcal{E}\).
+
+
 features:
   rate: 'The Shannon channel capacity (the maximum of the mutual information over input and output distributions) is the highest rate of information transmission through a classical (i.e., non-quantum) channel with arbitrarily small error rate \cite{doi:10.1002/j.1538-7305.1948.tb01338.x}.
   Corrections to the capacity and tradeoff between decoding error, code rate and code length are determined using small \cite{manual:{V. Strassen, “Asymptotische Absch¨atzungen in Shannons Informationstheorie,” Trans. Third Prague Conference on Information Theory, Prague, 689–723, (1962)},arxiv:0801.2242,doi:10.1109/TIT.2010.2043769}, moderate \cite{arxiv:1208.1924,doi:10.1109/ALLERTON.2010.5707068,arxiv:1701.03114} and large \cite{doi:10.1007/978-3-7091-2945-6,doi:10.1017/CBO9780511921889,doi:10.1109/TIT.1973.1055007,doi:10.1109/TIT.1979.1056003} deviation analysis.

codes/classical/properties/block/block.yml

@@ -8,10 +8,9 @@ code_id: block
 name: 'Block code'
 
 description: |
-  A code intended to encode a piece, or block, of a data stream on a \textit{block} of \(n\) symbols.
-  Each symbol is taken from some fixed possibly infinite alphabet \(\Sigma\) \cite[Ch. 3]{doi:10.1007/978-3-642-58575-3}, which can include bits, Galois fields, rings, or real numbers.
+  A code intended to encode a piece, or block, of a data stream on a \textit{block} of \(n\) symbols, with each symbol taking values from a fixed alphabet \(\Sigma\).
 
-  The overall alphabet of the code is \(\Sigma^n\), and \(n\) is called the \textit{length} of the code.
+  The overall alphabet of the code is \(\Sigma^n\), and \(n\) is called the \textit{length} of the code \cite[Ch. 3]{doi:10.1007/978-3-642-58575-3}.
   In some cases, only a subset of \(\Sigma^n\) is available to use for constructing the code.
   For example, in the case of spherical codes, one is constrained to \(n\)-dimensional real vectors on the unit sphere.
   The table below lists the most common alphabets used in block codes, along with names of the corresponding codewords.

codes/classical/properties/ecc_finite.yml

@@ -10,7 +10,7 @@ short_name: 'Finite ECC'
 introduced: '\cite{doi:10.1002/j.1538-7305.1948.tb01338.x}'
 
 description: |
-  A \textit{code} is a subset of a set or \textit{alphabet}, with each element called a \textit{codeword}. An \textit{error-correcting code} consists of \(K\) codewords over an alphabet with \(N\) elements such that it is possible to recover the codewords from errors \(E\) from some error set \(\mathcal{E}\).
+  An error-correcting code defined over a finite alphabet.
 
 protection: 'A code corrects errors associated with a noise channel if it is possible to recover any codeword after its coordinates have been changed after going through the channel. More technically, an error-correcting code \((u,\mathcal{E})\) is an \textit{encoder} function \(u:[1\cdots K]\to[1\cdots N]\) with a set of correctable errors \(E:[1\cdots N]\to [1\cdots M]\) with the following property: there exists a \textit{decoder} function \(d:[1\cdots M]\to [1\cdots K]\) such that for all \(E\in\cal{E}\) and states \(x\in[1\cdots K]\), \(d(E(e(x)))=x\) \cite{preset:GottesmanBook}.'