612 research outputs found
Comments on 'A class of codes for axisymmetric channels and a problem from the additive theory of numbers' by Varshanov, R. R.
In the above paper [1], Varshamov considers discrete channels with q inputs and q outputs, q being an arbitrary integer
Some new results on majority-logic codes for correction of random errors
The main advantages of random error-correcting majority-logic
codes and majority-logic decoding in general are well known and
two-fold. Firstly, they offer a partial solution to a classical
coding theory problem, that of decoder complexity. Secondly, a
majority-logic decoder inherently corrects many more random error
patterns than the minimum distance of the code implies is possible.
The solution to the decoder complexity is only a partial one
because there are circumstances under which a majority-logic decoder
is too complex and expensive to implement. [Continues.
On vocabulary size of grammar-based codes
We discuss inequalities holding between the vocabulary size, i.e., the number
of distinct nonterminal symbols in a grammar-based compression for a string,
and the excess length of the respective universal code, i.e., the code-based
analog of algorithmic mutual information. The aim is to strengthen inequalities
which were discussed in a weaker form in linguistics but shed some light on
redundancy of efficiently computable codes. The main contribution of the paper
is a construction of universal grammar-based codes for which the excess lengths
can be bounded easily.Comment: 5 pages, accepted to ISIT 2007 and correcte
An improvement to multifold euclidean geometry codes
This paper presents an improvement to the multifold Euclidean geometry codes introduced by Lin (1973).The improved multifold EG codes are proved to be maximal, and therefore they are more efficient than the multifold EG codes. Relationships between the improved multifold EG codes and other known majority-logic decodable codes are proved
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