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A Broad Class of Additive Error Coding, Channels and Lower Bound on the Probability of Error for Block Codes using SK- Metric
There being errors of various different kinds, it is natural to consider classes of different additive errors. Earlier studies have been made by measuring errors in terms of Hamming metric over binary channels, which for q-nary cases do not critically take into account the magnitude and other possibilities of patterns of errors. Sharma-Kaushik approach allows to have a class of metrics and to suitably match the channel with an appropriate metric chosen from this class, Additive Class errors are defined in this paper that fit well in SK-class setting partitions giving an SK metric. The idea is used in exploring new classes of perfect codes. The paper then takes up the main problem of introducing a very general way of the q-nary channel, generalizing BSC, with channel matrix in terms of probabilities of class errors. There are results on probabilities of errors for different kinds of errors as also bounds on probability of error for code correcting designed additive class errors that address to the reliability aspect of block coding.
Error Coding, SK-Metric, Symmetric Channel, Probability of Error Bounds.
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