A Closer Look Into The Rectangular Codes: Where The Parity Check Predominates

Romi Banerjee, Saptarshi Naskar, Samar Sen Sarma

Abstract


Information transmission in the presence of ‘white noise’ is error prone, but is not as elusive as any arbitrary noise prone channel. With respect to this restriction, the parity check is the only feasible error handling scheme that could be adopted in, at least, any intra-system digital communication (e.g. All existing computing systems use the ASCII codes); while the repetition of messages (e.g. The triplicate transmission scheme) is not a viable alternative. In this paper, we propose simple algorithms to clearly prove the greater practical efficiency of the 2-dimensional parity check based coding systems in the ‘rectangular’ framework – as opposed to the established notion of the ‘square code’ being more efficient. These algorithms are further corroborated by theorems, associated hypotheses and experimental results. The lower and the upper bound of our algorithms are clearly explained.

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