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Modulo-N code is alossy compression algorithm used to compresscorrelated data sources usingmodular arithmetic.

When applied to two nodes in anetwork whose data are in close range of each other modulo-N code requires one node (say odd) to send the coded data value as the raw data${\displaystyle M_o=D_o}$; the even node is required to send the coded data as the${\displaystyle M_e=D_{e}modN}$. Hence the name modulo-N code.

Since at least${\displaystyle {\log }_{2}K}$ bits are required to represent a numberK in binary, the modulo coded data of the two nodes requires${\displaystyle {\log }_2{M}_o+{\log }_2{M}_e}$ bits. As we can generally expect${\displaystyle {\log }_2{M}_e\le {\log }_2{M}_o}$ always, because${\displaystyle M_e\le N}$. This is how compression is achieved.^[1]

A compression ratio achieved is${\displaystyle \text{C.R.}=\frac{{\log }_2{M}_o+{\log }_2{M}_e}{2{\log }_2{M}_o}.}$

At the receiver, by joint decoding, we may complete the process of extracting the data and rebuilding the original values. The code from the even node is reconstructed by theassumption that it must be close to the data from the odd node. Hence the decoding algorithm retrieves even node data as

${\displaystyle \mathrm{CLOSEST}(M_o,N.k+M_e).}$

The decoder essentially finds the closest match to${\displaystyle M_o\simeq N.k+M_e}$ and the decoded value is declared as${\displaystyle N.k+M_e}$

For a mod-8 code, we haveEncoder

D_o=43,D_e=47M_o=43,M_e=47 mod(8) = 7,

Decoder

 M_o=43,M_e=47 mod(8) = 7, D_o=43,D_e=CLOSEST(43,8⋅k + 7)${\displaystyle 43\simeq 8\cdot 5+7}$ D_o=43,D_e=47

Modulo-N decoding is similar tophase unwrapping and has the same limitation: If the difference from one node to the next is more thanN/2 (if the phase changes from one sample to the next more than${\displaystyle \pi }$), then decoding leads to an incorrect value.

• DISCUS is a more sophisticated technique for compressing correlated data sources.
• Delta encoding is a related algorithm used in lossless compression algorithms designed for correlated data sources.

• Information theory
• Data compression
• Wireless sensor network

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