Modulo-N code
Encyclopedia
Modulo-N code is a lossy compression algorithm used to compress correlated data sources using modulo arithmetic.
requires one node (say odd) to send the coded data value as the raw data
; the even node is required
to send the coded data as the
. Hence the name Modulo-N code.
Since it is known that for a number K, at least
bits are required to represent it
in binary. So the modulo coded data of the two nodes requires totally
.
As we can generally expect
always, because 
.
This is the how compression is achieved.
A compression ratio achieved is
.
original values. The code from the even node is reconstructed by the assumption that it must be
close to the data from the odd node. Hence the decoding algorithm retrieves even node data as
.
The decoder essentially finds the closest match to
and the decoded
value is declared as
Encoder
D_o=43,D_e=47
M_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)
D_o=43,D_e=47
Modulo-N decoding is similar to phase unwrapping and has the same limitation: If the difference from one node to the next is more than N/2 (if the phase changes from one sample to the next more than
), then decoding leads to an incorrect value.
Compression
When applied to two nodes in a network whose data are in close range of each other Modulo-N coderequires one node (say odd) to send the coded data value as the raw data
; the even node is requiredto send the coded data as the
. Hence the name Modulo-N code.Since it is known that for a number K, at least
bits are required to represent itin binary. So the modulo coded data of the two nodes requires totally
.As we can generally expect
always, because .This is the how compression is achieved.
A compression ratio achieved is
.Decompression
At the receiver by joint decoding we may complete the process of extracting the data and rebuilding theoriginal values. The code from the even node is reconstructed by the assumption that it must be
close to the data from the odd node. Hence the decoding algorithm retrieves even node data as
.The decoder essentially finds the closest match to
and the decodedvalue is declared as
Example
For a mod-8 code, we haveEncoder
D_o=43,D_e=47
M_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)
D_o=43,D_e=47
Modulo-N decoding is similar to phase unwrapping and has the same limitation: If the difference from one node to the next is more than N/2 (if the phase changes from one sample to the next more than
), then decoding leads to an incorrect value.See also
- DISCUSDISCUSFor the American trade association that has the same acronym, see Distilled Spirits Council of the United StatesDISCUS is an acronym for Distributed source coding Using Syndromes.-Introduction:...
is a more sophisticated technique for compressing correlated data sources. - Delta encodingDelta encodingDelta encoding is a way of storing or transmitting data in the form of differences between sequential data rather than complete files; more generally this is known as data differencing...
is a related algorithm used in lossless compression algorithms designed for correlated data sources.