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Modulo-N code

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Title: Modulo-N code  
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Subject: Data compression, DISCUS, Wireless sensor network, Augmented sixth chord, Information theory
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Modulo-N code

Modulo-N code is a lossy compression algorithm used to compress correlated data sources using modulo arithmetic.


  • Compression 1
  • Decompression 2
  • Example 3
    • See also 3.1


When applied to two nodes in a network 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 M_o = D_o; the even node is required to send the coded data as the M_e = (D_e) mod (N) . Hence the name Modulo-N code.

Since it is known that for a number K, at least log_2(K) bits are required to represent it in binary. So the modulo coded data of the two nodes requires totally log_2(M_o) + log_2(M_e). As we can generally expect log_2(M_e) \le log_2(M_o) always, because M_e \le N. This is the how compression is achieved.

A compression ratio achieved is C.R = \frac{log_2(M_o) + log_2(M_e)}{2log_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 the assumption that it must be close to the data from the odd node. Hence the decoding algorithm retrieves even node data as
CLOSEST(M_o,N.k+ M_e).

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


For a mod-8 code, we have Encoder

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


 M_o=43,M_e=47 mod(8) = 7,
 D_o=43,D_e=CLOSEST(43,8.k + 7)
 43 \simeq 8.5 + 7

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 \pi), then decoding leads to an incorrect value.

See also

  • 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.
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