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An ultimate form of multiplexing used in parts of the cellular telephone system and for some satellite communication is called Code Division Multiplexing (CDM). The specific version of CDM used in cell phones is called Code Division Multi-Access (CDMA).

CDM does not rely on physical properties, including frequency or time. It can depend on an interesting numerical idea such as values from orthogonal vector spaces can be merged and separated without interference. The specific form used in the telephone network is the easiest to learn. Each sender is created a unique binary code Ci that is called chip sequence.

Chip sequences are chosen to be orthogonal vectors (i.e., the dot product of any two-chip sequences is zero). At that time, each sender has a value to transmit, V_{i}. The senders each multiply C_{i}☓V_{i}, and transmit the results. In essence, the senders transmit at a similar time, and the values are inserted together. To extract value V_{i} , a receiver generates the sum by C_{i}.

Example: Values for use with Code Division Multiplexing

Sender | Chip Sequence | Data Value |
---|---|---|

A | 1 0 | 1 0 1 0 |

B | 1 1 | 0 1 1 0 |

The first step includes converting the binary values into vectors that use −1 to represent 0−

C_{1} = ( 1, −1 ) V_{1} = ( 1, −1, 1, −1 ) C_{2} = ( 1, 1 ) V_{2} = ( −1, 1, 1, −1 )

Multiplying C_{1}× V_{1} and C_{2} × V_{2} produces−

((1, −1), (−1, 1), (1, −1), (−1, 1)) ((−1, −1), (1, 1), (1, 1), (−1, −1))

If we think of the resulting values as a sequence of signal strengths to be send at the similar time, the resulting signal will be the sum of the two signals−

1 −1 −1 1 1 −1 −1 1

+ −1 −1 1 1 1 1 −1 −1

_____________________

0 −2 0 2 2 0 −2 0

A receiver considers the sequence as a vector, evaluates the product of the vector and the chip series, treats the result as a sequence, and modifies the result to binary by calculating positive values as binary 1 and negative values as binary 0.

The benefit of CDM arises from its ability to scale and because it offers lower delay in a highly utilized network. Once a sender sends, a TDM multiplexor allows N−1 other sender to transmit before providing the first sender with another turn. Therefore, if all senders are active, the probable delay between successive communications from a given sender can be high.

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