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Walsh code

Also known as "Walsh-Hadamard code," it is an algorithm that generates statistically unique sets of numbers for use in encryption and cellular communications. Known as "pseudo-random noise codes," Walsh codes are used in direct sequence spread spectrum (DSSS) systems such as Qualcomm's CDMA. They are also used in frequency hopping spread spectrum (FHSS) systems to select the target frequency for the next hop. See CDMA.


          Walsh Code Algorithm

          (a', b') = (a+b, a-b)





CDMA

(Code Division Multiple Access) A method for transmitting multiple digital signals simultaneously over the same carrier frequency (the same channel). Although used in various radio communications systems, the most widely known application of CDMA is for cellphones. For example, in 2011, there were more than 500 million CDMA cellular users worldwide, with more than half in Asia. Verizon and Sprint are CDMA carriers in the U.S., while TELUS uses CDMA in Canada. Qualcomm designs the chips for the CDMA air interface.

For years, CDMA and GSM were the two primary cellular transmission systems, but both technologies have mostly given way to Long Term Evolution (see LTE).

CDMA provides up to 10 times the calling capacity of earlier analog networks (AMPS) and up to five times the capacity of GSM systems. CDMA is also the basis for the WCDMA and HSPA 3G technologies used by GSM carriers (see WCDMA and HSPA). See IS-95 and CDMA2000.

Spread Spectrum
Unlike GSM and earlier digital systems, both of which use TDMA to divide the channel into time slots, CDMA's spread spectrum overlaps every transmission on the same carrier frequency by assigning a unique code to each conversation. Each voice conversation uses the full bandwidth simultaneously, and the often-used analogy is the ability to detect one's own language in a room full of people speaking other languages.

After the speech codec converts the caller's voice to digital, CDMA spreads the digital stream over the full 1.25 MHz bandwidth of the channel with a unique coding pattern. The rate of the spreading signal is known as the "chip rate," as each bit in the spreading signal is called a "chip," with no relation at all to an integrated circuit chip. Each bit of a conversation is multiplied into 128 coded bits, giving the receiving circuit an enormous amount of data it can average just to determine the value of a single bit when decoding the signal.

More Secure
CDMA transmission has been used by the military for secure phone calls. Unlike FDMA and TDMA, CDMA's wide spreading signal makes it difficult to detect and jam. For more information, contact the CDMA Development Group (CDG) at www.cdg.org. See BREW, cellular generations, IS-95, CDMA2000, WCDMA, GSM, FDMA, TDMA, CDPD, CDG and spread spectrum.

How the Technology Works
The following illustration, which was created with the assistance of Klein Gilhousen, co-inventor of CDMA, shows how bits are encoded at the base station and decoded in the cellphone. A single bit example is used to take you through the Boolean math.

Transmitting from the Base Station
Each voice conversation is compressed with a vocoder. The output is doubled by a convolutional encoder that adds redundancy for error checking. Each bit from the encoder is replicated 64 times and exclusive OR'd with a Walsh code that is used to identify that call from the rest.

The output of the Walsh code is exclusive OR'd with the next string of bits (PN sequence) from a pseudo-random number generator, which is used to identify all the calls in a particular cell's sector. At this point, there is 128 times as many bits as there were from the vocoder's output. All the calls are combined and modulated onto a carrier frequency in the 800 MHz range.





Receiving at the Cellphone
The received frequencies are quantized into bits ("chips") by the analog-to-digital converter (ADC). The output is run through the Walsh code and PN sequence correlation receiver to recover the transmitted bits of the original signal. When 20 milliseconds of voice data are received, a Viterbi decoder corrects the errors using the convolutional code. The Viterbi output goes to the vocoder and digital-to-analog converter (DAC), which decompresses the bits and turns them back into waveforms (sound).








Follow the Single Bit Example
This exclusive OR truth table shows you the Boolean algebraic rules to prove the single bit example in the illustrations above. The example bit is a 1, and the Walsh and PN codes are 0.






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