Bagenstose
ECE Brian 459 Presentation write-up
Some Schemes in Practice: Coding for Wireless
Wireless systems are in use everywhere today. From radios to clocks to wireless networks to cell phones, wires are seen more and more as a restraint rather than a necessity. When it comes to coding theory, these systems have their own challenges along with the ones that wire-based systems have. My goal is to summarize some of these challenges and report on how they are dealt with in real systems today. Wireless Coding Challenges There are two major challenges when it comes to wireless coding: multiple antennas and the Rayleigh fading effect. The former is dealt with using space-time codes; two of the other papers for this class deal with that, so instead I will focus on the Rayleigh effect. I call it that because it can be seen in the so-called Rayleigh channel, in which the channel is modeled as a Markov process, and is not independent in time. Mathematically, h(t + 1) = ah(t ) + 1 - a 2 w(t ) , where h(t) is the channel at time t, a is the "channel update factor" (typically 0.9 or 0.99), and w(t) is a complex Gaussian, w(t ) ~ CN (0, 2 ) . For more information, see [2], pp. 3-5. As a result, when the channel goes bad, it can stay bad for a couple of timesteps. An example is using a cell phone during a thunderstorm--if lightning strikes, several consecutive bits can be switched. To get around this, an interleaver is used. This is best demonstrated by an example. Example using a [3,1,3] repetition code Coded input: 111 000 111. Assume there is no interleaver, and that bits 4, 5, and 6 go bad. Then 111 111 111 will be received, which will be decoded incorrectly. Now assume there is a 3-slot interleaver. As a result, after the interleaver, the input will be interleaved to become 101 101 101. Again, assume that bits 4, 5, and 6 go bad. Then 101 010 101 will be received, which will be deinterleaved to 101 010 101, which will be decoded properly. The interleaver moved the errors around so that there was one per 3-bit block instead of 3 errors all in the same block. The other item commonly used in wireless coding is cyclic redundancy codes (CRCs). For these, there is a generator polynomial g(x), and the input is treated as a polynomial, r(x). For example, if the input is 101, r(x) would be x 2 + 1 . Then the codeword c(x)=r(x)g(x). Thus the length of the codeword will equal the length of the input plus the degree of g(x). The decoder c( x) takes r ' ( x) = and checks to see if there is a remainder. If there is, then an error is reported; g ( x) otherwise, r'(x) is decoded as the input. Note that this is only an error detecting code, not an error correcting code.
12/16/02
To glory the of God!
Brian Bagenstose
ECE 459 Presentation write-up
Wireless systems in use: wireless network frames The first system for analysis is a wireless network. The 802.11 standard dictates that each frame looks like:
Figure 1. The 802.11 standard frame ([1], p.34) The last 4 octets are the FCS (frame control sequence). This is another way of stating that it uses a 32-bit CRC. The standard generator polynomial for this CRC is g ( x) = x 32 + x 26 + x 23 + x 22 + x 16 + x 12 + x 11 + x 10 + x 8 + x 7 + x 5 + x 4 + x 2 + x + 1 ([1], p.40.) Thus if there is an error, it will only be detected, not corrected. Example 2: The U.S. Digital Cellular System (USDC) standard The USDC standard applies to cell phones. The cell phone receives the voice as input in 20 ms intervals. Each 20 ms interval is translated into 159 bits, which are separated into 77 class-1 bits and 82 class-2 bits. The 82 class-2 bits are considered the least important bits, and receive no form of error protection at all. The 77 class-1 bits are protected with a rate convolutional code. Of those 77 bits, the 12 perceptually most significant bits go through a CRC before going through the convolutional code. After all that, all 260 bits go through an interleaver to protect against Rayleigh fading. Overall, the setup looks like this:
Figure 2. USDC standard encoding for cellular phones ([4], p. 889) Conclusion The field of wireless technologies is ever expanding, and new techniques are being developed all the time. This paper highlights some of the ones in use, but there are many more possibilities out there, including turbo codes, LDPC's...