Channel Model

• Definition:
  The channel model is used to approximate the way errors are introduced in a data stream when it is transmitted over a lossy medium. The two models you may use in the Workshop are the Binary Symmetric Channel(BSC) and the Additive White Gaussian Noise channel(AWGN). Both of these channel models are memoryless, meaning that the distortion of one bit is independent of all other bits in the data stream.

  The BSC defines a finite probability of bit error which is the probability that the value of a bit in the data stream is toggled. Decoders using the BSC are considered to be hard decision decoders because they first quantize the received bits before decoding.

  The AWGN channel models the distortion incurred by transmission over a lossy medium as the addition of a zero-mean Gaussian random value to each bit. Decoders can take advantage of the added information of "how close" a received value is to a valid bit value(0 or 1 for our purposes). This type of decoding is called soft decision decoding. Because decoders that use soft decision decoding take advantage of information that the BSC throws away, soft decision decoders often have better error correcting capability.

• Usage:
  When selecting the channel model, make sure you are aware that the channel parameter values mean different things depending on what channel model you use. For the BSC, the parameters are the actual and estimate bit error probability. Likewise, for the AWGN channel, the parameters are the actual and estimate noise variance.
• Illustration of the two Channel Models:

Binary Symmetric Channel(BSC)
with bit error probability defined as: Pe

Additive White Gaussian Noise Channel
with noise variance defined as: sigma squared