py of a stationary source). Let Xn transmission R = 1/2. be a stationary source. The entropy of the source (also often called the entropy rate of the source) is defined as H= limn. Hn. 3.4.3 Channel coding and error With this definition, Shannon's noiseless coding the- orem can be extended to stationary sources that satisfy control for bit errors and packet the asymptotic equipartition property [3]. The source losses coding theorem can also be extended to sources with abstract alphabets, including the set of real numbers in Channel codes can be divided into two classes: linear and particular [22]. nonlinear. Linear codes are easier to implement and, as Shannon's channel coding theorem can be extended to a result, have received a greater amount of attention other channels, the most famous one being the additive historically. We will also confine our attention to linear white Gaussian noise (AWGN) channel. In the time- codes in this section. We first describe linear block codes, discrete AWGN channel, both the channel input alphabet including cyclic redundancy check (CRC) codes for error Ax and the channel output alphabet Ayare the set of real detection, Reed-Solomon codes, low-density parity- numbers R. The relationship between the random vari- check (LDPC) codes, irregular repeat-accumulate (IRA) able Xn that gives the nth input to the channel and the codes, tornado codes, digital fountain codes, and lattice random variable Yn that gives the nth output of the codes. We then describe convolutional codes, rate- channel is given by Yn = X + Zn, where {Zn} is a compatible punctured convolutional (RCPC) codes, and sequence of independent, identically distributed, turbo codes. We discuss the properties of these codes and Gaussian random variables with mean 0 and variance No/ mention efficient algorithms for encoding and decoding, CHAPTER 3.4 Channel protection fundamentals emphasizing their computational complexity. We also ex- noise that it can remove. The performance is usually de- plain how the problem of burst erro