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## Channel capacity and coding

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Channel capacity characterizes the maximum transmission rate that a channel can support for error-free information delivery. As the performance upper limit for arbitrary transmission system, channel capacity provides valuable guidances for real-world transceiver design. The mathematical theory of channel capacity was established by Claude Shannon in the late 1940s, through his coding theorems. The advanced modulation and coding schemes developed afterward validate Shannon's pioneering vision. Error-control coding serves an effective capacity achieving solution. This chapter studies capacity and coding for wireless fading channels. We first discuss the capacity definition and sample error-control coding schemes for additive white Gaussian noise (AWGN) channels. We then present the commonly used capacity definition for both flat and selective fading channels. In addition to the ergodic capacity and capacity with outage, we also introduce and derive the optimal power and rate adaptation (OPRA) capacity. We conclude the chapter with the discussion of interleaving technique, which is widely used in wireless systems to mitigate the effect of deep fade on coded transmission.

Chapter Contents:

• 8.1 Capacity of AWGN channels
• 8.2 Channel coding for AWGN channels
• 8.2.1 Block codes
• 8.2.2 Performance benefit with coding
• 8.2.3 Convolutional codes and turbo codes
• 8.3 Capacity of flat fading channels
• 8.3.1 Ergodic capacity
• 8.3.2 Capacity with outage
• 8.3.3 Optimal power and rate adaptation
• 8.4 Capacity of selective fading channels
• 8.5 Interleaving for fading channels
• Problems
• Bibliography

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