As explained in the Introduction to this chapter, channel coding can be used to reduce the Eb/N0 required for a prescribed error performance or reduce the size of the receiving antenna for a prescribed Eb/N0. In this problem we explore these two practical benefits of coding by revisiting Example 8.2 in Chapter 8 on the downlink power calculations for a domestic satellite communication system. In particular, we now assume that the design of the down link includes the use of a coding scheme consisting of a rate-112 convolutional encoder with length K = 7 and Viterbi decoding. The coding gain of this scheme is 5.1 dB, assuming the use of soft quantization. Hence do the following:

(a) Recalculate the required Eb/N0 ratio of the system.

(b) Assuming that the required Eb/N0 ratio remains unchanged, calculate the reduction in the size of the receiving dish antenna that is made possible by the use of this coding scheme in the downlink.