Repeat the analysis of exercise 50.2 (p.592) but now aim to have the expected number of packets o

Repeat the analysis of exercise 50.2 (p.592) but now aim to have the expected number of packets o

Repeat the analysis of exercise 50.2 (p.592) but now aim to have the expected number of packets of degree 1 be ht(1) = 1+S for all t, instead of 1. Show that the initial required number of packets is

The reason for truncating the second term beyond d = K/S and replacing it by the spike at d = K/S (see equation (50.4)) is to ensure that the decoding complexity does not grow larger than O(K lnK).
Estimate the expected number of packets  and the expected number of edges in the sparse graph  (which determines the decoding complexity) if the histogram of packets is as given in (50.6).Compare with the expected numbers of packets and edges when the robust soliton distribution (50.4) is used.