In digital transmission systems with pulse interval modulation (PIM) having alphabet {0,…,M -…

In digital transmission systems with pulse interval modulation (PIM) having alphabet {0,…,M − 1}, we associate to the symbol value n the transmission of a particular waveform h(t) with limited support (0, Tb), preceded by a “mute” interval of length nTb. For example, we have
a) Show that the modulator can be decomposed into the cascade of a source encoder and an interpolate filter
where the message # bq $ has a binary alphabet Ab = {0, 1}. Give the encoder map µs and state whether Db is a prefix code.
b) Find the information rate of # bq $ when {ak} is made of iid symbols with equally likely values, M = 8 and Tb = 1 ns.
c) Under the same hypotheses as in b) find the statistical power of the transmitted signal s(t). Assume h(t) has energy