Polytec

Polytechnic University, Dept. Electrical and Computer Engineering

EE3414 Multimedia Communication System I

Spring 2006, Yao Wang__________________________________________________________________________________________________

Homework 11 (Digital Communication)

Reading Assignment:

A. Leon-Garcia, I. Widjala, Communication networks, Chap 3: Digital transmission fundamentals.

Copies provided.Written Assignment:

1. Consider the two digital modulation schemes shown in the figure below. For each scheme, determine the minimum distance between two symbols dmin , the average energy per symbol Eav, and the average energy per transmitted bit Eb. Which scheme is more efficient in terms of transmission energy usage?

2. What is the function of parity check? Consider the scheme where we append a parity bit to each group of 7 bits to generate 1 byte so that each byte has an even parity. What is the parity bit you will add to 1010100? With this added parity bit, can you detect that some bits in a received byte get inverted? What cases of errors can be detected and what cases cannot be detected?

3. Consider repetition coding with a redundancy factor of 3, i.e., to send an information bit 0, we send 000; to send an information bit 1, we send 111. Suppose the probability that any one bit gets inverted during transmission is p=0.1, what is the probability that an information bit is decoded wrong?

4. Consider a channel with bandwidth 1MHz.

(a) Suppose the channel is noiseless, what is the maximum number of bits that can be transmitted reliably if you use 2-ASK for modulation? What if you use 8-ASK?

(b) Suppose the channel suffers from noise with a signal to noise ratio of 10 dB. What is the maximum number of bits that can be transmitted reliably? What if the channel SNR is 30 dB?

(a) 4-ary PAM (b) 4-QAM