EE 5511 :Advanced Digital Communications - IT Assignment Help

Assignment Task:

Task:

1.
a) For the following codes:
C1={0, 1}
C2={0, 10, 010, 100}
C3={0, 01, 10}
Indicate which are:
i) Uniquely decodable?
ii) Instantaneously decodable?
Explain your reasoning.

b) A (n, k) systematic linear block code can correct 1 bit error. It has the following syndrome table

Suppose that y=[0 1 1 0 0] is received. Determine the most likely coded vector and the source vector.

c) A memoryless source has the alphabet {a, b, c, d, e} and symbol probabilities
Symbol a b c d e
Probability 0.4 0.3 0.15 0.1 0.05
We want to perform lossless coding of the output of the source and keep the average rate low. Which of the following three codes should we
choose?
Symbol Code 1 Code 2 Code 3
a 0 0 1
b 10 100 01
c 110 101 00
d 1110 110 010
e 1111 111 001
Error e Syndrome S
0 0 0 0 1 0 0 1
0 0 0 1 0 0 1 0
0 0 1 0 0 1 0 0
0 1 0 0 0 1 0 1
1 0 0 0 0 1 1 0

2. a) Consider a wired communication channel with symbol period of T. An appropriately shaped symbol with zero-crossings at t =kT (k is an integer) is distorted by the channel. Assume that the received symbol x(t) is normalised to 1 volt at t=0, i.e., x(0)=1.0. In the absence of channel noise, voltages of x(t) at t = ±T and ±2T are as follows x(-2T)= 0.1, x(-T)= 0.3, x(T)= -0.2, x(2T)=0.15.
Inter-symbol interference is to be removed by a 3-tap zero-forcing equalizer.
Design a 3-tap zero forcing equalization filter for this channel.

b) An OFDM system with a minimum bitrate of Rb = 30 Mbit/s is to be realized. The subcarrier spacing is 20 kHz and the total bandwidth is less than 40 MHz. The guard time is 25% of the duration of the OFDM core symbol period. Each subcarrier is modulated using QPSK. For efficient implementation of the IFFT, the number of subcarriers needs to be a power of two. The required passband energy of an OFDM core symbol at the transmitter is 1.024 Ws. White Gaussian noise with a power spectral density of N0= 10-3 W/Hz is added. Calculate the bit error rate of the transmission system.

3.
a) Consider a Universal Mobile Telecommunication System (UMTS) terminal operated on board a high-speed train (250 km/h) passing through a rural environment. The carrier frequency of UMTS is 2 GHz and the symbol period is about 10 ms. Determine if the channel is considered to be slow or fast fading.

b) Figure Q3b shows a convolution encoder, where ui is the input bit, and 1

x i

and 2 x i are the output bits.

Suppose that 4 data bits and 1 dummy 0 were sent out over a binary symmetric channel with cross-over probability of p=0.01 and the sequence y = [11 01 10 10 11] is received. Derive the most likely bit sequence ui using the Viterbi decoding algorithm.

c) 24 speech signals, each of bandwidth 3 kHz, are to be transmitted simultaneously by binary pulse coded modulation (PCM). Each signal is sampled 1/3 higher than the Nyquist rate. The maximum acceptable quantization error is 0.5% of the peak amplitude mp. Design a uniform quantizer for this system and calculate the minimum possible data rate

where ? is in seconds, and P0 and A are constants. Derive the delay spread of this system.
bol interference (ISI).

Design an efficient modulation scheme with maximum power efficiency. Sketch the constellation of your selected modulation scheme and the normalized magnitude response of the RRC filter.

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