# ass4 - decisions on a trellis diagram, labelling the...

This preview shows page 1. Sign up to view the full content.

Carleton University SYSC 5504 Department of Systems and Computer Engineering ELG 6154 Principles of Digital Communications Fall 2010/11 Assignment #4 Due on Tuesday, November 30, 2010 1. For the convolutional encoder shown below: a i - s (1) i - s (2) i s (3) i * ] Y j ^ ± ² - c (1) i - c (2) i (a) Draw the state diagram. (b) What is the code sequence corresponding to the message sequence a = 10110? Do not forget about the trellis termination (c) Suppose that a four-bit message sequence has been encoded using this encoder and sent via a binary symmetric channel with crossover probability p =0 . 1. The received sequence is r =11110101101111 . Use the Viterbi algorithm with hard-decision decoding to ±nd the most likely message sequence. Trace the
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: decisions on a trellis diagram, labelling the partial path metric of each survivor at each time unit. What is the smallest possible Hamming distance between any of the possible code sequences and this received sequence? 2. Consider the recursive systematic convolutional encoder shown below. a i--s (1) i-s (2) i ?-?-c (1) i-c (2) i (a) Draw the state diagram. (b) Find the transfer function T ( D ) of the code. (c) Find the minumum free distance ( d free ) of the code. (d) What is the code sequence for the message sequence a = 10110? (e) What is the code sequence for the message sequence a = 1000? SYSC 5504 1 Fall 2010/11...
View Full Document

## This note was uploaded on 01/25/2011 for the course SCE 5201 taught by Professor Huang during the Spring '10 term at Carleton CA.

Ask a homework question - tutors are online