20092ee132A_1_hwk7

20092ee132A_1_hwk7 - EE132A Spring 2009 Prof John...

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EE132A, Spring 2009 Prof. John Villasenor Communication Systems TAs: Pooya Monajemi and Erica Han Handout# 21 Homework 7 Assigned: Monday, May 18, 2009 Due: Wednesday, May 27, 2009 Reading Assignments: Chapter 12 (12.4 – 12.6), Chapter 13 (13.1, 13.2) 1. A single parity bit is appended to a block of 3 message bits [ ] 3 2 1 , , m m m . The single parity bit b is chosen so that the codeword satisfies the following rule 1 3 2 1 = b m m m where the symbol denotes modulo-2 addition . List all possible code words in the code defined by this rule. 2. Consider the following parity check matrix H = 0 1 0 1 0 0 1 1 1 1 0 1 1 1 1 1 0 1 H (a) What is the rank of H ? (b) Find a generator matrix G and verify that t GH = 0. (c) Using the generator matrix in (b), find the codeword that correspond to [101]. 3. Cell Capacity. Consider the following cell phone system: For simplicity assume that communication occurs in one direction only (e.g. each user transmits to a base station, but there is no transmission from a base station to a user): .
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