Information rate and minimum distance

Error

There was an error loading the page.

Contributors

Feedback

From users who are members of Content created by Newcastle University :

Newcastle University Mathematics and Statistics

said

Ready to use

6 years, 8 months ago

From users who are not members of Content created by Newcastle University :

Hu Yuntao

said

Ready to use

5 years, 1 month ago

History

○

Hu Yuntao 5 years, 1 month ago

Gave some feedback: Ready to use

○

Christian Lawson-Perfect 6 years, 8 months ago

Published this.

○

Newcastle University Mathematics and Statistics 6 years, 8 months ago

Gave some feedback: Ready to use

○

Christian Lawson-Perfect 6 years, 8 months ago

Created this.

There is only one version of this question that you have access to.

Question statement

Find the information rates and minimum distances of the following three codes.

Round your answers to 3 decimal places.

Give any introductory information the student needs.

			Name	Type	Generated Value

word_lengths	list	[ 6, 4, 6 ]
num_words	list	[ 7, 7, 5 ]
codes	list	List of 3 items
minimum_distances	list	[ 2, 1, 1 ]
information_rates	list	List of 3 items

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
repeat(random(3..6),3)

JME function reference

Description

Lengths of the words in each code

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `list`

[ 6, 4, 6 ]

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
Part b) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
Part c) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

$C_1 = \var{codes[0]}$

Information rate: Gap 0.

Minimum distance: Gap 1.

Advice

a)

$C_1 = \var{codes[0]}$ has $\var{num_words[0]}$ words, each of length $\var{word_lengths[0]}$.

Its information rate is therefore $\displaystyle\frac{\log_2 \var{num_words[0]}}{\var{word_lengths[0]}} = \var{precround(information_rates[0],3)}$ to 3 decimal places.

The minimum distance $d(C_1)$ of $C_1$ is the smallest Hamming distance between distinct codewords of $C_1$.

Here's a table of the Hamming distances between the words in $C_1$.

{distance_table(codes[0])}

The minimum distance between distinct codewords of $C_1$ is $d(C_1) = \var{minimum_distances[0]}$.

b)

$C_2 = \var{codes[1]}$ has $\var{num_words[1]}$ words, each of length $\var{word_lengths[1]}$.

Its information rate is therefore $\displaystyle\frac{\log_2 \var{num_words[1]}}{\var{word_lengths[1]}} = \var{precround(information_rates[1],3)}$ to 3 decimal places.

The minimum distance $d(C_2)$ of $C_2$ is the smallest Hamming distance between distinct codewords of $C_2$.

Here's a table of the Hamming distances between the words in $C_2$.

{distance_table(codes[1])}

The minimum distance between distinct codewords of $C_2$ is $d(C_2) = \var{minimum_distances[1]}$.

c)

$C_3 = \var{codes[2]}$ has $\var{num_words[2]}$ words, each of length $\var{word_lengths[2]}$.

Its information rate is therefore $\displaystyle\frac{\log_2 \var{num_words[2]}}{\var{word_lengths[2]}} = \var{precround(information_rates[2],3)}$ to 3 decimal places.

The minimum distance $d(C_3)$ of $C_3$ is the smallest Hamming distance between distinct codewords of $C_3$.

Here's a table of the Hamming distances between the words in $C_3$.

{distance_table(codes[2])}

The minimum distance between distinct codewords of $C_3$ is $d(C_3) = \var{minimum_distances[2]}$.

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Hu Yuntao 5 years, 1 month ago

Christian Lawson-Perfect 6 years, 8 months ago

Newcastle University Mathematics and Statistics 6 years, 8 months ago

Christian Lawson-Perfect 6 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

a)

b)

c)

Loading...

Error

Information rate and minimum distance

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Hu Yuntao 5 years, 1 month ago

Christian Lawson-Perfect 6 years, 8 months ago

Newcastle University Mathematics and Statistics 6 years, 8 months ago

Christian Lawson-Perfect 6 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

a)

b)

c)

Generated value: `list`