You are asked to design binary codes to be used to transmit a list of numbers which are made up of the digits 2 – 8 only: the list is separated by dashes (so every - character in the list is one of the symbols 2, 3, 4, 5, 6, 7, 8, and -. You sample 1000 characters from a typical list and find the number of occurrences of each symbol to be as follows, where a, b, c are a = 9, b = 1, and c = 5

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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You are asked to design binary codes to be used to transmit a list of numbers which
are made up of the digits 2 - 8 only: the list is separated by dashes (so every
character in the list is one of the symbols 2, 3, 4, 5, 6, 7, 8, and -. You sample 1000
characters from a typical list and find the number of occurrences of each symbol to
be as follows, where a, b, c are
a = 9, b = 1, and c = 5
(a)
(b)
Dash
300
2
240 + a
3
160+ b
4
99-c
5
82 - a
6
60-b
7
30+ c
8
29
Use each of the Huffman and Shannon-Fano methods to create prefix-free
codes for this alphabet.
Calculate the expected average wordlength for each of your codes.
(c)
Calculate the entropy for the distribution.
(d)
Explain whether your answers for (b) and (c) correspond to the theoretical
bounds.
Transcribed Image Text:1 You are asked to design binary codes to be used to transmit a list of numbers which are made up of the digits 2 - 8 only: the list is separated by dashes (so every character in the list is one of the symbols 2, 3, 4, 5, 6, 7, 8, and -. You sample 1000 characters from a typical list and find the number of occurrences of each symbol to be as follows, where a, b, c are a = 9, b = 1, and c = 5 (a) (b) Dash 300 2 240 + a 3 160+ b 4 99-c 5 82 - a 6 60-b 7 30+ c 8 29 Use each of the Huffman and Shannon-Fano methods to create prefix-free codes for this alphabet. Calculate the expected average wordlength for each of your codes. (c) Calculate the entropy for the distribution. (d) Explain whether your answers for (b) and (c) correspond to the theoretical bounds.
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