Please write matlab codes and annotations for this question
HUFFMAN ALGORITHM
Step 1: Arrange the symbols in order of decreasing probability. If the probabilities are equal, break the tie randomly.
Step 2: Combine the two smallest values in the list to form a new entry whose probability is the sum of the two original entries.
Step 3: Continue combining two smallest values in the modified list (original untouched values and the new entry) until the root of the tree is reached.
Step 4: Assign bits from left to right on the tree: at each branch, assign a 0 to the higher valued branch and a 1 to the other.
Step 5: Form the codewords by reading from the root to the node of the symbol.
The Huffman coding algorithm is described in Prob. 2.40 (above). In this project, you will measure the average information, code the given message using the Huffman algorithm, transmit the coded message over a simple binary channel, reconstruct the message, and compare the performance to that without coding.
The following schematic diagram illustrates the sequence for implementing these operations.
1. Consider the following message for source coding and transmission:
APPARENTLY NEUTRAL'S PROTEST IS THOROUGHLY DISCOUNTED
AND IGNORED. ISMAN HARD HIT. BLOCKAGE ISSUE AFFECTS PRETEXT
FOR EMBARGO ON BY-PRODUCTS, EJECTING SUETS AND
VEGETABLE OILS.
(This message is included in the data package for this book as the file ‘msg.txt'.)
2. Determine the average information for this message. (You may ignore hyphens, spaces, and punctuation.)
3. Using the Huffman algorithm, code the above message.
4. Deterinine the average codeword length.
5. Transmit the codewords in binary form across the binary symmetric communication channel specified in Project 2.1.
6. Reconstruct the message from the received codewords.
7. Determine the average information of the received message. Would you expect it to be larger or smaller than that of the transmitted message?