Problem $(160$pts$)$:

Take or write any text of about $100-120$ words as a message Message. For example,

Compression methods are either lossless or lossy. Lossless methods restore completely data, i$.$e$.$ the

restored data file is identical to the original file. Lossless methods used for codes, word processing

files, tabulated numbers, text documents, etc. For those data, it is absolutely necessary to keep the

data in perfect condition for storage and transmission. No single bit of the information should be

misplaced. Lossy compression methods allow a small amount of noise in the restored data. Such

methods are much more effective for storage, because of high compression rate. But, more noise is

added to the original data, when the compression rate becomes high.

Use the Huffman method to encode the message, ${?}^1$ fill the table and calculate the average length

of the codewords, the entropy of the alphabet, and the redundancy of the code:

$\frac{?}{\text{b}\text{a}\text{r}}(l)=$

$=$

$R=$

Calculate the number of bits for encoding this message

Write your code in MATLAB to encode this message.

Hide the encoding message in the last insignificant bit$-$plane of the image "boat$512.$tiff" at the

pixels which start from the random pixel $(x_0,y_0).$

Display the original image together and the new image with the encoded message.