Encoding/decoding messages

Decoding - The decoder, depicted in Figure 4, receives the attacked version of the image, denoted i, and estimates the encoded message using the following procedure ... 

Bob makes the pair of numbers r = 5 and n = 35 public. They are the public key. In particular, be gives them to Alice so that she can send him a coded message. Cindy can also have these numbers. They are used only to encode messages, not to decode them. 

The process of communication requires three basic components a sender, a message, and a receiver. The sender encodes information into a message to send to the recipient for decoding. The message usually has an overt purpose, based on the sender s desire to inform, educate, persuade, or entertain. Some messages can also be covert to attract attention, make connections, gain support, or sell something. 

In general, the decoding reliability can be improved by decoding an entire watermark letter sequence d, where the known encoding of m into d can be exploited to estimate the most likely d, or equivalently, to estimate the most likely watermark message m. The simple codebook structure of SCS can be exploited to efficiently estimate d. First, data y is extracted from the received data r. This extraction process operates sample-wise, where the extraction rule for the nth element is... 

For binary SCS, yn < A/2, where yn should be close to zero if dn =0 was transmitted, and close to A/2 for dn = 1. Second, depending on the type of error correction encoding of d, soft-input decoding algorithms, e g. a Viterbi decoder for convolutional codes, can be used to decode from y the most likely transmitted watermark message m. 

This argument proves the lemma for the case where for each message m the codewords F(m, s) and F(m, s ) are distinct when s 7 s. Consider now the case where for some message rn there are k side information sequences Si,..., which are encoded by the same codeword. We have showed, that for any codeword F(m, s), there is a procedure that produces a different codeword F m, s) which is acceptable for an encoding and decoding scheme for H and has lower decoding error probability. Note that this procedure depends on the sequence s, and hence even if one starts with the same codeword F(m, S ) for / = 1,.., k, the procedure may produce different outputs. Hence, if one replaces the unique codeword,... 

To decode the binary message b from the channel output one needs to estimate the encoding sequence u from the output sequence y. As a basis for this estimation we consider a linear dependence U = (3Y + V, where V is a Gaussian r.v. with zero mean, and the constant (3 has... 

To a large extent, we can perform the task of reading aloud, by decoding a written signal into a message, and the re-encode this into a speech signal. 

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