Question

consider sending a message of <Hi> that consists of 16-bit from source to destination. Your message must go through the channel coding anf line coding before transmit. (design own information interchange code)

(a) consider the use if hamming codes in the channel coding to endocode the 16-bit message
(i) construct the hamming codeword for this message.
(ii) bt inverting one message bit in Hamming codeword(to represent a 1bit-error) and demonstrate how the recipient can use thr check bits to correct the inverted bit.

(b) encode the output message frim channel coding into the following line codes.
(i) non return to zero-mark (NRZ-M)
(ii) manchester

Answer 1

Consider a frame having m data bits (message to be sent) and r redundant bits (used for checking). The total number of bits in the frame will be n(m + r), which is referred as n-bit code word. Consider two code-words, 11,001,100 and 11,001,111, and perform Exclusive OR and then count number of 1’s in the result. The number of bits in which the codewords are different is called Hamming distance. Suppose the code words are Hamming distance d- apart, it will require d single-bit errors to connect one code word to another. The properties of error detection and error correction depend on the Hamming distance.

• A distance (d + 1) code is required to detect d errors because d-single bit errors cannot change a valid codeword into another valid code. Thus the error is detected at the receiver.

• A distance (2d + 1) code is required to correct d errors because the codewords will be so apart that the transmitted codeword will be still closer than any other valid codeword, and thus the error can be determined.