Error correction code: Difference between revisions

Revision as of 21:02, 23 July 2018

Revision as of 03:31, 21 August 2018

Line 197:

'''Transmission without interleaving''':

Error-free message: {{not a typo|aaaabbbbccccddddeeeeffffgggg}}

Transmission with a burst error: {{not a typo|aaaabbbbccc____deeeeffffgggg}}

Here, each group of the same letter represents a 4-bit one-bit error-correcting codeword. The codeword cccc is altered in one bit and can be corrected, but the codeword dddd is altered in three bits, so either it cannot be decoded at all or it might be [[falsing|decoded incorrectly]].

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'''With interleaving''':

Error-free code words: {{not a typo|aaaabbbbccccddddeeeeffffgggg}}

Interleaved: {{not a typo|abcdefgabcdefgabcdefgabcdefg}}

Transmission with a burst error: {{not a typo|abcdefgabcd____bcdefgabcdefg}}

Received code words after deinterleaving: {{not a typo|aa_abbbbccccdddde_eef_ffg_gg}}

In each of the codewords aaaa, eeee, ffff, gggg, only one bit is altered, so one-bit error-correcting code will decode everything correctly.

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'''Transmission without interleaving''':

Original transmitted sentence: {{not a typo|ThisIsAnExampleOfInterleaving}}

Received sentence with a burst error: {{not a typo|ThisIs______pleOfInterleaving}}

The term "AnExample" ends up mostly unintelligible and difficult to correct.

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'''With interleaving''':

Transmitted sentence: {{not a typo|ThisIsAnExampleOfInterleaving...}}

Error-free transmission: {{not a typo|TIEpfeaghsxlIrv.iAaenli.snmOten.}}

Received sentence with a burst error: {{not a typo|TIEpfe______Irv.iAaenli.snmOten.}}

Received sentence after deinterleaving: {{not a typo|T_isI_AnE_amp_eOfInterle_vin_...}}

No word is completely lost and the missing letters can be recovered with minimal guesswork.