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Comparison of the 3-out-of-7 ARQ with Bose-Chaudhuri-Hocquenghem Coding Systems

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1 Author(s)
M. Nesenbergs ; National Bureau of Standards,Central Radio Propagation Lab., Boulder

The performance of coding schemes can be expressed by two criteria: the useful transmission rate R , and output character-error probability P . Both quantities are expressed in a form applicable to a binary forward channel coupled with an arbitrary feedback channel. Using these criteria the 3-out-of-7 ARQ code is compared with various error-correcting and detecting alternatives of the Bose-Chaudhuri-Hocquenghem codes of length 2^{m} - 1 , where m = 3, 4, 5, 6, 7, 8 . It is found that for a specified binary element-error probability Peone can often find a Bose-ChaudhuriHocquenghem code which is considerably superior. If the element errors are independent of each other a purely error-correcting arrangement looks attractive. If the errors are correlated (i.e., occur in bursts) error detection holds more promise. A (255, 187) code, which is used to correct up to 8 errors and to detect others, shows a superiority which extends over all significant values of Pe.

Published in:

IEEE Transactions on Communications Systems  (Volume:11 ,  Issue: 2 )