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An upper bound on the minimum Euclidean distance for block-coded phase-shift keying

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2 Author(s)
Nilsson, M. ; Dept. of Technol., Univ. Coll. of Kalmar, Sweden ; Lennerstad, H.

We present an upper bound on the minimum Euclidean distance dEmin(C) for block-coded PSK. The bound is an analytic expression depending on the alphabet size q, the block length n, and the number of codewords |C| of the code C. The bound is valid for all block codes with q⩾4 and with medium or high rate-codes where |C|>(q/3) n. There are several well-known block codes whose dEmin (C) is equal to our upper bound. Hence these codes are the best possible in the sense that there does not exist a code with the same q, n, and |C| and with a larger dEmin(C). It also follows that for many choices of q, n, and |C|, in particular for high rates, our upper bound on dEmin(C) is optimal

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Information Theory, IEEE Transactions on  (Volume:46 ,  Issue: 2 )