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A new evaluation method of a block error probability of a block modulation code over an AWGN channel

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3 Author(s)
K. Tomita ; Dept. of Inf. & Comput. Sci., Osaka Univ., Japan ; T. Takata ; T. Kasami

Let L be a finite set of symbols, and let C be a block code of length n over L. Let h be a positive integer. For u∈L, let s(u) denote the signal point in ℛh which represents u, where ℛh denotes the set of all h-tuples of real numbers, and for u=(u1,u2,…,un) over L, let s(u) denote the hn-tuple (s(u1),s(u2),…,s(u n)). For z and z' in ℛhn let ||z-z'|| denote the Euclidean distance between z and z'. For u∈C/{0}, let pe(r,u) denote the probability of an incorrect decoding of s(0) into u under the condition that ||s(0)-z||=r where r is a non-negative real number. Then, f(r)=Σu∈C{0}/pe(r,u). For u∈C{0}, let Cu be a subcode of C which contains u. Let P(r,Cu) denote the probability that for every v∈Cu other than u, a received z satisfies ||s(u)-z||⩽||s(v)-z|| under the condition that ||s(0)-z||=r. In the examples given, we present a tighter evaluation method of pe(r,u) or the sum of pe(r,u) over all the nearest neighbor us of 0

Published in:

Information Theory. 1997. Proceedings., 1997 IEEE International Symposium on

Date of Conference:

29 Jun-4 Jul 1997