In Problem 11.4.5, we used simulation to estimate the probability of symbol error. For transmitting a binary
Question:
(a) Find the acceptance sets {A0,..., A7}.
(b) Simulate m trials of the transmission of symbol So- Estimate the probabilities {P0j|j = 0,1,..., 7}, that the receiver output is s0 when so was sent. By symmetry, use the set {P0j} to determine Pij for all i and j.
(c) Let b(i) = [b2(i) b1(i) b0(i)] denote the input bit sequence that is mapped to si. Let dij denote the number of bit positions in which b(i) and h(j) differ. For a given mapping, the bit error rate (BER) is
(d) Estimate the BER for the binary index mapping.
(e) The Gray code is perhaps the most commonly used mapping:
Does the Gray code reduce the BER compared to the binary index mapping?
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Related Book For
Probability and Stochastic Processes A Friendly Introduction for Electrical and Computer Engineers
ISBN: 978-1118324561
3rd edition
Authors: Roy D. Yates, David J. Goodman
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