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Unformatted text preview: EE 5501 Prof. N. Jindal Digital Communication Nov. 5, 2009 Homework 6 Due: Thursday, Nov. 12, 11:15 AM 1. In class we have found the log-likelihood ratio of each information bit by computing the likelihood’s of the trellis transitions associated with different information bits. In this problem we will see that the same can be done by computing the likelihood of each codeword (although this is very computationally inefficient). We assume that K information bits plus 2 terminating bits are sent, so the information bit sequence ~u is length K + 2 and the received symbol vector ~ y is length 2( K + 2). (a) Show that the likelihood of a particular information bit sequence ~u conditioned on the received symbols ~ y can be written as: P [ ~u | ~ y ] = P [ ~ y | ~u ] P [ ~u ] P [ ~ y ] (b) Show that P [ ~ y | ~u ] = 1 p (2 πσ 2 ) 2( K +2) exp •- 1 2 σ 2 || ~ y- ~ c ( ~u ) || 2 ‚ where ~ c ( ~u ) is the codeword (including the energy scaling) corresponding to infor- mation bit sequence...
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This note was uploaded on 11/21/2011 for the course EE 5501 taught by Professor Lops during the Fall '08 term at Minnesota.
- Fall '08