In this problem you identify an optimal extension of the rat

In this problem you identify an optimal extension of the rate-1/2 convolutional code presented in lecture to rate-1/3. (a) Implement a forward trellis search algorithm in Matlab and use it to find the best choice (i.e. the choice that provides the maximum free distance) of binary values a, b, and c for the rate-1/3 generator matrix of the form [1 + D + D^2 1 + D^2 a + bD + cD^2]. (3) Use your forward trellis search routine to identify Lp, the number of trellis branches required for

Solution

Trellis Search (Modified Viterbi) Algorithm INITIALIZE: (1) path scores; (2) arc ranking indices; (3) backpointers (optional) LOOP I: loop over time indices from left to fight LOOP II: loop over grammar nodes LOOP III: loop over arcs of a grammar node LOOP IV: loop over states of an arc (word) Evaluate dynamic programming recursion Update accumulated likelihood arrays -- Update backpointer arrays (optional) LOOP IV control For every grammar node, -- sort accumulated likelihood path scores -- register arc ranking index arrays -- register \"from frame\" arrays (optional) LOOP III control LOOP II control LOOP I control After all bookkeeping arrays are initiated, four nested loops are performed. The dynamic programming starts first from the outermost loop, a loop over the time indices from left to right frame synchronously, over a loop of all grammar nodes, then over all arcs (words) of a grammar node and finally, over the innermost loop of all ,states associated with an arc (word). Since the best path will be obtained in the backward tree search as the first sentence hypothesis output, it is not necessary to register any backpointer arrays and all backtracking operations are only optional. The arc (word) ranking index arrays are recorded only when the number of possible arcs (words) at a node exceeds N, the number of sentences hypotheses to be found. In addition to the best partial path, an the other partial paths that lead to a grammar node.