By Giuseppe Longo (eds.)
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Extra resources for Coding and Complexity
1 (a), we show an N = 2, K = 1 (R = 1/2) binary FCE with memory M = 2. We have not yet specified L or T and, in fact, the versatility of convolutional codes arises partly from the fact that these parameters can be chosen to fit the practical situation at hand. The signal flowchart for this encoder is shown in Fig. 1 (b) and is constructed as follows. There is a node for every "state" [iu·1 , iu_ 2] which is shown with the state as its label. From each state, there is a directed edge to each of the possible successor states, [0, iu.
7) 15. Sequential Decoding--The Stack Algorithm Sequential decoding is a generic name for any decoding procedure for a tree code which searches for the likely transmitted path for a given received sequence Y[ 0 L + T) by successively exploring the encoded tree with the following constraints on the nature of the exploration : ( 1) Any new nodes explored must be at the next depth beyond an already explored node, and (2) No knowledge of the unexplored part of the tree is available except knowledge of the statistical distribution Q(x) which characterizes the ensemble of tree codes for which the code is use may be considered a "typical" member.
Whether implemented in hardware or software, it is clear that the "complexity" of a Viterbi decoder grows exponentially with M, the encoder memory. M = 6 or 7 appears to be about the limit of practicality. Rate 1/2 FCE's with memory M 9!! 6 are, however, surprisingly good for their short constraint lengths N t = (M + 1) N ::!!! 14. L. Massey 42 an error probabability of 1