Design of ring convolutional trellis codes for MAP decoding of MPEG-4 imagery

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“…Furthermore, the number of delay elements in the realization of m-D convolutional encoder cannot be computed by adding the row-wise constraint length (constraint length is undefined in m-D convolutional code). The attempt here is to determine an alternative m-D approach similar to the algorithm given in 3,5,6,22,23 . By inspection, it can be inferred that the total number of delay elements required for realizing a given convolutional code depends greatly on the maximum total degree of each row vector of its generator matrix G. Using this fact, one can remove the unnecessary delays during the implementation by first finding a lower row-wise maximum total degree equivalent generator matrix G = U G, where U is the unimodular matrix, and use it for the realization instead.…”

“…While 1-D convolutional code and its variants have been thoroughly understood [1][2][3][4][5][6] , the m-D counterpart still lacks unified notation and efficient implementation. In this paper, the partial aim is to emphasize the recent development [7][8][9] of m-D convolutional code theory as well as to point out the bottleneck and open problems to the multidimensional community.…”