Two 16-State, Rate Trellis Codes Whose Free Distances Meet the Heller Bound
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چکیده
For rate R = 1=2 convolutional codes with 16 states there exists a gap between Heller’s upper bound on the free distance and its optimal value. This correspondence reports on the construction of 16state, binary, rate R = 2=4 nonlinear trellis and convolutional codes having dfree = 8; a free distance that meets the Heller upper bound. The nonlinear trellis code is constructed from a 16-state, rate R = 1=2 convolutional code over 4 using the Gray map to obtain a binary code. Both convolutional codes are obtained by computer search. Systematic feedback encoders for both codes are potential candidates for use in combination with iterative decoding. Regarded as modulation codes for 4-PSK, these codes have free squared Euclidean distance d E; free = 16.
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