2 16-STATE, RATE R = 2 4 TRELLIS CODES WHOSE FREE DISTANCES MEET THE HELLER BOUND/

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 val ue. This correspondence reports on the construction of 16-state, binar y, rate R = 2/4 nonlinear trellis and convolutional codes having d(fre e) = 8; a free distance that meets the Heller upper bound. The nonline ar trellis code is constructed from a 16-state, rate R = 1/2 convoluti onal code over Z(4) using the Gray map to obtain a binary code. Both c onvolutional codes are obtained by computer search. Systematic feedbac k encoders for both codes are potential candidates for use in combinat ion with iterative decoding. Regarded as modulation codes for 4-PSK, t hese codes have free squared Euclidean distance d(E,free)(2) = 16.