A two-track matched spectral-null code with rate ¾ for the binary dicode channel

The paper shows, via a special case, the advantage of multi-track matched spectral-null codes. We consider the dicode channel (1-D) end use the cross product of two canonical diagrams to construct a two-track sliding block code with a rate 3/4. The maximum runlength of zero samples at the channel output is equal to 1. This code doubles the minimum squared-Euclidean distance at the output of the dicode channel and provides an asymptotic coding gain of 1.76 dB. The encoder is implemented as a finite state machine with 4 states. The decoder is a block decoder, implementable as a look-up table. The decoding of a codeword of length 4 depends on the contents of a 2×2 two-dimension decoder window that contains uniquely the codeword in question. In this way, a single incorrectly detected bipolar symbol can propagate into a burst of at most three user binary elements. The reduced complexity detector trellis for this code has 12 states