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We extend earlier work on the design of convolutional code-specific CRC codesto $Q$-ary alphabets, with an eye toward $Q$-ary orthogonal signaling. Startingwith distance-spectrum optimal, zero-terminated, $Q$-ary convolutional codes,we design $Q$-ary CRC codes so that the CRC/convolutional concatenation isdistance-spectrum optimal. The $Q$-ary code symbols are mapped to a $Q$-aryorthogonal signal set and sent over an AWGN channel with noncoherent reception.We focus on $Q = 4$, rate-1/2 convolutional codes in our designs. The randomcoding union bound and normal approximation are used in earlier works asbenchmarks for performance for distance-spectrum optimal convolutional codes.We derive a saddlepoint approximation of the random coding union bound for thecoded noncoherent signaling channel, as well as a normal approximation for thischannel, and compare the performance of our codes to these limits. Our bestdesign is within $0.6$ dB of the RCU bound at a frame error rate of $10^{-4}$.

CRC-Aided Short Convolutional Codes and RCU Bounds for Orthogonal Signaling