CRC-Aided Short Convolutional Codes and RCU Bounds for Orthogonal Signaling
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We extend earlier work on the design of convolutional code-specific CRC codes to Q-ary alphabets, with an eye toward Q-ary orthogonal signaling. Starting with distance-spectrum optimal, zero-terminated, Q-ary convolutional codes, we design Q-ary CRC codes so that the CRC/convolutional concatenation is distance-spectrum optimal. The Q-ary code symbols are mapped to a Q-ary orthogonal 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 random coding union bound and normal approximation are used in earlier works as benchmarks for performance for distance-spectrum optimal convolutional codes. We derive a saddlepoint approximation of the random coding union bound for the coded noncoherent signaling channel, as well as a normal approximation for this channel, and compare the performance of our codes to these limits. Our best design is within 0.6 dB of the RCU bound at a frame error rate of 10^-4.
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