Transfer function bounds on performance of turbo codes for M-ary orthogonal signals

We obtain upper bounds on the bit-error rate (BER) for maximum-likelihood (ML) decoding of turbo codes constructed with uniform interleavers for M-ary orthogonal signals. We use transfer function bounding techniques to obtain the above bounds. Thus, the upper bounds result in the average bound over all interleavers of a given length. We apply the techniques to parallel concatenated coding (PCC) schemes where recursive convolutional codes are used as constituent codes. We present the average bounds on the BER of turbo codes with constraint length 3 for M-ary orthogonal signals on additive white Gaussian noise (AWGN) channels. We show that the performance advantage of turbo-coded 4-ary orthogonal signals over turbo-coded binary orthogonal signals is smaller than the performance advantage in the absence of coding, which is 3.0 dB.