On Low-Rate Convolutional Codes for Code-Spread Code Division Multiple Access

The performance in terms of bit-error probability of low-rate convolutional codes is addressed. The Heller bound on the free distance is revised and an alternative formulation is given. A discussion of the key parameters determining the code performance and how to obtain good codes is followed by a comparison of codes of various rates for a fixed constraint length. It is concluded that simply lowering the rate does not give a great performance gain, but the encoder complexity must be increased to increase the coding gain. This observation is used to propose modifications to a previously suggested code-spread CDMA system. Keywords— low-rate convolutional codes, code-spread CDMA, Heller bound, distance spectrum, code performance.