This paper considers a technique for very low rate channel coding. The main application for such codes is in spread-spectrum systems where significant bandwidth spreading is possible. New, very low rate binary channel codes based on a combination of a trellis code with a first-order Reed-Muller block code (trellis/Reed-Muller (TRM) codes) are presented. The construction technique for TRM codes, which is considered in this paper, is related to Kerdock (1972) codes. It is shown that these TRM codes provide a better tradeoff between rate and gain than other existing very low rate codes, such as the orthogonal or superorthogonal convolutional codes, and the IS-95 uplink code. Due to their improved performance, TRM codes can significantly increase the bandwidth efficiency of spread-spectrum multiple-access systems.

This work considers a new low rate coding scheme, based on the combination of a trellis code with a first order Reed-Muller code. This construction, which we refer to as a trellis/Reed-Muller (TRM) code is presented. A maximum-likelihood decoding method is introduced, and the performance of the code analyzed. Both upper and lower bounds on the bit error probability are derived. The TRM codes are then compared with biorthogonal convolutional codes, and shown to provide a significant improvement.