Low-rate channel coding with complex-valued block codes

This paper addresses aspects of channel coding in orthogonal frequency-division multiplexing–code-division multiple access (OFDM-CDMA) uplink systems where each user occupies a bandwidth much larger than the information bit rate. This inherent bandwidth expansion allows the application of powerful low-rate codes under the constraint of low decoding costs. Three different coding strategies are considered: the combination of convolutional and repetition codes, the code-spread system consisting of one single very low-rate convolutional code and a serial concatenation of convolutional, Walsh–Hadamard and repetition code. The latter scheme is improved by combining the Walsh–Hadamard codes with an additional -phase-shift keying modulation resulting in complex-valued Walsh–Hadamard codes (CWCs). Analytical performance evaluations will be given for these codes for the first time. The application of CWCs as inner codes in a serial code concatenation is also addressed in this paper. We derive a symbol-by-symbol maximum a posteriori decoding algorithm in the complex signal space in order to enable iterative decoding for the entire code. A comprehensive performance analysis by simulation of all the proposed coding schemes shows that the Walsh–Hadamard-based schemes are the best choice for low-to-medium system load. Note that even for fully loaded OFDM-CDMA systems, the concatenation with an inner complex-valued Walsh–Hadamard code leads to a bit-error rate less than 10 5 for an 0 of about 6 dB.