This paper deals with the analysis and design of orthogonal frequency-division multiplexing interleave-division multiple-access (OFDM-IDMA). We begin with the analysis of the information-theoretical advantages of non-orthogonal transmission schemes in fading multiple-access channels. We then turn attention to practical design issues. A signal-to-noise ratio (SNR) evolution technique is developed to predict the bit-error-rate (BER) performance of OFDM-IDMA. This technique is applied to system design and optimisation. Through proper power allocation, OFDM-IDMA can achieve the multi-user gain (MUG) predicted by information-theoretical analysis. It is also an attractive option in compensating for the clipping effect caused by peak-power limitation. Numerical examples show that OFDM-IDMA can (i) alleviate the PAPR problem commonly suffered by OFDM-based schemes; (ii) deliver significant MUG compared with other orthogonal alternatives; (iii) provide robust communications in frequency-selective channels; and (iv) support high single-user throughput. Copyright © 2008 John Wiley & Sons, Ltd.