Analysis of Finite Field Spreading for Multiple-Access Channel

Finite field spreading scheme is proposed for a synchronous multiple-access channel with Gaussian noise and equal-power users. For each user, $s$ information bits are spread \emph{jointly} into a length-$sL$ vector by $L$ multiplications on GF($2^s$). Thus, each information bit is dispersed into $sL$ transmitted symbols, and the finite field despreading (FF-DES) of each bit can take advantage of $sL$ independent receiving observations. To show the performance gain of joint spreading quantitatively, an extrinsic information transfer (EXIT) function analysis of the FF-DES is given. It shows that the asymptotic slope of this EXIT function increases as $s$ increases and is in fact the absolute slope of the bit error rate (BER) curve at the low BER region. This means that by increasing the length $s$ of information bits for joint spreading, a larger absolute slope of the BER curve is achieved. For $s, L\geq 2$, the BER curve of the finite field spreading has a larger absolute slope than that of the single-user transmission with BPSK modulation.

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