9304763 Rimoldi We are approaching the era of personal communication which requires an infrastructure capable of providing untethered access to a global network from any point on (and above) the surface of the earth. Implementation of this scenario requires efficient communication via a wireless network. One major component of a wireless network is the Gaussian multiple-access channel. The objective of the proposed research is to extend recent results of the principal investigator leading to a novel procedure to construct codes for this channel. The following two steps have led to the proposed procedure. Step 1 A simpler channel model called G-adder channel was considered and multiple-access codes for this channel were studied. The G-adder channel associated to some finite group G has inputs that are elements of G and output that is the sum (over G) of the inputs. To start on a more familiar ground it was assumed that G is the additive group of a finite field F. It was shown that multiple-access codes for such G-adder channels can be studied and constructed in a framework that is akin to the algebraic theory of error control codes. Two simple procedures to construct multiple-access codes with desirable properties via maximum distance separable codes were given. A G-adder channel does not arise naturally. It can be created on a local area network by means of "smart" nodes that add information symbols according to the arithmetic in G. A stronger motivation for the study or G-adder channels came from step two. Step 2: It has been shown that it is possible to decompose the Gaussian multiple-access channel into a number of independent G-adder channels provided that each such channel is then used to transmit multiple-access codewords over G considered in step one. The decomposition is obtained via T "modulators" (one for each channel input node) and a "demodulator." The modulator outputs are lattice-type signal-space codewords for the Gaussian channel. *** Compared to spread spectrum (the common practice) the codes resulting from steps 1 and 2 above have the following advantages: (l) They are designed keeping in mind that interference and noise are two distinct problems that need different solutions. In particular, active users do not contribute to the noise level of other users; (2) Decoding is simple and algebraic; (3) There is no bandwidth expansion. in the sense that while taking care of the problem of assigning the channel to busy users. the codes allow transmission of the same amount of information that would be possible via time-division multiple-access (or frequency-division multiple-access). (4) They support transmission of several bits per dimension which is an important attribute for codes designed to operate in a bandlimited environment. (5) They are natural offspring of the powerful coding and shaping techniques that have revolutionized the design of signal-space codes for the (single-user) bandlimited Gaussian channel. (6) They have the properties that are needed for the codes assumed in recently proposed random-access protocols with multiple reception capability. These protocols can achieve throughputs arbitrarily close to 1.
