Coding for T-user multiple-access channels

Abstract

Coding schemes for the binary memoryless <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</tex> -user adder channel are investigated in this paper. First upper and lower bounds on the capacity sum, which are asymptotically tight with increasing <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</tex> , are derived for the noiseless case. Second, a class of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</tex> -user uniquely decodable codes with rates, asymptotically in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</tex> , equal to the maximal achievable values is constructed. A decoding algorithm for these codes is also presented. Next, a class of error-correcting codes for the noisy <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</tex> -user adder channel is constructed. It is shown that these codes can he used to construct multilevel codes suitable for use on the additive white Gaussian noise channel.