Distance Enumerator Analysis for Interleave Division Multi User Codes
Consider an interleave division multi user coding model for a Gaussian multiple access channel (MAC) Each user's message is encoded by a separate channel encoder followed by a user interleaver, which is employed for user separation. All the users' codewords are jointly regarded as one multi user codeword, and the distance between two multi user codewords is defined as the Euclidean distance after the inter user superposition caused by the MAC. A distance enumerator analysis estimates the multi user maximum likelihood decoding performance. By introducing user scramblers, a multi user code ensemble is defined, and its distance enumerator is calculated as concatenated multiple single user codes and a superposition code. Both finite length and asymptotic analyses are given and it is shown that interleave division multi user codes have much better distance properties than conventional random direct sequence code division multiple access. In fact, the codes achieve almost the same asymptotic uniquely decodable performance as a multi user random code.
IEEE Transactions on Information Theory