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-This paper provides a comprehensive study of interleave-division multiple-access (IDMA) systems. The IDMA receiver principles for different modulation and channel conditions are outlined. A semi-analytical technique is developed based on the density evolution technique to estimate the bit-error-rate (BER) of the system. It provides a fast and relatively accurate method to predict the performance of the IDMA scheme. Simulation examples are provided to demonstrate the advantages of the IDMA scheme in terms of both bandwidth and power efficiencies. For example, with simple convolutional/repetition codes, overall throughputs of 3 bits/chip with one receive antenna and 6 bits/chip with two receive antennas are observed for systems with as many as about 100 users.

Abstract-This paper is concerned with a class of low-rate codes constructed from Hadamard code arrays. A recursive encoding principle is employed to introduce an interleaving gain. Very simple trellis codes with only two or four states are sufficient for this purpose, and the decoding cost involved in the trellis part is typically negligible. Both simulation and analytical results are provided to demonstrate the advantages of the proposed scheme. The proposed scheme is of theoretical interest as it can achieve performance of BER = 10 5 at 0 1.2 dB (only about 0.4 dB away from the ultimate low-rate Shannon limit) with an information block size of 65534. To the authors' knowledge, this is the best result achieved to date with respect to the ultimate Shannon limit. With regard to practical issues, the decoding complexity of the proposed code is considerably lower than that of existing low-rate turbo-type codes with comparable performance.Index Terms-A posteriori probability (APP) decoding, Hadamard codes, iterative decoding, spread spectrum, turbo codes.

This paper is concerned with a family of concatenated tree (CT) codes. CT codes are special low-density paritycheck (LDPC) codes consisting of several trees with large spans. They can also be regarded as special turbo codes with hybrid recursive/nonrecursive parts and multiple constituent codes. CT codes are decodable by the belief-propagation algorithm. They combine many advantages of LDPC and turbo codes, such as low decoding cost, fast convergence speed, and good performance.

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