The tangential sphere bound (TSB) of Poltyrev (1994) is a tight upper bound on the word error probability P/sub w/ of linear codes with maximum likelihood decoding and is based on the code's distance spectrum. An extension of the TSB to a bound on the bit-error probability P/sub b/ is given by Sason/Shitz (see IEEE Trans. Inform. Theory, vol.46, p.24-47, 2000). We improve the tangential sphere bound on P/sub b/ and apply the new method to some examples. Our comparison to other bounds as well as to simulation results shows an improved tightness, particularly for signal-to-noise ratios below the value corresponding to the computational cutoff rate R/sub o/.

In CDMA systems combining several traffic channels leads to a multi-code (MC) CDMA system offering higher user data rates without increasing the system bandwidth. Due to imperfect spreading sequences, the transmission quality degrades in case of multipath propagation. The additional noise power caused by co-channel interference increases linearly with the number of traffic channels. In this paper, we demonstrate how to reduce this noise by cancelling out the co-channel interference in an iterative way using soft values of the decoded bits. The gain depends on the operating point of the coded system. Simulation results for turbo codes and convolutional codes are close to the results for an AWGN channel.

Iterative decoding is applied to code division multiple access (CDMA) systems with two-stage serial concatenated channel coding. For a direct sequence (DS) CDMA system like in the uplink of the standard IS-95(A) using M-ary orthogonal modulation (inner code) and an outer convolutional code with interleaving we give the optimum symbol-by-symbol maximum a posteriori (MAP) decoding rules for the inner block code in a coherent and noncoherent receiver design. Further suggestions for suboptimum MAP decoders with lower complexity are made. The inner decoding rule is extended to use a priori information for the systematic bits, which is delivered from the outer decoding stage. These algorithms are essential for iterative decoding of the system. Simulation results show a decoding gain of about 0.6 dB for a bit error rate (BER) of 10/sup -3/ by replacing the maximum likelihood (ML) decoder for the inner code by a MAP decoder. A total gain of about 1.2 dB is achieved by the use of iterative decoding after only three to five iterations.