Soft-Input Soft-Output Sphere Decoding
  Soft-input soft-output (SISO) detection algorithms form the basis for iterative decoding. The associated computational complexity often poses significant challenges for practical receiver implementations, in particular in the context of multiple-input multiple-output wireless systems. In this paper, we present a low-complexity SISO sphere decoder which is based on the single tree search paradigm, proposed originally for soft-output detection in Studer et al., IEEE J-SAC, 2008. The algorithm incorporates clipping of the extrinsic log-likelihood ratios in the tree search, which not only results in significant complexity savings, but also allows to cover a large performance/complexity trade-off region by adjusting a single parameter. 
Christoph Studer and Helmut B\"olcskei