Data width requirements in SISO decoding with module normalization

This letter studies the numerical properties of log-MAP-based soft-input soft-output decoding. The ranges of the differences between the path metrics, the soft output, and the complete information are derived. Since the log-MAP algorithm is functionally dependent only upon the differences between path metrics, not their magnitudes, a module normalization technique that is automatically implemented in two's complement arithmetic can be used to accommodate overflow of the path metrics. An expression for the minimum internal data width of a soft-input soft-output decoder that employs the module normalization technique is derived. As an application, the minimum internal data width of a decoder for the turbo code used in third-generation mobile communication systems is determined.