Data width requirements in SISO decoding with modulo normalization

This letter studies the numerical properties of Log-MAP-based soft-input so ft-output decoding. The ranges of the differences between the path metrics, the soft output, and the complete information are derived. Since the Log-M AP algorithm is functionally dependent only upon the differences between pa th metrics, not their magnitudes, a modulo normalization technique that is automatically implemented in two's complement arithmetic can be used to acc ommodate overflow of the path metrics. An expression for the minimum intern al data width of a soft-input soft-output decoder that employs the modulo n ormalization 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.