Reduced complexity symbol-by-symbol soft output algorithms

This paper presents and characterizes the performance of complexity reduction techniques applied to optimum soft output demodulation algorithms for a general modulation model. The optimum soft output algorithm (OSA) recursively computes the posterior probability mass function (PMF) of the modulation state and each information symbol conditioned on the modulation state up to a decoding lag of K. The recursion has complexity O(||σ_k||M²K) where ||σ_k|| is the cardinality of the modulation state and M is the cardinality of the information symbols. This paper focuses on two complexity reduction techniques: (1) retaining states in the OSA recursion only if their PMF is above a threshold (T-OSA) and (2) a reduced state version of OSA (RSSOA) where demodulation occurs assuming a modulation state of lower cardinality than the true modulation state. These algorithms greatly reduce the complexity of OSA while in many cases retaining near optimum performance. Examples are considered for known intersymbol interference channels, concatenated convolution codes, and continuous phase modulation