educed Complexity Symbol-by-Symbol emodulat ion
Michael P. Fitdand, Saul B. Gelfand · 1990
Reduced complexity symbol-by-symbol demoldulation is examined. We examine the perfor- mance with standard complexity reduction techniques (e.g., M-algorithm and T-algorithm) and then derive a reduced state symbol-by-symbol demodulation al- gorithm which makes symbol-by-symbol demodula- tion performance and complexity competitive with se- quence estimation. I. INTRODUCTION Symbol-by-symbol demodulation (SYD) structures, (e.g.,(l)) while (optimum in terms minimizing symbol error probability, typically have a complexity greater than sequence demodula- tion (SED) techniques (e.g.,the Viterbi algorithm) for a fixed decodiing lag. Consequently when only hard decision outputs are required SED techniques are invariably used in practice. However, soft decision metrics are often needed (e.g., inter- leaved or concatenated coding schemes), and hence reduced complexity high performance SYD structures are of inter- est. In this paper we propose a new algorithm that produces symbol-by-symbol metrics at roughly the same complexity as SED without a significant loss in performance and examine methods to significantly reduce the complexity of SYD. 11. OVERVIEW OF OPTIMUM RECURSIVE ESTIMATION Consider a modulation with memory described by a time in- variant Markov chain transmitting m bits of information per symbol corrupted by an AWGN. Define K as the decoding lag, ulc to be the modulation state, llokll to be the cardinality of the modulation state, and w(k) to be all the observations until time Ik. We also use as the transmitted symbol space and In (IC) = {Ik-nrIk-n+lr a * ,Ik}