Optimal Sequence Detection and Optimal Symbol-by-Symbol Detection: Similar Algorithms

Abstract

Abstract-An algorithm is derived which performs optimal symbolby-symbol detection of a pulse amplitude modulated sequence. The algorithm is similar to the Viterhi algorithm with the optimality criterion optimal symbol detection rather than optimal sequence detection. A salient common feature is the merge phenomenon which allows common decisions to be made before the entire sequence is received.

Sequence detection analysis based on canonical correlation for steady-state visual evoked potential brain computer interfaces

“…In this paper, we proposed an innovative frequency recognition approach based on sequence detection (SD), which made use of CCA coefficients for solving this problem. The method was widely used for predicting the exponent of the probability of symbol error in the communication engineering (Bussgang and Middleton, 1955;Hayes et al, 1982;Chaudhari et al, 2009).…”

Theory of Segmentation

“…By segmentation we refer to estimation of the unobserved realization y n =( y 1 ,...,y n ) of the underlying Markov chain Y, given the observations x n =( x 1 ,...,x n ) of X n .I n communications literature segmentation is also known as decoding (Bahl et al, 1974;Viterbi, 1967) or state sequence detection (Hayes et al, 1982). Segmentation is often the primary interest of the HMM-based inference, but it can also be an intermediate step of a larger problem such as estimation of the model parameters Rabiner, 1989), which will be discussed in Subsection 4.2.…”

“…In the wider context of biological applications of discrete high-dimensional probability models this has also been called "consensus estimation", and in the absence of constraints, "centroid estimation" (Carvalho & Lawrence, 2008). In communications applications of HMMs, largely influenced by (Bahl et al, 1974), the terms "optimal symbol-by-symbol detection" (Hayes et al, 1982), "symbol-by-symbol MAP estimation" (Robertson et al, 1995), and "MAP state estimation" (Brushe et al, 1998) have been used to refer to this method. Note that the introduced risk-based formalism does not impose any special conditions on Y.…”

Near-optimal parallel distributed data detection for page-oriented optical memories

“…The former minimizes the BER, while the latter minimizes the probability of a page error. In practice, either criterion is logical and the resulting algorithms provide good performance under either measure [46]. Since an efficient implementation of either approach is unknown, the difference is conceptual; however, we will present algorithms for approximating both approaches.…”