Improved bound on optimal reception error probability for an intersymbol interference channel
Keywords:
maximum likelihood reception, union bound on the error probability, pairwise error probability, characteristic function, intersymbol interference channelAbstract
Introduction: Since the exact value of error probability for the optimal reception in an intersymbol interference channel cannot be usually calculated an upper bounding technique is used. The standard approach for obtaining the upper bound on the error probability of the maximum likelihood reception is based on the use of the union bound and the Chernoff bound, as well as its modifications. This approach is still not accurate enough for many cases of the transmission over an intersymbol interference channel. Purpose: To develop a method for exact calculation of the union bound on the error probability of the maximum likelihood reception in the intersymbol interference channel. Results: The resulting exact union bound on the reception error probability combines the use of the characteristic functions and an error-state diagram which make it possible to obtain the final expression in an integral form convenient for numerical integration. An important feature of the proposed procedure is that it allows one to accurately calculate the union bound using an approach based on the use of transfer (generating) functions. With this approach, the edge labels in the error-state diagram are replaced by their corresponding characteristic functions. The final expression and standard methods of numerical integration allow one to calculate the values of the union bound on the reception error probability with the required accuracy. Practical relevance: The results presented in this paper make it possible to significantly improve the accuracy of the bound of the reception error probability, and thereby increase the efficiency of decisions made when designing transmission and/or data storage systems using intersymbol interference channels.