Generalized Performance Upper Bounds for Terminated Convolutional Codes

Hichan MOON  Donald C. COX  

IEICE TRANSACTIONS on Communications   Vol.E90-B   No.6   pp.1360-1366
Publication Date: 2007/06/01
Online ISSN: 1745-1345
DOI: 10.1093/ietcom/e90-b.6.1360
Print ISSN: 0916-8516
Type of Manuscript: PAPER
Category: Fundamental Theories for Communications
convolutional code,  upper bound,  weight enumerator,  

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In this paper, we propose tight performance upper bounds for convolutional codes terminated with an input sequence of finite length. To obtain the upper bounds, a generalized weight enumerator of single error event is defined to represent the relation between the Hamming distance of the coded output and the Hamming distance of the selected input bits of a terminated convolutional code. In the generalized weight enumerator of single error event, codewords composed of multiple error events are not counted to provide tighter performance upper bounds. The upper bounds on frame error rate (FER) and average bit error rate (BER) of selected bits are computed from the generalized weight enumerators of single error event. A simple method is presented to compute the weight enumerator of a terminated convolutional code based on a modified trellis diagram.