Bounds on the Frame Error Rate of Finite-State Codes over Deletion Channels

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Haghighat J., Duman T. M.

2026 IEEE International Symposium on Information Theory, ISIT 2026, Guangzhou, China, 28 June - 03 July 2026, (Full Text)

• Publication Type: Conference Paper / Full Text
• Doi Number: 10.1109/isit62367.2026.11654138
• City: Guangzhou
• Country: China
• TED University Affiliated: Yes

Abstract

We derive an upper bound on the frame error rate (FER) of coded transmission schemes over deletion channels. We show how this bound can be evaluated numerically for a finite-state code, such as a convolutional code. To this end, we develop a trellis diagram that jointly tracks the behavior of two independent encoders and their corresponding independent deletion channels. We show that the upper bound can be evaluated by counting the number of paths on this trellis diagram that satisfy certain conditions, and we develop a recursive approach to perform this counting. The numerical results confirm that the derived upper bound on the error probability closely follows the simulation results.