## List Viterbi Decoding with Continuous Error Detection for Inter-Symbol Interference Channels

Dragan Petrovic

(Professors Borivoje Nikolic and Kannan Ramchandran)

In this project, we propose and analyze the list Viterbi algorithm (LVA) with an arithmetic coding-based continuous error detection (CED) scheme for transmission on inter-symbol interference (ISI) channels. We have shown that the system localizes error occurrences to the end of the transmission and that the proportion of bits where errors are likely to occur asymptotically approaches zero as the inverse of the number of transmitted bits. We analytically derived an upper bound on the bit error rate (BER) of the LVA-CED system as a function of the redundancy added by the CED code, the number of bits transmitted, and the BER when the standard maximum likelihood detector is used on the same channel. We analytically derived the number of paths required by the LVA for a target error rate. To show the benefits of these theoretical results in a practical setting, we have applied the system to high-order partial-response magnetic recording channels. Simulations show that this system results in a 2 dB improvement over maximum transition run (MTR) encoded EEPR4 partial response decoding with maximum likelihood sequence detection (EEPRML) at a BER of 2 x 10^{-6} in additive white Gaussian noise, and confirm the theoretical predictions.

Figure 1: Proposed LVA-CED system for magnetic recording

- [1]
- D. Petrovic, B. Nikolic, and K. Ramchandran, “List Viterbi Decoding with Continuous Error Detection for Magnetic Recording Channels,”
*Proc. IEEE Global Conf. Communications, Globecom,* San Antonio, TX, November 2001.

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