This lecture covers the Viterbi algorithm, focusing on state metric updates with probabilities and branch metrics computation. It explains the transition branches, likelihood calculations, and the decoding process for AWGN channels. The instructor discusses the importance of log-likelihood ratios (LLRs) and the decoding challenges faced in hard-decision decoding. Additionally, the lecture delves into the computation of LLRs for BPSK and QPSK modulation schemes, emphasizing the significance of maximizing probabilities to minimize decoding errors.