Viterbi Algorithm (1967) › Implementation Details: Managing Memory and Precision

Implementing the Viterbi algorithm efficiently requires careful attention to numerical stability and memory management. When computing probabilities, multiplying many small numbers together can lead to numerical underflow.probabilities become so small that they round to zero in floating-point arithmetic. To avoid this, implementations typically work in the log domain, converting multiplications to additions:

Working with log-probabilities prevents underflow and can improve computational efficiency, since addition is faster than multiplication. The algorithm computes the same optimal sequence whether using probabilities or log-probabilities, since the logarithm is a monotonic function that preserves ordering.

Memory requirements are modest. The algorithm needs to store $v_t(j)$ for all states $j$ at the current time step, plus the backpointers for all states at all time steps. For a sequence of length $T$ with $N$ states, this requires $O(T \times N)$ memory, which is typically manageable. In practice, if only the final optimal sequence is needed, backpointers for old time steps can be discarded once they're no longer needed, though this requires more complex bookkeeping.

The algorithm can be parallelized to some extent. Within each time step, computing $v_t(j)$ for different states $j$ can be done in parallel, since these computations are independent. However, the sequential nature of the algorithm.processing time steps in order.limits the overall parallelization. Still, for systems with many states, this intra-timestep parallelism provides significant speedups on modern hardware.