Which forward error correction code is commonly decoded with the Viterbi algorithm to find the most likely transmitted bit sequence?

Which forward error correction code is commonly decoded with the Viterbi algorithm to find the most likely transmitted bit sequence?

• A. Hamming code
• B. Reed-Solomon code
• C. Convolutional code
• D. Shannon limit

Answer: (C)

The key idea here is that the Viterbi algorithm is designed to find the most likely transmitted sequence when the encoder introduces memory, creating a stateful, trellis representation of the code. Convolutional codes achieve this memory by feeding the input bits through shift registers, so each output bit depends on several consecutive input bits. The Viterbi algorithm works through the trellis by evaluating branch metrics (how likely a transition is given the received symbols) and keeping only the best path to each state as it progresses. At the end, the survivor paths are traced back to yield the most likely entire transmitted bit sequence. This Maximum Likelihood Sequence Estimation is exactly what Viterbi does efficiently for convolutional codes, making it the standard pairing. Hamming codes are block codes decoded with syndrome checks and simple bit flips, not using a trellis or sequence-based estimation. Reed-Solomon codes are block codes over finite fields decoded with algebraic methods, not the Viterbi approach. Shannon limit refers to a channel capacity bound, not a specific decoding technique or code. So, the code most commonly decoded with the Viterbi algorithm to recover the transmitted bit sequence is the convolutional code.

The key idea here is that the Viterbi algorithm is designed to find the most likely transmitted sequence when the encoder introduces memory, creating a stateful, trellis representation of the code. Convolutional codes achieve this memory by feeding the input bits through shift registers, so each output bit depends on several consecutive input bits. The Viterbi algorithm works through the trellis by evaluating branch metrics (how likely a transition is given the received symbols) and keeping only the best path to each state as it progresses. At the end, the survivor paths are traced back to yield the most likely entire transmitted bit sequence. This Maximum Likelihood Sequence Estimation is exactly what Viterbi does efficiently for convolutional codes, making it the standard pairing.

Hamming codes are block codes decoded with syndrome checks and simple bit flips, not using a trellis or sequence-based estimation. Reed-Solomon codes are block codes over finite fields decoded with algebraic methods, not the Viterbi approach. Shannon limit refers to a channel capacity bound, not a specific decoding technique or code.

So, the code most commonly decoded with the Viterbi algorithm to recover the transmitted bit sequence is the convolutional code.