How does Viterbi decoder work?

The Viterbi decoder examines an entire received sequence of a given length. The decoder computes a metric for each path and makes a decision based on this metric. All paths are followed until two paths converge on one node. Then the path with the higher metric is kept and the one with lower metric is discarded.

Why Viterbi decoding is efficient?

The Viterbi decoding method uses the maximum likelihood decoding (MLD) algorithm, which finds the most likely pattern from the received data, and is known as the optimum decoding method [1]. When erroneous L-bit data are received, the closest codeword is selected using the MLD algorithm.

Which decoding method is used for Viterbi algorithm?

The Viterbi algorithm is based on the Maximum-Likelihood decoding technique. The main purpose of the decoder is to select the code word with the minimum distance between the received signal and the code word. The Viterbi algorithm can use either hard or soft decisions.

What is the time complexity of the Viterbi algorithm?

The time complexity of the Viterbi algorithm is O ( K 2 n ) .

Where is Viterbi decoder used?

The Viterbi decoding algorithm is widely used in the following areas: Radio communication: digital TV (ATSC, QAM, DVB-T, etc.), radio relay, satellite communications, PSK31 digital mode for amateur radio.

Why does Viterbi algorithm work?

The Viterbi algorithm is a dynamic programming algorithm for obtaining the maximum a posteriori probability estimate of the most likely sequence of hidden states—called the Viterbi path—that results in a sequence of observed events, especially in the context of Markov information sources and hidden Markov models (HMM).

What are the limitations of Viterbi decoding?

Limitations. A physical implementation of a viterbi decoder will not yield an exact maximum-likelihood stream due to quantization of the input signal, branch and path metrics, and finite traceback length. Practical implementations do approach within 1dB of the ideal.

What is traceback depth in Viterbi decoder?

The traceback depth influences the decoding delay. The decoding delay is the number of zero symbols that precede the first decoded symbol in the output. For the continuous operating mode, the decoding delay is equal to the number of traceback depth symbols.

Is Viterbi algorithm optimal?

We show that the Viterbi algorithm runtime is optimal up to subpolynomial factors even when the number of distinct observations is small.

Is Viterbi algorithm greedy?

The Viterbi algorithm is not a greedy algorithm. It performs a global optimisation and guarantees to find the most likely state sequence, by exploring all possible state sequences. An example of a greedy algorithm is the one for training a CART.

What do you mean by surviving path of Viterbi decoding?

The Viterbi algorithm computes a metric (the metric of a path is defined as the Hamming distance between the sequence represented by that pat hand the received sequence) for every possible path, and chooses the one with the smallest metric. The paths that are retained are called the survivors.

Where is Viterbi algorithm used?

The algorithm has found universal application in decoding the convolutional codes used in both CDMA and GSM digital cellular, dial-up modems, satellite, deep-space communications, and 802.11 wireless LANs.

What type of decision was used in the Viterbi decoder Simulink model?

The Perform Fixed-Point Hard Decision Viterbi Decoding and Perform Fixed-Point Soft Decision Viterbi Decoding examples configure the Viterbi decoder block to use fixed-point processing for hard- and soft-decision convolutional decoding.

Is Viterbi algorithm dynamic programming?

Is Viterbi algorithm recursive?

Fig. 5 Recursive determination of the shortest path via the Viterbi algorithm. store L(ck+1) and the corresponding survivor S(ck+1). With finite state sequences C the algorithm terminates at time n with the shortest complete path stored as the survivor S(cK).

What is trellis encoding?

Trellis coded modulation (TCM) combines modulation and encoding processes to achieve better efficiency without increasing the bandwidth. Bandwidth-constrained channels operate in the region R / W > 1, where R = data rate and W = bandwidth available.

Why do we use Viterbi algorithm?

The purpose of the Viterbi algorithm is to make an inference based on a trained model and some observed data. It works by asking a question: given the trained parameter matrices and data, what is the choice of states such that the joint probability reaches maximum?

What is a trellis Viterbi?

The Viterbi algorithm finds the maximum-likelihood code sequence x(D) using a diagram called a trellis. In Section 4.1, we saw that a convolutional encoder can be represented by a state diagram. The trellis diagram shows every possible sequence of state transitions of the state diagram.

What are the advantages of trellis codes?

Trellis coding offers a means of increasing data rate without increasing transmitted bandwidth. This is ideally suited to experimental verification. The gain is achieved with multi-level, multi-phase signalling.