Viterbi decoder

A Viterbi decoder uses the Viterbi algorithm for decoding a bitstream that has been encoded using convolutional code or trellis code.

There are other algorithms for decoding a convolutionally encoded stream (for example, the Fano algorithm). The Viterbi algorithm is the most resource-consuming, but it does the maximum likelihood decoding. It is most often used for decoding convolutional codes with constraint lengths k<=10, but values up to k=15 are used in practice.

Viterbi decoding was developed by Andrew J. Viterbi and published in the paper "Error Bounds for Convolutional Codes and an Asymptotically Optimum Decoding Algorithm", IEEE Transactions on Information Theory, Volume IT-13, pages 260-269, in April, 1967.

There are both hardware (in modems) and software implementations of a Viterbi decoder.

A hardware Viterbi decoder for basic (not punctured) code usually consists of the following major blocks:

A branch metric unit's function is to calculate branch metrics, which are normed distances between every possible symbol in the code alphabet, and the received symbol.

There are hard decision and soft decision Viterbi decoders. A hard decision Viterbi decoder receives a simple bitstream on its input, and a Hamming distance is used as a metric. A soft decision Viterbi decoder receives a bitstream containing information about the reliability of each received symbol. For instance, in a 3-bit encoding, this reliability information can be encoded as follows:

Of course, it is not the only way to encode reliability data.

The squared Euclidean distance is used as a metric for soft decision decoders.

A path metric unit summarizes branch metrics to get metrics for $2^{K-1}$ $2^{K-1}$ paths, where K is the constraint length of the code, one of which can eventually be chosen as optimal. Every clock it makes $2^{K-1}$ $2^{K-1}$ decisions, throwing off wittingly nonoptimal paths. The results of these decisions are written to the memory of a traceback unit.

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