Effective Trellis Decoding Techniques for Block Codes

The trellis and tree diagrams of a code provide a highly structured combinatorial representation of the code as a graph. This permits the soft-decision (SD) decoding of the code by mapping the received sequence of values from the channel onto the branches of the graph and computing the likelihood of each path so formed by means of an additive function of the (estimated) channel, called the metric. The extra information provided by the SD decoding is equivalent to around 2 dB of gain in the signal-to-noise ratio when compared to hard-decision decoding for an additive white Gaussian noise channel. Graph-decoding techniques have traditionally been restrained to convolutional codes, giving them the primacy over the block codes, whose algebraic SD decoding algorithms [4] resulted much more complex in comparison. However, there are many applications, such as mobile radio communications, where block codes are advantageous, because they avoid error propagation problems and they can be well matched to the characteristics of the information source and the channel.