MAPdekodning

MAPdekoding, short for maximum a posteriori decoding, is a method used in digital communications and coding theory to estimate transmitted data from a received signal. The goal is to choose the transmitted sequence that is most probable given what was received, using both the channel model and any prior information about the data.

Formally, MAP decoding selects the transmitted symbol sequence X that maximizes the posterior probability P(X|Y), where Y is the received signal. By Bayes’ rule, P(X|Y) is proportional to P(Y|X) P(X). Thus MAP decoding maximizes P(Y|X) P(X). If the prior P(X) is uniform, MAP decoding reduces to maximum-likelihood decoding. Unlike ML decoding, MAP can exploit nonuniform priors and soft information about the symbols.

MAP decoding is implemented in practice through algorithms that compute or approximate the posterior probabilities for candidate sequences. Notable examples include the BCJR algorithm (forward-backward) for convolutional codes, and sum-product or belief-propagation methods on factor graphs. MAP decoders often provide soft outputs, such as posterior probabilities or log-likelihood ratios, which can be passed to other decoders in iterative schemes (e.g., turbo codes and LDPC codes). While MAP decoding is optimal in a Bayesian sense, it is typically more computationally intensive than ML decoding, especially for long sequences or complex codes, and it requires accurate channel statistics and priors.

MAP decoding is widely used in wireless and data communication systems to achieve improved error performance, particularly in coded systems where soft information and prior knowledge can be leveraged. It remains a foundational concept in modern decoding strategies and Bayesian inference for communications.