A systematic polar encoder with data checks includes a data mapper receiving input data containing information to be polar coded for transmission and generating modified data, and a nonsystematic polar encoder implementing a transform matrix encoding the modified data to produce a codeword x such that, for some sub-sequence of coordinates S, xS=d. For nonsystematic encoding, a transform input u includes first and second parts for words independent of the data, the second part for an inverse puncture word, a third part carrying the modified data, and a non-null part carrying a check word derived from the modified data. A transform output includes a punctured part for a puncture word, a part carrying the data, and a part serving as redundant symbols, with the codeword x related to the transform output by x=zQ where Q is the complement of the punctured part P.