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On adaptive linear programming decoding of ternary linear codes

In this work, we consider adaptive linear programming (LP) decoding of ternary linear codes, i. e., linear codes over the finite field Fq with q = 3 elements. In particular, we characterize completely the codeword polytope (or the convex hull) of the binary image, under Flanagan's embedding, of a ternary single parity-check code. Then, this characterization is used to develop an efficient adaptive LP decoder for ternary codes. Numerical experiments confirm that this decoder is very efficient compared to a static LP decoder and scales well with both block length and check node degree. Finally, we briefly consider the case of nonbinary codes over the finite field Fq with q = 3m elements, where m > 1 is a positive integer.