Joint encoding and decoding methods for improving the error rate performance are described. In one aspect, the systems and methods determine values and positions of L desired symbols. In encoding unit receives data symbols for encoding. The encoding unit calculates, responsive to receiving the data symbols, values and positions of H help symbols. The encoding unit inserts the help symbols into the data symbols at respective help symbols positions, thereby generating new data symbols. Encoding unit encodes the new data symbols to produce a codeword C′ that contains the L desired symbols. The codeword C′ is communicated to a decoder that is instructed to explore some or all L desired symbols in C′.