The A* algorithm for decoding linear block codes is an efficient tree-search method for decoding short linear block codes. The information contained in the parity bits are potentially useful for reducing the edges needed in the tree search. We propose to extract the information embedded in the parity bits by considering sums of parity bits which can be decided by part of the message bits. Analysis for the number of required message bits for obtaining sums of parity bits is provided. The information contained in the parity bits can help to reduce the number of search tree edges.

In this paper, we investigate the soft iterative decoding technique for ternary recoding systems with run-length-limited (RLL) constraints. We employ a simple binary-to-ternary RLL encoder following the LDPC (low density parity check) encoder. In the decoder, the iteratively passing of soft information between the LDPC decoder and a detector is used, where the detector is constructed for a combination of the RLL encoder, PLM (pulse length modulation) precoder and the partial response channel. We provide two different decoding algorithms. For one of the decoding algorithm, we are able to obtain bit-error-rate performance which is inferior to the comparable system without considering the RLL constraint for the high sign-to-noise ratio (SNR) regime and is better for the low-to-moderate SNR regime.