Art of constructing low-complexity encoders/decoders for constrained block codes

Abstract

Suppose we are given a block code, that is, a list of at least 2p q-bit self-concatenable codewords. A rate p : q block encoder is a dataword-to-codeword assignment from 2p p-bit datawords to 2p q-bit codewords, and the corresponding block decoder is the inverse of the encoder. We propose efficient heuristic computer algorithms (i) to eliminate the excess codewords; and (ii) to construct low hardware complexity block encoders/decoders. Constructing low-complexity encoder/decoders for very high rate codes is of immense economical value-as these codes may be implemented in mass-market magnetic recording systems. For several practical constraints, block encoders/decoders generated using the proposed algorithms are comparable in complexity to human-generated encoders/decoders, but are significantly simpler than lexicographical encoders/decoders.