Structured low-density parity-check codes over non-binary fields

This paper considers low-density parity-check (LDPC) codes defined over non-binary, finite fields GF(q),q = 2p. We find that the difficulty in constructing q-ary LDPC codes whose Tanner graphs are free of short cycles increases as the order of the field increases. By employing combinatorial designs to devise structured q-ary LDPC codcs with guaranteed minimum girth, we show that significant improvements in performance over binary LDPC codes are possible, particularly in the case of short, or high rate, codes. We present a simple construction for rank deficient q-ary LDPC codes.