Construction of structured low density lattice codes based on finite fields

Abstract

Finite fields were successfully used to construct algebraic low-density parity-check (LDPC) codes, especially Quasi-Cyclic LDPC codes. These LDPC codes with large minimum distances have lower error floor, linear complexity of encoding and are more practical for hard-decision algebraic decoding. In this paper, we show that finite fields can also be successfully used to construct algebraic low-density lattice codes (LDLC), denoted by structured LDLC. A general framework to construct algebraic LDLC is presented. LDLC constructed by this general framework have comparable performance to the corresponding random codes over addition white Gaussian noise (AWGN) channel with iterative soft-decision decoding in terms of symbol-error probability. Furthermore, the general framework is extended to complex low-density lattice codes (CLDLC) and results in algebraic CLDLC which perform very well for small dimensions.