CTH08-5: Efficient Encoding and Termination of Low-Density Parity-Check Convolutional Codes

Low-density parity-check convolutional codes (LDPC-CCs) have been shown to have similar capacity-approaching performance to LDPC block codes. Their encoder structure is simple and efficient. However, the encoder termination, which is required when applied to finite length data frames, increases the encoder complexity and reduces the effective code rate. The LDPC-CC encoding and termination problems are discussed in this paper. A novel all-phase termination scheme is proposed with less implementation complexity and less loss in code rate, compared to existing methods. Finally a system architecture for the LDPC-CC encoder with all-phase termination is given with some analyses.

I. Introduction

Low-density parity-check convolutional codes (LDPC-CCs), although less renowned than LDPC block codes (LDPC-BCs), are gradually attracting more attention due to both theoretical studies and implementation efforts. LDPC-CCs were first proposed in [1] as time-varying convolutional codes defined by a low-density parity-check matrix. Using similar iterative message passing decoding algorithms, LDPC-CCs can achieve performance comparable to LDPC-BCs [1]. It has been shown in [2] that the free distance of regular LDPC-CCs increases linearly with their memory, i.e. they are asymptotically good. On the implementation side, LDPC-CC encoders and decoders have very different architectures than LDPC-BCs. The original encoder structure based on shift registers proposed in [1] is very simple compared to the encoder of randomly constructed LDPC-BCs. The iterative decoding of LDPC-CCs can be done through a pipelined architecture [1], [3]. In [4], a few comparisons were carried out and LDPC-CCs have shown comparable performance under the same implementation constraints as LDPC-BCs.