Analysis of Check-Node Merging Decoding for Punctured LDPC Codes with Dual-Diagonal Parity Structure

In this paper, the authors propose new decoding scheme of punctured LDPC codes with dual-diagonal parity structure by merging check nodes connected to the punctured parity nodes. This check-node merging decoding not only needs smaller number of operations at each iteration but also shows faster decoding convergence speed than the conventional erasure decoding. For the binary erasure channel (BEC) and AWGN channel, the authors analyze and compare the check-node merging and the conventional erasure decoding schemes of the punctured LDPC codes with dual-diagonal parity structure using density evolution. Analytical results show that the check-node merging decoding gives faster convergence speed for both BEC and AWGN channel. Also, simulation results are provided to confirm the analytical results.

I. Introduction

In 1996, low-density parity-check (LDPC) codes, originally invented by Gallager [1], were rediscovered by MacKay and Neal [2]. Since then, LDPC codes have been the main research topic because they show the capacity approaching performance with feasible decoding complexity [3]. However, one drawback of LDPC codes is that the encoding complexity is quadratic in the code length, which results in slow encoding. Therefore, efficient encoding algorithms have been proposed [4] and various fast-encodable codes were proposed [5], [6], [7]. Most of the fast-encodable LDPC codes contain the dual-diagonal parity structure, i.e., accumulator, which produces degree-2 parity nodes. We will call such codes as LDPC codes with dual-diagonal parity structure.