A Survey on Protograph LDPC Codes and Their Applications

Abstract

Low-density parity-check (LDPC) codes have attracted much attention in the past two decades since they can asymptotically approach the Shannon capacity in a variety of data transmission and storage scenarios. As a type of promising structured LDPC codes, the protograph LDPC codes not only inherit the advantage of conventional LDPC codes, i.e., excellent error performance, but also possess simple representations to realize fast encoding and efficient decoding. This paper provides a comprehensive survey on the state-of-the-art in protograph LDPC code design and analysis for different channel conditions, including the additive white Gaussian noise (AWGN) channels, fading channels, partial response (PR) channels, and Poisson pulse-position modulation (PPM) channels. Moreover, the applications of protograph LDPC codes to joint sourceand-channel coding (JSCC) and joint channel-and-physical-layernetwork coding (JCPNC) are reviewed and studied. In particular, we focus our attention on the encoding design and assume the decoder is implemented by the belief propagation (BP) algorithm. Hopefully, this survey may facilitate the research in this area.

Improved read/write cost tradeoff in DNA-based data storage using LDPC codes

“…Irregular LDPC codes can achieve performance closer to capacity but need some fixes to achieve good finite block length performance. Protograph LDPC codes [3] offer the best of both worlds but require some tuning to find the best protograph for the channel at hand. In this work, we use regular LDPC codes for simplicity.…”

Analysis and Optimization of Tail-Biting Spatially Coupled Protograph LDPC Codes for BICM-ID Systems

“…A protograph, which has been proposed in [12], [52], can be represented by a small Tanner graph [52] G = (V, C, E) consisting of three different sets, i.e., a variable-node (VN) set V, a check-node (CN) set C, and an edge set E. The cardinalities of V, C, and E equal n p , m p , and E, respectively. For a protograph, each edge e i,j ∈ E connects a VN v j ∈ V with a CN c i ∈ C, and parallel edges are allowed since they can be thoroughly eliminated during an expansion procedure.…”

Protograph LDPC codes for STBC Rayleigh fading channels

“…To begin with, we briefly review the definition of protograph code [11]. A protograph can be seen as a Tanner graph with a relatively small number of nodes.…”

“…Consequently, quasi-cyclic LDPC (QC-LDPC) codes which can realize low-complexity encoding have been applied in multiple-antenna systems [10]. As a novel class of LDPC codes, protograph (LDPC) codes [11] have also attained much attention since it can produce outstanding performance with even lower complexity. Later, the accumulate repeat accumulate (ARA) code and accumulated repeat by-4-jagged accumulate (AR4JA) code, which possess simple protograph structures to realize linear encoding and decoding, have been proposed by Jet Propulsion Laboratory (JPL) [12], [13].…”