Protograph based LDPC codes with minimum distance linearly growing with block size

Abstract

We propose several LDPC code constructions that simultaneously achieve good threshold and error floor performance. Minimum distance is shown to grow linearly with block size (similar to regular codes of variable degree at least 3) by considering ensemble average weight enumerators. Our constructions are based on projected graph, or protograph, structures that support high-speed decoder implementations. As with irregular ensembles, our constructions are sensitive to the proportion of degree-2 variable nodes. A code with too few such nodes tends to have an iterative decoding threshold that is far from the capacity threshold. A code with too many such nodes tends to not exhibit a minimum distance that grows linearly in block length. In this paper we also show that precoding can be used to lower the threshold of regular LDPC codes. The decoding thresholds of the proposed codes, which have linearly increasing minimum distance in block size, outperform that of regular LDPC codes. Furthermore, a family of low to high rate codes, with thresholds that adhere closely to their respective channel capacity thresholds, is presented. Simulation results for a few example codes show that the proposed codes have low error floors as well as good threshold SNR performance.

LDPC codes from voltage graphs

“…In an entirely different context, various researchers have looked at constructing families of LDPC codes by taking random lifts of a specially chosen base graph, or "protograph", yielding the so-called "protograph codes" [24], [6], [7], [19]. The idea exploited in these constructions is that the properties of the base graph may shed light on the properties of the covering graphs, and therefore on the resulting codes.…”

Deriving Good LDPC Convolutional Codes from LDPC Block Codes

“…In this section we briefly discuss some other graph-coverbased LDPC code constructions proposed in the literature, namely by Ivkovic et al [44], by Divsalar et al [43], [45], by Lentmaier et al [46], [47], and by Kudekar et al [48].…”

“…Namely, in terms of our notation, Ivkovic et al [44] start with a parity-check matrix H, choose the set L {0, 1}, a collection of zero-one matrices [43], [45] is the so-called rate-1/2 AR4JA LDPC code construction, which was also considered earlier in Example 19. A particularly attractive, from an implementation perspective, version of this code construction is obtained by an iterated graph-cover construction procedure, where each graph-cover construction is based on a cyclic cover, as in the application of GCC1 in Example 4.…”

Spatially Coupled Protograph-Based LDPC Codes for Decode-and-Forward in Erasure Relay Channel

“…Achievable erasure probability region of accumulate repeat jagged accumulate (ARJA) code [22] with split-extension technique [17]. The black dashed line represents the theoretical limit Eq.…”