Generalized Low-Density Parity-Check coding scheme with Partial-Band Jamming

Abstract

In this study, a class of Generalized Low-Density Parity-Check (GLDPC) codes is designed for data transmission over a Partial-Band Jamming (PBJ) environment. The GLDPC codes are constructed by replacing parity-check code constraints with those of nonsystematic Bose-Chaudhuri-Hocquenghem (BCH), referred to as Low-Density Parity-Check (LDPC)-BCH codes. The rate of an LDPC-BCH code is adjusted by selecting the transmission length of the nonsystematic BCH code, and a low-complexity decoding algorithm based on messagepassing is presented that employs A Posteriori Probability (APP) fast BCH transform for decoding the BCH check nodes at each decoding iteration. Simulation results show that the LDPC-BCH codes with a code rate of 1/8.5 have a bit error rate performance of 1 10 6 at signal-noise-ratios of 6.97 dB, 4.63 dB, and 2.48 dB when the fractions of the band jammed are 30%, 50%, and 70%, respectively.

Generalized sparse codes for non-Gaussian channels: Code design, algorithms, and applications

“…Here, the original sparse code and the adopted algebraic code are referred to as the mother code and the component code, respectively. In this part, we will describe GS codes expanded from BCH code constraints as an example, which are also named low-density BCH-constraint (LDBCH) codes [10] . Note that an LDPC code can be considered as a special case of GS codes by regarding the SPC code as the component code.…”

“…To guarantee that there exists an all-one column in the BCH generator matrix, some post-processing on may be required, as described in Ref. [10] . Also, all the LDPC VNs can connect to other BCNs, while all the degree-1 BCH VNs will only connect to the -th BCN.…”

“…That is to say, includes an all-one column. If is odd, does not include an all-one column, which needs to be adjusted properly according to ref [10] . Thus, the commonly used systematic generator matrices of (7,4), (15,5), (31,6) BCH codes are listed in Eq.…”

“…Nevertheless, existing sparse coding schemes are originally designed to combat Gaussian noise in traditional applications, which cannot be readily applied to many other critical applications with non-Gaussian channels, such as anti-jamming communications [10] , helicopter-satellite communications [11] , and even quantum communications [12] . To this end, channel coding schemes with flexible block-lengths and coding rates are required for these diversified scenarios [13] .…”

“…To this end, channel coding schemes with flexible block-lengths and coding rates are required for these diversified scenarios [13] . In particular, ultra-low-rate channel codes are desired to recover data bits from highly attenuated and interfered transmission signals in extremely harsh electromagnetic environments [10] . Traditionally, concatenated coding aims to generate a powerful lower-rate code by cascading two types of channel codes [14] , [15] .…”