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In this paper, we give lower bounds on the size of $(a,b)$ elementary trapping sets (ETSs) of variable-regular LDPC codes with any girth, $g$ , and irregular ones with girth 8, where $a$ is the size and $b$ is the number of degree-one check nodes. Our proposed lower bounds are analytical, applicable to all values of $g$ and $b$ , based on graph theories and tighter than the existing ones in the literature. Our results mostly depend on the girth. We also propose results, which are independent of the girth and rely on the variables $a$ , $b$ , $\gamma $ , and the column weight value. We obtain the tightest lower bounds on the size of ETSs of variable-regular LDPC codes with girth eight. These results provide us with a chance to present a method to achieve the minimum size of ETSs of irregular LDPC codes with girth, especially those whose column weight values are a subset of {2, 3, 4, 5, 6} and fulfill the inequality $(b/a)<1$. Moreover, we present a range of numerical results about $(a,b)$ ETSs with girths 8 and 10 to compare the tightness between our proposed lower bounds and the existing bounds in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we deal with time-invariant spatially coupled low-density parity-check convolutional codes (SC-LDPC-CCs). Classic design approaches usually start from quasi-cyclic low-density parity-check block codes and exploit suitable unwrapping procedures to obtain SC-LDPC-CCs. We show that the direct design of the SC-LDPC-CCs syndrome former matrix or, equivalently, the symbolic parity-check matrix, leads to codes with smaller syndrome former constraint lengths with respect to the best solutions available in the literature. We provide theoretical lower bounds on the syndrome former constraint length for the most relevant families of SC-LDPC-CCs, under constraints on the minimum length of cycles in their Tanner graphs. We also propose new code design techniques that approach or achieve such theoretical limits. [ABSTRACT FROM PUBLISHER]

In this paper, we focus on the construction of a type of quasi-cyclic low-density-parity-check (QC LDPC) codes called cycle codes. Based on our previous work, the maximum cycle entropy (MCE) algorithm for constructing nonbinary LDPC codes can be extended to its QC form (QC-MCE), which maintains the QC structure of the parity-check matrix. With this method employed, an elegant distribution of nonzero entries over the Galois field GF(q) can be obtained among the cycles whose length is related to the girth. Thus, the independence of probabilistic information transferred during decoding is increased, leading to a better performance. Extensive simulation results show that the proposed QC-MCE algorithm behaves much better than the conventional random one and performs as well as the existing method over a pattern media channel with both additive white Gaussian noise (AWGN) and transition jitter noise (TJN). The decoding complexity of our proposed codes is reasonably low due to the QC structure of the codes. The codes constructed with the proposed method can be well applied over the patterned media storage. [ABSTRACT FROM AUTHOR]