Matryoshka Globally-Coupled LDPC Code
Hao Liu, Qi‐Yue Yu · IEEE Transactions on Communications · 2023
This paper proposes a new low-density parity-check (LDPC) code called Matryoshka globally-coupled (MGC) LDPC code. We give the definition of$N$-fold MGC-LDPC code which consists of$N$layers Matryoshka-style codes, i.e.,$\mathcal {C}_{\mathrm {mgc}}\left ({1}\right), \mathcal {C}_{\mathrm {mgc}}\left ({2}\right),\ldots,\mathcal {C}_{\mathrm {mgc}}\left ({N}\right)$. Moreover, the$N$Matryoshka-style codes can form a Matryoshka chain$\mathcal {C}_{\mathrm {mgc}}\left ({1}\right) \prec \mathcal {C}_{\mathrm {mgc}}\left ({2}\right) \prec \cdots \prec \mathcal {C}_{\mathrm {mgc}}\left ({N}\right)$, which indicates that a high-layer Matryoshka-style code contains a low-layer Matryoshka-style code just like the Matryoshka dolls. Thus, the proposed$N$-fold MGC-LDPC code naturally has rate-compatible feature. Based on the superposition (SP) construction, we present truncating and masking methods to construct the base matrices (BMs) of MGC-LDPC codes. More importantly, we introduce the double lower triangular (DLT) form of parity-check matrix for further developing a recursive encoding scheme for MGC-LDPC codes. With the help of the proposed encoding scheme, the local codes of MGC-LDPC code can be independently encoded, and the$n$th layer Matryoshka-style codeword can be recursively obtained by the$\left ({n - 1}\right)$th layer Matryoshka-style code and the local codes in$n$th layer Matryoshka-style code for$2 \leq n \leq N$. Simulations show that MGC-LDPC codes can perform well over both the additive white Gaussian noise channel (AWGNC) and binary erasure channel (BEC), and provide a flexible rate-compatible feature to satisfy the requirements of different scenarios.