Design of Rate-Compatible Irregular LDPC Codes Based on Edge Growth and Parity Splitting

The design of rate-compatible protograph LDPC codes

“…for HARQ applications. Several works in the literature design irregular LDPC rate-compatible codes using puncturing and code extension [2], [3], [5], [9], [14] in a manner that requires painstaking optimization and furthermore their encoders are unstructured therefore computationally complex. Our design avoids the weaknesses of puncturing by using a code extension approach.…”

“…Code extension starts with a highrate code (a daughter code), then lower rate codes are obtained by extending the parity check matrix of the daughter code [5], [9], [14], [15]. Most existing extension-based LDPC codes [5], [9], [14] are designed as rate-compatible irregular LDPC codes with highly optimized framework and unstructured design that does not promote low-complexity encoding. In contrast, the proposed rate-compatible protograph-based codes can achieve very good thresholds with low encoding complexity allowed by circulant permutations [11], [16].…”

Rate-compatible LDPC convolutional codes for capacity-approaching hybrid ARQ

“…3. Check submatrix extension of a rate-compatible LDPC convolutional code family (see as well [6], [7], [10] for block LDPC codes).…”

“…In [2]- [6], for example, higher rate codes are obtained by puncturing a low-rate mother code; however, these codes suffer from a suboptimal performance [2]. Graph extension is applied in e.g., [6], [7], where a high-rate base code is progressively extended to codes of lower rates. The drawback in [6], [7] is that an irregular degree distribution needs to be optimized for each rate.…”

“…Graph extension is applied in e.g., [6], [7], where a high-rate base code is progressively extended to codes of lower rates. The drawback in [6], [7] is that an irregular degree distribution needs to be optimized for each rate. Rate-compatible protograph-based LDPC codes were considered in [8]- [10].…”