🤖 AI Summary
Rate adaptation is required for high-throughput wireless/optical links employing binary modulation, fixed blocklength, and fixed inner-code constraints.
Method: This paper proposes a protograph-based rate-adaptive MacKay-Neal (MN) code design. An outer distribution matcher controls the overall code rate, while an inner coupled protograph LDPC code forms a nonlinear concatenated structure; a multi-channel equivalent communication model is established. Density evolution and shape analysis of the normalized logarithmic asymptotic input–output weight distribution are jointly employed to eliminate error-floor-prone code ensembles during design.
Contribution/Results: The scheme achieves performance within 1 dB of the Shannon limit across a wide code-rate range (0.2–0.9) using only a single LDPC protograph ensemble. It significantly enhances rate flexibility and hardware reusability without compromising error-floor mitigation or throughput efficiency.
📝 Abstract
Rate-adaptive MacKay-Neal (MN) codes based on protographs are analyzed. The code construction employs an outer distribution matcher (DM) to adapt the rate of the scheme. The DM is coupled with an inner protograph-based low-density parity-check (LDPC) code. The performance achievable by the resulting code structure, that is nonlinear, is studied by means of an equivalent communication model that reduces the problem to the analysis of the inner (linear) LDPC code with transmission that takes place in parallel over the communication channel, and over a suitably defined binary symmetric channel. A density evolution analysis of protograph MN code ensembles is outlined, and it is complemented by an error floor analysis that relies on the derivation of the average input-output weight distribution of the inner LDPC code ensemble. Conditions on the shape of the normalized logarithmic asymptotic input-output weight distribution are defined, which allow discarding code ensembles with bad error floor properties during the code design phase. Examples of code designs are provided, showing how the use of a single LDPC code ensemble allows operating within 1 dB from the Shannon limit over a wide range of code rates, where the code rate is selected by tuning the DM parameters. By enabling rate flexibility with a constant blocklength, and with a fixed LDPC code as inner code, the construction provides an appealing solution for very high-throughput wireless (optical) links that employ binary-input modulations.