High rate adaptive LDPC codes with short memory for better data reliability
Design of a Family of Rate-Adaptive LDPC Convolutional Codes with Short Constraint Length
Information Theory
Summary
Communication systems need codes to detect and correct errors in transmitted data. This paper presents a way to design special error-correcting codes called LDPC convolutional codes that can adjust their rate and have short memory to simplify processing. The authors use mathematical tools called Golomb rulers to build these codes while avoiding certain problems in their decoding structure. Their designs ensure good error correction performance and flexibility in how much data is sent versus how much quality is guaranteed.
What this means in practice
- •For wireless communication engineers: Design adaptive channel coding schemes with efficient decoding and variable data rates for dynamic wireless networks.
- •For satellite communication system designers: Implement rate-adaptive error correction codes with low decoding complexity suitable for limited hardware on satellites.
Authors
Massimo Battaglioni, Edoardo Carnevali, Franco Chiaraluce, Marco Baldi, Giovanni Cancellieri
Abstract
This paper studies the design of some high-rate, adaptive, low-density parity-check (LDPC) convolutional codes with short constraint length, based on interleaved parity-check polynomials. Starting from some known results regarding the selection of polynomials that yield codes free of short cycles in the associated Tanner graphs, we propose some new constructions based on Golomb rulers, along with relaxed variants that do not strictly satisfy the Golomb ruler condition, but retain similar structural properties. The result is a family of rate-adaptive code constructions with code rates of the form $R=(n_0-1)/n_0$. Conditions for the absence of length-4 cycles are derived, together with upper bounds on the free distance that are met in all considered examples.