Abstract:

Variable-rate low-density parity-check (LDPC) codes are one class of codes with various code rates and play an important role in most communication systems.Two representatives of such codes are multi-rate LDPC (MR-LDPC) codes with a constant codeword length and rate-compatible LDPC codes with a constant information length.Combining algebraic and superposition construction methods,this paper studies the design and construction of the Raptor-like multi-rate quasi-cyclic LDPC codes by progressively adjusting the lifting sizes for different code rates.Based on the proposed method,with the decrease in code rate,the sizes of the base matrix and exponent matrix of the constructed codes become large while the lifting sizes are reduced.Besides,to achieve a constant codeword length and various information lengths,both shortening of information bits and puncturing of parity bits are considered.Resulting codes simultaneously own quasi-cyclic and Raptor-like structures,so that the corresponding encoder/decoder can be easily implemented by hardware and the encoding can also be done directly based on the parity-check matrix.Moreover,exponent matrices of the constructed codes have a specific algebraic structure,and thus the storage complexity is very low.Numerical results show that,compared to some standard codes,e.g.,WiMAX LDPC codes,the constructed codes can obtain a better overall performance,which can provide a promising scheme for the coding method fusion design of the future ground network and other communication systems.

Key words: low-density parity-check codes, Raptor-like, multi-rate, algebraic construction