Systematic Low Density Parity Check Codes with Hard Decision Message Passing Algorithm for Non-binary Symbols

This paper proposes the use of systematic LDPC codes for hard decision Message Passing (hMP), which is a predecoder to Vector Symbol Decoding (VSD) for non-binary codes. VSD is a verification-based decoder whose outputs are decoded code words. LDPC are randomly generated and by nature, they are non-systematic codes. Using systematic instead of non-systematic codes allows the decoder to obtain the decoded data directly without a troublesome mapping step. In the simulations, 15 regular parity check matrices H are randomly generated and converted to their systematic forms. Results in a Gilbert-Elliot 2-state fading channel model with 6 different channel conditions show that hMP prefers codes with lower- weight H. For column weight of 9 bits and row weight of 18 bits, systematic H have lower weight after row operation and are better than the non-systematic ones for all channel conditions.