A Comparative Performance and Complexity Study of Short-Length LDPC and Turbo Product Codes

This paper presents a comparative performance and complexity study between low-density parity-check (LDPC) codes and turbo product codes (TPC) of short block length (within 2048 bits). The LDPC codes are of the semi-random (SR) type, characterized by low encoder complexity, and are further optimized by eliminating short cycles of length 4 (minimum girth 6). The TPC codes are obtained from 2D and 3D constructions chosen to match the LDPC codes´ parameters. The numerical results show that the SR-LDPC codes have slightly better error performance (to within 0.5dB at a BER of 10^-5 while demonstrating lower computational complexity per decoder iteration but the required number of decoding iterations is larger. However, this disadvantage is significantly reduced for moderately high signal-to-noise ratios (starting from 2.5dB). It is therefore concluded that SR-LDPC codes have a more competitive performance-complexity advantage overall