Low complexity soft demapping for non-binary LDPC codes

Abstract

This article focuses on non-binary wireless transmission, where "non-binary" refers to the use of non-binary Low Density Parity Check (LDPC) codes for Forward Error Correction. The complexity of the non-binary soft demapper is addressed in particular when one non-binary Galois Field (GF) symbol spreads across multiple Quadrature Amplitude Modulation (QAM) symbols and Space-Time Block Code (STBC) codewords. A strategy is devised to guarantee an efficient mapping at the transmitter, together with an algorithm at the receiver for low complexity soft Maximum Likelihood demapping. The proposed solution targets a trade-off between performance and complexity, and removes any restriction on the setting of the GF order, QAM constellation order, and STBC scheme. This makes the non-binary LDPC codes even more appealing for potential use in practical wireless communication systems.

Multi-non-binary turbo codes

“…But, due to the evolution of the processing capacity, it is expected that the complexity of non-binary codes to no longer pose a disadvantage in relation to binary codes. This is confirmed by the extensive studies of NB-LDPC codes, [13][14][15][16][17].…”

“…For (16) to be a compatible system, uniquely determined, it is necessary and sufficient to insert K = M redundant symbols.…”

“…The matrix Equation 16 should be regarded as a system of M scalar equations on GF(2 Q ), where the unknowns are redundant symbols u N , …, u N+K−1 with parameters the entries of s N . For (16) to be a compatible system, uniquely determined, it is necessary and sufficient to insert K = M redundant symbols.…”