On Low-density Parity-check Codes For Broadband Digital Communication Systems

Low-density parity-check codes, as a family of Shannon-limit approaching error-correction codes, have been a hot research spot in coding theory over the years. With the advent of the new century, the theoretical foundation is gradually perfected and more novel code structures are proposed, and this kind of codes have been adopted by many standard communication systems. As the applicable scenario multiplies, LDPC codes are faced with more and more challenges arising from grounds of practical uti-lization.This dissertation will focus on four practical aspects of LDPC codes, which are code design, improvement of decoding algorithm, code shortening and the issue of combination with high-order modulations. The details are summarized as follows. Firstly, a code design method is proposed, which is based on the combinatorial struc-ture of lines and points over lattice plane. The code constructed by this method con-forms well to the required degree distribution pair, and has a compact structure easy to be described. Moreover, by column and row permutation the constructed parity-check matrix can be converted into quasi-cyclic form, which facilitates parallel encoding and decoding. Two codes are constructed by use of the proposed method in accordance to the length and rate of DVB_C2/T2/S2 and DTMB standards. Simulation results show that the designed codes possess better BER and FER performance than the standard codes. Secondly, a modified BP algorithm is proposed. By examining the innate drawbacks of conventional BP algorithm, a multiplying factor is introduced to atten-uate the sign-flipped extrinsic messages emitted from the check nodes. As a result, the fluctuation in number of erroneous bits with decoding iteration is contained, and thus the probability of decoding convergence is increased. In addition, this modifi-cation can be applied to the joint-row-and-column BP decoding. Simulation results show that the performance is improved for both conventional and JRC BP algorithms. Thirdly, an LDPC code shortening algorithm is proposed inspired by the peeling de-coder over bipartite graph. The criteria are discussed concerning the selection and deletion of candidate information nodes, by which the efficiency of the algorithm can be increased and the threshold of the residual code can be lowered. By use of the proposed algorithm, the LDPC codes of DTMB standard are shortened ensuring low decoding thresholds with lowered code rates. Simulation shows consistent results with the predicted improvement of thresholds. Finally, a coded modulation scheme called bit-mapping is proposed, which exploits the UEP property of high-order modulation and the irregularity of LDPC codes. Density evolution can be applied to optimize the bit-mapping polynomials ensuring the decoding threshold. In this setting, the DTMB LDPC coded modulation is optimized, and lower decoding thresholds are achieved than those of the default sequential mapping. Simulation results verifies that the actual improvement in BER is in consistency with the numerical results.