Low density parity check coding

Abstract

This thesis explores the properties of the family of Low Density Parity Check Codes (LDPCC). In addition to Gallager's original binary regular LDPCCs, the class of irregular LDPCCs and non-binary LDPCCs developed from the binary regular LDPCC is also studied. Further, a novel reliability ratio based bit flipping decoding algorithm is proposed for providing a low-complexity decoding solution. A novel three-layer iterative decoding scheme is also designed for the symbol-based joint decoding of non-binary LDPCC aided space-time coding operating at a low complexity. Furthermore, classic binary LDPCCs have been concatenated with both space time coding and source coding schemes for the sake of enhancing the achievable system performance. Gallager's binary regular LDPCCs achieve a near-capacity performance, while maintaining a relatively low decoding complexity. Furthermore, Gallager suggested that the family of LDPCCs exhibits good distant properties, provided that certain Parity Check Ivlatrix (PClvI) construction constraints are satisfied. A novel LDPC Block Coded Modulation (LDPC-BCM) scheme was proposed, which was shown to outperform the Turbo Trellis Coded Ivlodulation (TTCM) ba..~ed benchmark scheme by 1.5 dB at a BER of 10-5 , when communicating over an uncorrelated Rayleigh fading channel using QPSK modulation, while maintaining an effective throughput of 1 bit per symbol. Rather than assigning each message node or check node in the PCM a constant weight, the class of irregular LDPCCs constructs the PCl\l using a pre-determined density profile, i.e. provides a non uniform weight distribution. This approach may introduce weight-two message nodes into the PCM, which can result in less attractive distance properties for the code, potentially resulting in an error floor. Hence, a technique referred to as Yang's method is invoked for reducing this potential error floor, while still benefiting from the irregular construction of the PCM. We found that the employment of Richardson's PCM construction approach is more feasible applications, which are not delay sensitive, while Yang's approach is more attractive in applications having a moderate coded block length, especially at high coding rates. Davey and MacKay further developed the family of LDPCCs in order to create non-binary LDPC codes. The advantage of non-binary LDPCCs is that they may achieve a reduced probability of incurring short cycles in the PCM in comparison to the LDPCCs having an equivalent binary PCM. However, non-binary LDPCCs do not always perform better than binary LDPCCs. The choice of the decoding field, column weight and also the coding rate will affect the attainable performance of non-binary LDPCCs. We have applied these non-binary LDPCCs to design a purely symbol-based joint decoding and demodula tion aided transmit diversity scheme, which is capable of exploiting the soft information generated by the LDPC decoder by re-evaluating the soft channel output provided by the demodulator. Upon employing non-binary LDPCCs defined over the Galois field GF(q) chosen according to the specific modulation scheme used, the proposed non-binary-LDPCC aided transmit diversity scheme achieved a coding gain of nearly 2dB at a BER

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