Low-density parity-check codes unequal error protection and reduction of clipping effects

Abstract: The invention of low-density parity-check (LDPC) codes made reliable communication possible at transmission rates very close to the theoretical limit predicted by Shannon. However, communication close to the Shannon limit requires very long codes and results in long delay and high encoder and decoder complexity. In many communication scenarios, constraints on delay, complexity and power prohibit communication with arbitrarily low error probability. To achieve good performance it is then important that the code is appropriately matched to the other parts of the communication system. In this thesis, LDPC codes for two different communication scenarios are studied. A common scenario is communication of information bits with unequal importance for the perceptual quality after source decoding. This is the case for example in many networks and for transport of multimedia data, where one frame may consist of a header, some payload and additional payload for increased quality. Errors in the header data may cause the whole frame to be useless, while errors in the additional payload generally cause only a small quality reduction. A code with unequal error protection (UEP) is designed to protect some bits more than others, thus providing a reduced bit-error rate (BER) for the important bits. This work studies design of LDPC codes with UEP capability for bandwidth-efficient higher order constellations. A flexible design algorithm for irregular UEP-LDPC codes is proposed, which is applicable to arbitrary signal constellations, an arbitrary number of classes of bits with different importance and arbitrary sizes of the classes. Simulations using 8-PSK modulation show that the overall BER is reduced if codes are properly designed for the modulation scheme, compared to the BER achieved by standard UEP codes designed for BPSK modulation. Codes designed by the proposed algorithm also provide more UEP capability, especially at high SNR. Moreover, further work shows that the UEP capability of an irregular LDPC code is not only dependent on the variable node degrees as is widely believed. The LDPC construction algorithms, that place the edges in the graph according to the degree distributions, also play a critical role for the UEP behavior of an LDPC code. The differences in UEP capability are explained by introduction of detailed check node degree distributions that describe differences in the code structure. LDPC codes for the orthogonal frequency division multiplexing (OFDM) system are also studied. OFDM enables simple equalization and has been adopted in several standards. However, OFDM is sensitive to frequency-selective fading and introduces a large peak-to-average power ratio (PAPR) of the transmitted signal. These problems can be alleviated by pre-multiplying the OFDM block with a spreading matrix that both reduces the PAPR of the transmitted signal and increases the frequency diversity. Simulation of an OFDM system with clipping shows that the performance gain by spreading is substantial also when an LDPC code, which on its own improves the performance significantly, is applied to the OFDM system. PAPR reduction may also be achieved by deliberate clipping of the signal, prior to the transmitter high-power amplifier. Clipping will however introduce losses and receiver methods to mitigate such clipping losses are investigated. We consider Bayesian estimation of the unclipped signal as well as statistical characterization of the clipping distortion, that is fed to the LDPC decoder. The results show that for an LDPC coded OFDM system, the improvement by these clipping mitigation methods is minimal.