Low-density parity-check (LDPC) codes with power reallocation

Abstract

In this thesis, we consider the power reallocation problem in regular low-density parity-check (LDPC) codes. In general, certain number of errors that are within the correction capability of a code can be corrected regardless of the received signal-to-noise ratio (SNR) for those erroneous symbols. This motivates to redistribute the power resource among the code symbols in such a way to minimize the post-decoding error probability. We allocate no power to the symbols experiencing a less favorable channel (e.g. low channel gain) and allocate more power to the remaining symbols to make them received with a higher reliability. We consider three conventional power reallocation schemes such as truncated fixed transmission, truncated channel inversion, and water-pouring. For each three schemes, we find the optimal cut-off threshold that minimizes the required ${\bar E}_b/N_0$ for error-free communications for rate-1/2 and rate-1/4 regular LDPC codes. Both analytical and simulation results show that the truncated channel inversion provides the best performance and the water-pouring provides the worst performance among the three schemes. Then, we propose a generalized power reallocation scheme where the previous three conventional schemes can be considered as a special case. The analytical and simulation results show that the generalized power reallocation provides a power gain of 0.2 dB over the truncated channel inversion and 1.8 dB over the equal power allocation.