Analysis on nonuniform channels and LDPC codes in the finite block length regime

Abstract

One of the main purposes of communication systems is the reliable convey of information through a noisy and distorted channel in the spatial or time domains. In 1943, Shannon defined the channel capacity as the maximum information transfer rate per channel use in the infinite block length regime. After that, much of research has been done in order to implement the communication systems which approach the channel capacity. In order to mitigate the channel distortion, the various channel coding schemes can be used from the classical codes to the modern channel codes. Usually, the practical communication systems experience the nonuniform channels, but the many portions of the characteristics of the nonuniform channel have not yet been reported. If the features of the nonuniform channels are revealed, then the corresponding channel coding methods can be analyzed and designed. Therefore, in this thesis, the properties of the nonuniform channels and the corresponding channel codes are investigated.

In order to compare the performances of communication systems, channel capacity has been used as a figure of merit. However, channel capacity is too ideal to measure the performance of practical systems since channel capacity requires infinite block length. In this thesis, the achievable rate and outage rate are used as the performance metrics for the practical communication systems. In the nonuniform channels with the finite block length codes, there are three kinds of channel coding strategies: the separate coding, interleaved coding and joint coding. All these methods have the same capacity, but the achievable rates and outage rates of them are different because the achievable rate and the outage rate are the functions of the channel dispersion value as well as the channel capacity. Even though the separate coding scheme outperforms, it can be prohibited in the practical communication systems due to complex multiple encoder/decoder pairs and the long latency of signal...