Design and analysis of short packet and concatenated coded communication systems.

Abstract

For many wireless communication systems it is important to achieve energy efficient operation with a reasonably small delay. Error control coding is an important component of such a system. One commonly used code is a Reed-Solomon (RS) code. RS codes are widely used as outer codes and concatenated with other codes to enhance system robustness against burst errors. They are also widely used with M-ary modulation. In this case the <italic>M</italic>-ary modulation can be viewed as an inner code. Typically, when an RS code over GF(2<italic><super> m</super></italic>) is used with an M-ary modulation, the number of bits per coded symbol <italic>m</italic> is an integer multiple of log₂(<italic> M</italic>). This limits the number of choices of the number of bits used to represent an RS symbol. If <italic>m</italic> is large, we need to use a large <italic>M</italic> for orthogonal/biorthogonal modulation. This means a large bandwidth/delay. For M-ary phase shift, keying modulation this means a large energy. In this thesis, we provide an analytical method for performance analysis of RS coded systems with arbitrary inner codeword lengths. We derive the bit error performance of RS coded <italic>M</italic>-ary modulation using Markov Chain analysis. We also demonstrate that the bit/packet error performance of RS codes can be improved with the use of interleaver acid iterative decoding. Energy is consumed in the transmitter in order to radiate an appropriate amplitude signal as well as the receiver in processing such signals. Most research ignores the effect of amplifier efficiency, distance between transmitter and receiver and processing power of the receiver. If these factors are considered, coding may deteriorate the error probability. In this thesis, we present a study of the energy analysis of short packet data length by using the cutoff rate and capacity theorem in our investigation. We show that there exists an optimum code rate that achieves a minimum total energy consumed. Using the cutoff rate for in additive white Gaussian noise (AWGN) channel, we derive a closed form expression that approximate the optimum code rate. We also present numerical results using practical coding schemes, using RS codes and convolutional codes.