Performance Analysis Of Linear Codes Under Maximum Likelihood Decoding PDF Download

Most coding schemes used in today's communication systems are designed for memoryless channels. These codes break down when they are transmitted over channels with memory, which is in fact what real-world channels look like since errors often occur in bursts. Therefore, these systems employ interleaving to spread the errors so that the channel looks more or less memoryless (for the decoder) at the cost of added delay and complexity. In addition, they fail to exploit the memory of the channel which increases the capacity for a wide class of channels. On the other hand, most channels with memory do not have simple and mathematically tractable models, making the design of suitable channel codes more challenging and possibly not practical. Recently, a new model has been proposed known as the queue-based channel (QBC) which is simple enough for mathematical analysis and complex enough for modeling wireless fading channels. In this work, we examine the performance of linear block codes when transmitted over this channel. We break down our focus into two parts. First, we investigate the maximum likelihood decoding of binary linear block codes over the QBC. Since it is well known that for binary symmetric memoryless channels, maximum likelihood decoding reduces to minimum Hamming distance decoding, our objective here is to explore whether there exists a similar relation between these two decoding schemes when the channel does have memory. We give a partial answer for the case of perfect and quasi perfect codes. Next, we study Reed-Solomon (RS) codes and analyze their performance when transmitted over the QBC under the assumption of bounded distance decoding. In particular, we examine the two interleaving strategies encountered when dealing with non-binary codes over a binary input channel; namely, symbol interleaving and bit interleaving. We compare these two interleaving schemes analytically and show that symbol interleaving always outperforms bit interleaving. Non-interleaved Reed-Solomon codes are also covered. We derive some useful expressions pertaining to the calculation of the probability of codeword error. The performance of non-interleaved RS codes are compared to that of interleaved ones for the simplest scenario of the QBC which is the additive (first-order) Markov noise channel with non-negative noise correlation.