Block Markov Encoding & Decoding

Various Markov encoding and decoding techniques are often proposed for specific channels, e.g., the multi-access channel (MAC) with feedback, the relay channel, the MAC with cribbing encoders [1], [2], [3]. The goal of this report is to summarize the basic ideas of some block Markov coding techniques and present them using two simple channels, namely the point-to-point channel and the relay channel. Transmission using block Markov coding operates over a number of blocks. In each block, with the exception of the first or the last block, a new message is sent. However, the codeword to send at each block depends on not only “fresh” information but also “past” information from one or more previous blocks. Hence the name “Markov encoding”. The information from previous blocks can be refined information for the previous message or cooperative information for other users, etc. At the receiver, since the channel output at each block is related with messages from previous blocks, different decoding schemes have been proposed. The rest of this summary is organized as follows. Section II discusses the application of Markov coding in the point-to-point, discrete memoryless channel (DMC). Block Markov coding is unnecessarily complicated for a simple point-to-point DMC, but studying this setting allows for a simplified treatment of the scheme’s mechanics. To illustrate the benefits of block Markov coding in multi-user information theory, Section III applies block Markov coding techniques to prove an achievable rate for the relay channel. Section IV concludes the paper.