Coding and information theory is at the heart of modern communication and computer technologies. Shannon’s seminal work shows that you can transmit bits on a noisy channel using code, and the probability of error can be made arbitrarily small provided the code rate is less than the channel capacity [1]. Since this work, many researchers have tried to construct codes close to channel capacity. However, despite so many efforts, none were able to construct codes that achieve channel capacity (capacity-approaching codes are known). In 2009, in a remarkable work, Arikan invented such codes using the idea of channel polarization [2]. In his original paper, his work was restricted to binary input memoryless channels; it was later extended to other channels. The importance of this work is clear: the original paper has been cited more than 1100 times and more than 26 patents refer to it.

The present book (in five chapters, including a reference and index) describes the basics of polar coding. Usually, polar code construction is done recursively in three parts: code construction (for parameters), encoding, and decoding. Chapter 1 introduces information theory from the perspective of polar codes, including the general idea of recursive code construction. Chapter 2 focuses on the recursive decoding (known as successive cancellation decoding) of polar codes on binary erasure channels (BECs). The polarization of BECs is discussed in detail in chapter 3. Chapter 4 provides mathematical descriptions of polar codes and channels. Finally, chapter 5 focuses its attention on performance and polarization rate.

The book is easy to read. It has numerous examples and exercise problems and hence can be used as a textbook on polar codes. I recommend it to engineers who want to learn about these powerful codes. An analysis of these codes with respect to decoding low-density parity-check (LDPC) codes and so on could be a useful addition (which is missing). However, the book is still useful for many senior undergraduate and graduate students. I enjoyed reading the book.