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Review: Finite Fields for Computer Scientists and Engineers June 17, 2011

Posted by flashbuzzer in Research.
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I recently finished “Finite Fields for Computer Scientists and Engineers” by R.J. McEliece. I originally used this book for a course taught by Dr. McEliece in the Winter 2002-03 quarter.

This book has two reviews on Amazon, so I hope to provide some additional insights for people who are considering obtaining the book.

In this book, the author presents the theory of finite fields with an eye towards their application in the design of communication systems. He begins by introducing the concept of a Euclidean domain along with the familiar – yet vital – construct of Euclid’s algorithm, which he then uses to show how primes can be uniquely factored in a Euclidean domain. With these results in hand, he shows how Euclidean domains can be used to construct fields, which forms a nice transition to the book’s core material: a discussion of the properties of finite fields, including existence and uniqueness, and how these properties can be used to factor polynomials over these fields. The rest of the book forms a set of advanced topics that draw on these fundamental concepts, including

  • the notion of the trace (relative to a subfield)
  • properties of linear recurrences over finite fields
  • the fundamentals of m-sequences and their cross-correlation properties.

The author skillfully motivates and presents the central results of this book. Indeed, his self-deprecating writing style triggered many fond memories from my days as an undergrad, as I took three courses from him. Somehow the author pulls off the difficult balancing act of presenting mathematically challenging material without truly sacrificing mathematical rigor, which is quite remarkable. The book also contains several fascinating concepts that I enjoyed learning, including Euler’s phi function, the Mobius inversion formula and the Chevalley-Warning theorem.

One aspect of the book that I did find to be a bit bothersome, though, was that each chapter was not divided into separate sections. In my opinion, this would have improved the flow of the book and provided many helpful “signposts” for the reader, especially while studying a rather lengthy chapter. More often than not I would be shown a result, eventually understand the proof, and then be unsure as to its importance in the context of the chapter in question.

Overall I would strongly recommend this book to those who want a gentle introduction to finite fields while gaining a healthy appreciation for their theoretical underpinnings.


Review: Space-Time Block Coding for Wireless Communications December 19, 2010

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I recently finished Space-Time Block Coding for Wireless Communications by E.G. Larsson and P. Stoica. I originally used this book for a course taught by my advisor in the Fall 2005 semester.

This book only has one review on Amazon, so I hope that my thoughts will be useful for people who are considering obtaining the book.

In this book, the authors introduce the fundamental concepts of multi-input multi-output (MIMO) wireless communications and space-time block coding (STBC), and they show how STBC can significantly improve the performance of MIMO systems in many ways. They begin by presenting the tools that are necessary for a thorough understanding of MIMO systems, including channel modeling, information theory and error probability analysis. They then recap the familiar concept of receive diversity and use it to motivate the breakthrough concept of transmit diversity, which leads to the introduction of STBC. The rest of the book is a compendium of advanced topics for STBC, including coding for ISI channels, the design of coherent/non-coherent STBC receivers, coding for transmitters with partial/full CSI, and coding in the presence of interference.

The authors do a fantastic job of presenting and teaching fundamental concepts to the reader. A painstaking amount of effort is made to hammer home key points and build the right level of intuition. In particular, the authors set the tone for the remainder of the book in Chapter 1 by presenting a simple example that considers 2×1 and 1×2 systems; moreover, the book contains numerous examples of systems that employ one or two transmit/receive antennas, which is invaluable in terms of enhancing the learning process. The book is also well-organized; to wit, the authors present several theorems and results in Chapters 4 (“Error Probability Analysis”) and 7 (“Linear STBC for Flat Fading Channels”). By constantly referring to results in these two chapters, it is clear that they are meant to serve as a focal point for understanding the rest of the book. In addition, the authors have put a great deal of effort into generating performance plots; they are properly labeled, and the various curves in each plot are easy to distinguish.

It should be noted that the authors engage in some degree of self-promotion in the book, especially in the latter chapters (9-11); in my view, this detracts (albeit slightly) from its quality. Now it should also be noted that such self-promotion is difficult to avoid, especially when discussing a (relatively) nascent research area in which the authors have obtained many of the major results. A more balanced approach to describing these concepts would have been in order, though. In particular, the authors should have more fully elucidated the drawbacks of using OSTBC in MIMO systems, in order to not perpetuate the impression that OSTBC are the “best choice” in terms of transmit-side strategies. Also, the book has only four errata listed on this page, though I am quite certain that the book has more than four errata. In addition, the book relies heavily on a thorough understanding of matrix analysis; at this point I’m not aware of a good textbook on that topic, though. For those who would cite the text by Horn and Johnson, my thought is that it is more of a reference book than an actual teaching tool.

Overall I would strongly recommend this book to those who want to gain a more solid understanding of MIMO systems and the role that STBC can play in terms of improving their performance.

Review: The Double Helix – A Personal Account of the Discovery of The Structure of DNA November 9, 2010

Posted by flashbuzzer in Books, Science.
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I recently finished The Double Helix – A Personal Account of the Discovery of The Structure of DNA by James D. Watson.

This book has already been thoroughly reviewed on Amazon, but I figured that I would add my two cents to the ongoing discussion.

In this book, the author presents his recollection of the events that culminated in the discovery of the structure of DNA. In particular, he describes his tenure as a researcher at Cambridge and discusses the fine points of working with his most famous collaborator, Francis Crick. Besides Crick, the reader is introduced to other prominent post-World War II DNA researchers, including Linus Pauling, Maurice Wilkins and Rosalind Franklin.

I enjoyed the fact that the author pulled off the difficult balancing act of 1) continuously referring to concepts from biochemistry while 2) keeping the book accessible to non-scientists. I hadn’t taken any biology courses since my freshman year of college, so it was helpful to get a refresher on DNA biochemistry. I also enjoyed how the author described the various misguided approaches that he and Crick pursued, especially their hypothesis that the nitrogenous base pairs resided on the exterior of the DNA structure while the sugar-phosphate backbone resided on its interior. Based on my experiences, I can attest to the fact that every research breakthrough is accompanied by a litany of failures. In addition, the descriptions of the “rivalry” between the Crick-Watson collaboration at Cambridge and 1) the Wilkins-Franklin group at King’s College London and 2) the Pauling group at Caltech were enlightening. As expected, I had never heard these stories in my biology courses.

In terms of quibbles, the author’s depiction of Rosalind Franklin left me wishing that she had not passed away before writing her own perspective on the discovery of DNA. In this book, Franklin comes across as a brilliant yet stubborn, prideful, closed-minded researcher. The author attempts to paint a more agreeable picture of Franklin in the epilogue, but this fails to compensate for the picture that has been painted in the first 29 chapters of the book. It would have been interesting and enlightening to read Franklin’s thoughts on arguably the most significant scientific breakthrough of the 20th Century, especially if sexism influenced the portrayal of her actions towards Watson, Crick and Wilkins.

Overall, I would recommend this book to those who are interested in a blow-by-blow account of the discovery of the structure of DNA and desire 1) a refresher on the underlying concepts from biochemistry and 2) an expose of the interpersonal dynamics among researchers that is typically avoided in biology curricula.

Review: Surviving Paradise – One Year on a Disappearing Island July 4, 2010

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I recently finished Surviving Paradise – One Year on a Disappearing Island by Peter Rudiak-Gould. Peter happens to be one of my friends from high school, and we competed together on our school’s Science Bowl team.

This book has already been thoroughly reviewed on Amazon, but I figured that I would add my two cents to the ongoing discussion.

In this book, the author focuses on the year that he spent as a volunteer English instructor for WorldTeach on the Marshall Islands. In particular, he details his adventures on Ujae Atoll, where his school was located, and in the capital city of Majuro. He methodically recounts a variety of experiences that he had on this Pacific island nation, including his struggles with teaching unruly and unmotivated students, his baptism by fire in learning how to speak Marshallese, and even his triumphs and failures in terms of spearfishing.

As noted by other reviewers, the author does an excellent job of keeping this book from being a run-of-the-mill travel narrative along the lines of “instead of me changing them, they changed me.” In particular, at several points the author notes that while he has learned a great deal from his experiences in the Marshall Islands, he retains a deep appreciation for Western culture and would not willingly surrender the privileges of being an American. The author also shows an attention to detail that figuratively transports the reader to Ujae, especially his unflattering take on Marshallese food staples including breadfruit, pandanus and bwiro. In addition, the writing is marked by a mirthful, self-deprecating tone that greatly enhances the reading experience. I had been relatively unfamiliar with the Marshall Islands before picking up this book, and the plethora of hilarity was invaluable in helping me to absorb the presented information.

My only quibble with this book concerns the subtitle. Based on the subtitle, the reader would think that the specter of global warming would loom large; instead, it only explicitly rears its head in the epilogue, which describes the author’s return to Ujae to conduct fieldwork related to his graduate studies. It would have been better to either remove the subtitle or modify it to be more consistent with the theme of the author’s initial stay on Ujae.

Overall, I would recommend this book to those who are either interested in visiting the Marshall Islands, desire to learn more about a truly fascinating island nation and/or just want to read a lively, entertaining and truly atypical travel narrative.

Review: Introduction to Space-Time Wireless Communications January 25, 2010

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I recently finished Introduction to Space-Time Wireless Communications by A. Paulraj, R. Nabar and D. Gore. I originally used this book for a course taught by my advisor in the Fall 2005 semester. On a (possibly) related note, savvy Internet denizens will discover that Paulraj is my “academic grandfather.”

This book has already been reviewed (some would say “thoroughly castigated”) on Amazon, so I’ll just contribute some of my observations and hope that they provide some additional data points for people who are considering obtaining the book.

I had a conversation regarding this book with one of my former research group-mates that proved to be enlightening. He encouraged me to re-read the preface, where the authors state, “this area of technology has grown so large in the past few years that this book cannot cover all aspects in moderate detail. Rather, our aim has been to provide a coherent overview of the key advances in this field emphasizing basic theory and intuition. We have attempted to keep the presentation as simple as possible without sacrificing accuracy.”

When I viewed the book in this light, I was able to tolerate the first eight chapters, which appear to be (mostly) presented at the stated level of detail. In those first eight chapters, the authors do a reasonable job of presenting (without much in the way of rigorous proofs, as expected) fundamental concepts including space-time channel modeling, space-time channel capacity and space-time coding. They even cover a somewhat advanced topic, transmit-side precoding, at a reasonable level.

In my opinion, the book really “goes off the rails” in the last four chapters, which make a half-hearted attempt at presenting more advanced topics including MIMO-OFDM, the MIMO MAC/BC channels and the (much celebrated) diversity-multiplexing tradeoff. Unfortunately, this degrades the cohesion of the book and even left me with a sour taste in my mouth as I finished the last section. Various results were presented without even a modicum of intuition or insight, including the entire chapter on space-time co-channel interference mitigation, which suffered from lazy and uninspired writing (note that interference is a critical issue in multi-antenna wireless networks).

Overall, I would recommend this book to “graduate students in wireless communications” and “wireless designers in industry” (as noted in the text) with the following caveats. Readers would be advised to focus only on the first eight chapters and become familiar with their basic results. After achieving this goal, they should employ a variety of methods to gain deep intuition and insight on all of the material in the text, including reading through the relevant references, attempting to re-derive the key results, and discussing them with motivated colleagues. For example, I should note that I acquired a much better understanding of the diversity-multiplexing tradeoff after an extensive whiteboard-aided discussion with one of my former research group-mates.

Perhaps a more hard-hitting (and well-written) book on space-time wireless communications is in the works (heh heh).