Algebraic and Stochastic Coding Theory (Hardcover)

Using a simple yet rigorous approach, Algebraic and Stochastic Coding Theory makes the subject of coding theory easy to understand for readers with a thorough knowledge of digital arithmetic, Boolean and modern algebra, and probability theory. It explains the underlying principles of coding theory and offers a clear, detailed description of each code. More advanced readers will appreciate its coverage of recent developments in coding theory and stochastic processes.

After a brief review of coding history and Boolean algebra, the book introduces linear codes, including Hamming and Golay codes. It then examines codes based on the Galois field theory as well as their application in BCH and especially the Reed–Solomon codes that have been used for error correction of data transmissions in space missions.

The major outlook in coding theory seems to be geared toward stochastic processes, and this book takes a bold step in this direction. As research focuses on error correction and recovery of erasures, the book discusses belief propagation and distributions. It examines the low-density parity-check and erasure codes that have opened up new approaches to improve wide-area network data transmission. It also describes modern codes, such as the Luby transform and Raptor codes, that are enabling new directions in high-speed transmission of very large data to multiple users.

This robust, self-contained text fully explains coding problems, illustrating them with more than 200 examples. Combining theory and computational techniques, it will appeal not only to students but also to industry professionals, researchers, and academics in areas such as coding theory and signal and image processing.

《代數和隨機編碼理論》以簡單而嚴謹的方法，使編碼理論對於具有深入了解數位算術、布林和現代代數以及概率論的讀者來說易於理解。它解釋了編碼理論的基本原理，並對每個編碼進行了清晰而詳細的描述。更進一步的讀者將欣賞到它對編碼理論和隨機過程的最新發展的涵蓋。

在簡要回顧編碼歷史和布林代數之後，本書介紹了線性編碼，包括漢明碼和高雷碼。然後它檢查了基於伽羅瓦場理論的編碼以及它們在BCH和特別是Reed-Solomon編碼中的應用，這些編碼已被用於太空任務中的數據傳輸錯誤修正。

編碼理論的主要展望似乎是針對隨機過程，而本書在這方面迈出了大膽的一步。隨著研究集中在錯誤修正和擦除恢復上，本書討論了信念傳播和分佈。它檢查了低密度奇偶校驗碼和擦除碼，這些編碼開辟了改善廣域網絡數據傳輸的新途徑。它還描述了現代編碼，如Luby轉換和Raptor編碼，這些編碼使大量數據高速傳輸到多個用戶成為可能。

這本內容豐富、自成一體的教材完全解釋了編碼問題，並通過200多個例子加以說明。結合理論和計算技術，它不僅適合學生，也適合行業專業人士、研究人員和編碼理論、信號和圖像處理等領域的學者。