EE Seminar: Puncturing, Expurgating and Expanding the q-ary BCH Based Robust Codes
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Speaker: Nir Admaty
M.Sc. student under the supervision of Prof. Simon Litsyn
Wednesday, June 1st, 2016 at 15:30
Room 011, Kitot Bldg., Faculty of Engineering
Puncturing, Expurgating and Expanding the q-ary BCH Based Robust Codes
Abstract
A code that can detect errors with high probability is called a security oriented code. A security oriented code that can detect any non-zero error is called robust. A BCH based robust code is a code that is based on the columns of the check matrix of a linear BCH code. The non-binary BCH based robust code is derived from the one-error-correcting BCH code. The binary BCH based robust code is derived from the two-error-correcting BCH code. The undetected error probability Q(e) of an error e is determined by the set of codewords that mask e. The maximal error masking probability is denoted by Q ̅. A robust code is said to be optimum if there is no other code with a larger number of codewords with the same length and the same Q ̅.
The thesis presents four constructions for optimum and nearly optimum robust codes that are based on modifications of the BCH based robust codes. In particular, they generalize, puncture, expurgate, and expand the codes while preserving their robustness.
The generalized codes are a class of codes from which the BCH based code is derived. When puncturing, u redundancy symbols are deleted from the code. When expurgating, codewords which have the same value in u predefined redundancy symbol positions are grouped together and these u redundancy symbols are deleted. When expanding, a new robust code is constructed by fusing two robust codes.
The generalized and punctured codes have Q ̅ which is a power of q (the field alphabet size), and the expurgated and expanded code have Q ̅ which is not a power of q. The generalized code has a fixed code rate which is half. However, the other three constructions can increase the robust BCH based code rate while preserving its robustness.
