Nonlinear, Nonbinary Cyclic Group Codes
نویسنده
چکیده
New cyclic group codes oflength 2"1 over (m j)-bit symbols are introduced. These codes can be systematically encoded and decoded algebraically. The code rates are very close to Reed-Solomon (RS) codes and are much better than BoseChaudhuri-Hocquenghem (BCH) codes (a former alternative). The binary (m j)tuples are identified with a subgroup of the binary m-tuples which represent the field GF(2m). Encoding is systematic and involves a two-stage procedure consisting of the usual linear feedback register (using the division or check polynomial) and a small table lookup. For low rates, a second shift-register encoding operation may be invoked. Decoding uses the RS error-correctingprocedures for the m-tuple alphabet, i.e., the elements of the field GF(2m). Appendices A and B list (m j)-tuple codes for m = 4, 5, and 6.
منابع مشابه
Nonbinary Quasi-Cyclic LDPC Cycle Codes with Low-Density Systematic Quasi-Cyclic Generator Matrices
In this letter, we propose an appealing class of nonbinary quasi-cyclic low-density parity-check (QC-LDPC) cycle codes. The parity-check matrix is carefully designed such that the corresponding generator matrix has some nice properties: 1) systematic, 2) quasi-cyclic, and 3) sparse, which allows a parallel encoding with low complexity. Simulation results show that the performance of the propose...
متن کاملA Class of Nonbinary Codes and Their Weight Distribution
Nonlinear functions have important applications in coding theory and cryptography [16, 7]. Linear codes constructed from functions with high nonlinearity [17, 11, 2, 6] can be good and have useful applications in communications [9, 19, 10, 18] or cryptography [5, 4, 3, 21]. For a code, its weight distribution is important to study its structure and to provide information on the probability of u...
متن کاملConstructions of new families of nonbinary asymmetric quantum BCH codes and subsystem BCH codes
Two code constructions generating new families of good nonbinary asymmetric quantum BCH codes and good nonbinary subsystem BCH codes are presented in this paper. The first one is derived from q-ary Steane’s enlargement of CSS codes applied to nonnarrow-sense BCH codes. The second one is derived from the method of defining sets of classical cyclic codes. The asymmetric quantum BCH codes and subs...
متن کاملApplication of Nonbinary LDPC Codes for Communication over Fading Channels Using Higher Order Modulations
In this paper, we investigate the application of nonbinary low density parity check (LDPC) codes over Galois field GF(q) for both single-input single-output (SISO) and multipleinput multiple-output (MIMO) fading channels using higher order modulations. As opposed to the widely studied binary systems that employ joint detection and channel decoding, we propose a nonbinary system where optimal si...
متن کاملAn Unnoticed Strong Connection Between Algebraic-Based and Protograph-Based LDPC Codes, Part II: Nonbinary Case and Code Construction
This paper is the second part of a series of two papers on the investigation of the connection between two methods for constructing LDPC codes, namely the superposition and the protograph-based methods. In the first part, by taking the graph point of view, we established a strong connection between these two construction methods and showed that, in the binary case, the protograph-based construc...
متن کامل