A new concept of /spl lambda/-order orthogonalization, and a general threshold decoding method is introduced. Many codes decodable using general threshold decoding can be constructed and are superior in performance to other majority-logic decodable codes.
In the search for multiple-error-correcting codes which can be easily and rapidly decoded, some coding theorists have turned their attentions to threshold (majority logic) decoding. Much work has been done in this area recently, and quite a few classes of new codes suitable for threshold decoding have been developed. The main desirable feature of majority logic decoding is that it can be very simply implemented. Furthermore majority decoding can also automatically correct many more patterns of errors other than those guaranteed by the decoding schemes without any additional equipment. This paper is a survey of the L-step majority decoding.
The attractiveness of majority-logic decoding is its simple implementation. Several classes of majority-logic decodable block codes have been discovered for the past two decades. In this paper, a method of constructing a new class of majority-logic decodable block codes is presented. Each code in this class is formed by combining majority-logic decodable codes of shorter lengths. A procedure for orthogonalizing codes of this class is formulated. For each code, a lower bound on the number of correctable errors with majority-logic decoding is obtained. An upper bound on the number of orthogonalization steps for decoding each code is derived. Several majority-logic decodable codes that have more information digits than the Reed-Muller codes of the same length and the same minimum distance are found. Some results presented in this paper are extensions of the results of Lin and Weldon [11] and Gore [12] on the majority-logic decoding of direct product codes.
Abstract Soft decision decoding is a decoding method which tries to improve the error‐correcting capability by utilizing the information concerning the reliability of the received symbol. One of the soft decision decoding methods for practically useful block code, is APP (a posteriori probability) decoding applicable to the majority‐logic de‐codable code. In APP decoding, the error is decided for each symbol as in majority‐logic decoding. This paper proposes a new decoding method (variable threshold APP decoding), in which the error‐correcting capability is improved by controlling the order of error decisions in APP decoding. the performance is evaluated by simulation. As a result, it is shown that the variable threshold APP decoding exhibits better characteristics than APP decoding and approximate APP decoding both in bit error rate and block error rate. When, for example, the proposed decoding is applied to (73, 45) difference set cyclic code, a coding gain of 1.0 dB is obtained compared with the approximate APP decoding. In the proposed decoding method, the time required for decoding is increased, while the hardware scale is almost the same as that of the approximate APP decoding.