Multiple-rate error-correcting coding scheme.

Error-correcting codes that can effectively encode and decode messages of distinct lengths while maintaining a constant blocklength are considered. It is known conventionally that a k-dimensional block code of length n defined over GF (q n) is designed to encode a k-symbol user data in to an n-length codeword, resulting in a fixed-rate coding. In contrast, considering q = p λ , this paper proposes two coding procedures (for the cases of λ = k and λ = n ) each deriving a multiple-rate code from existing channel codes defined over a composite field GF (q n) . Formally, the proposed coding schemes employ λ codes C 1 (λ , 1) , C 2 (λ , 2) , ... , C λ (λ , λ) defined over GF (q) to encode user messages of distinct lengths and incorporate variable-rate feature. Unlike traditional block codes, the derived multiple-rate codes of fixed blocklength n can be used to encode and decode user messages m of distinct lengths | m | = 1 , 2 , ... , k , k + 1 , ... , k n , thereby supporting a range of information rates—inclusive of the code rates 1 / n 2 , 2 / n 2 , ... , k / n 2 and 1 / n , 2 / n , ... , k / n ! A simple decoding procedure to the derived multiple-rate code is also given; in that, orthogonal projectors are employed for the identification of encoded user messages of variable length. [ABSTRACT FROM AUTHOR]