A coding scheme that increases the code rate

Abstract

Codes having higher information rates are desirable, since a higher rate code implies a more efficient use of redundancy than a lower rate code. However, when choosing a code for a particular application, we must also consider the error-correcting capabilities of the code. There is a basic trade-off between code rate andminimum distance. The smaller the code rate, the larger is the minimum distance and vice-versa. This paper proposes a simple coding scheme that can construct a code with higher information rate from an existing code. First, the paper derives a low-rate C (n , k , d )-code from an existing C(n, k, d)-code, where kn ≥ k n . An associated decoding procedure for the newly derived class of low-rate codes is also described. Finally, the proposed coding scheme combines C and a set of C s to obtain a C (n , k , d )-code with k n ≥ kn ≥ k n . Kronecker product is used as a basic tool in the coding procedure.