Some results on linear unequal-error-protection codes specified by their generator matrix

Abstract

There are many applications in which it is required to design a code that protects messages against different levels of noise (or messages with different levels of importance over a noise stable channel). Examples of such situations are: broadcast channels, multi-user channels, and PCM digital telemetry systems, among others. A code that offers multiple levels of error protection is called an unequal-error-protection (UEP) code. In this paper, the UEP capabilities of certain classes of linear codes, obtained by combining shorter linear codes, are investigated. Linear UEP (LUEP) codes based on generator matrices of shorter codes were considered previously in [1], for the case of the \(\left| {\bar u\left| {\bar u + \bar v} \right.} \right|\)construction of MacWilliams and Sloane [3]. In this paper, we examine linear codes obtained from combining shorter codes using the more interesting constructions X and X4 of Sloane et al. [2]. Both construction X and construction X4 use cosets of a subcode in a linear code as building blocks, and constitute generalizations to the \(\left| {\bar u\left| {\bar u + \bar v} \right.} \right|\)construction. We provide specific examples of families of codes obtained from construction X, using very simple component codes, which yield good LUEP codes. Furthermore, we discuss two-stage decoding methods for LUEP codes obtained using these constructions. Finally, we present the alternative of using an LUEP code as one of the component codes in construction X. An example shows that in this way optimal LUEP codes may be constructed.