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On Trellis Structure of LUEP Block Codes and a Class of UEP QPSK Block Modulation Codes
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 1994/08/25
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
unequal error protection codes, trellis diagram, coded modulation,
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Recently there has been considerable interest in coded modulation schemes that offer multiple levels of error protection. That is, constructions of (block or convolutional) modulation codes in which signal sequences associated with some message symbols are separated by a squared Euclidean distance that is larger than the minimum squared Euclidean distance (MSED) of the code. In this paper, the trellis structure of linear unequal-error-protection (LUEP) codes is analyzed. First, it is shown that LUEP codes have trellises that can be expressed as a direct product of trellises of subcodes or clouds. This particular trellis structure is a result of the cloud structure of LUEP codes in general. A direct consequence of this property of LUEP codes is that searching for trellises with parallel structure for a block modulation code may be useful not only in analyzing its structure and in simplifying its decoding, but also in determining its UEP capabilities. A basic 3-level 8-PSK block modulation code is analyzed under this new perspective, and shown to offer two levels of error protection. To illustrate the trellis structure of an LUEP code, we analyze a trellis diagram for an extended (64,24) BCH code, which is a two-level LUEP code. Furthermore, we introduce a family of LUEP codes based on the |||-construction, using Reed-Muller (RM) codes as component codes. LUEP codes in this family have the advantage of having a well known trellis structure. Their application in constructing LUEP-QPSK modulation codes is presented, and their error performance over an AWGN channel examined.