Abstract
We conduct a code search restricted to the recently introduced class of generalized punctured convolutional codes (GPCCs) to find good unequal error protection (UEP) convolutional codes for a prescribed trellis complexity. The trellis complexity is taken to be the number of symbols per information bit in the minimal trellis module for the code. The GPCC class has been shown to possess codes with good distance properties under this decoding complexity measure. New good UEP convolutional codes and their respective effective free distances are tabulated for a variety of code rates and minimal trellis complexities. These codes can be used in several applications that require different levels of protection for their bits, such as the hierarchical digital transmission of video or images.
Highlights
In several applications of digital transmission, the importance of different bits in the input sequence of the channel encoder often varies and certain blocks of this sequence need higher protection level than other blocks, when this sequence is transmitted through a noisy channel
This module consists of one trellis section with 2ν initial states and 2ν final states; each initial state is connected by 2k directed edges to final states, and each edge is labeled with n bits
To illustrate the code search conducted in this work, consider the (4, 3) generalized punctured convolutional codes (GPCCs) with matrix module defined by where only the nonzero rows are shown
Summary
In several applications of digital transmission (e.g., video [1], images [2], voice [3], and data [4]), the importance of different bits in the input sequence of the channel encoder often varies and certain blocks of this sequence need higher protection level than other blocks, when this sequence is transmitted through a noisy channel. The convolutional codes of rate R = k/n with UEP capabilities considered in the literature [8,9,10,11] are represented by their conventional trellis module, denoted by Mconv This module consists of one trellis section with 2ν initial states and 2ν final states; each initial state is connected by 2k directed edges to final states, and each edge is labeled with n bits. The general idea is to have convolutional codes, of different code rates, with different “minimal” (decoding) trellis complexities and different dispositions of error protection levels among the information bits to serve a wide range of applications.
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