Unequal Message Protection: Asymptotic and Non-Asymptotic Tradeoffs

Abstract

We study a form of unequal error protection that we term "unequal message protection" (UMP). The message set of a UMP code is a union of m disjoint message classes. Each class has its own error protection requirement, with some classes needing better error protection than others. We analyze the tradeoff between rates of message classes and the levels of error protection of these codes. We demonstrate that there is a clear performance loss compared to homogeneous (classical) codes with equivalent parameters. This is in sharp contrast to previous literature that considers UMP codes. To obtain our results we generalize finite block length achievability and converse bounds due to Polyanskiy-Poor-Verdú. We evaluate our bounds for the binary symmetric and binary erasure channels, and analyze the asymptotic characteristic of the bounds in the fixed error and moderate deviations regimes. In addition, we consider two questions related to the practical construction of UMP codes. First, we study a "header" construction that prefixes the message class into a header followed by data protection using a standard homogeneous code. We show that, in general, this construction is not optimal at finite block lengths. We further demonstrate that our main UMP achievability bound can be obtained using coset codes, which suggests a path to implementation of tractable UMP codes.

Second-order coding rate for m-class source-channel codes

“…In fact, [11] shows a stronger result for m scaling in n. In the setting of this paper m is fixed. The log 1 n,i will turn out to be negligible asymptotically.…”

“…The m-class approach also decomposes the problem of source-channel coding into two problems: source partitioning and UMP coding. As shown in [11], UMP codes can be constructed from linear codes, and their decoding complexity scales in m. In other words, the problem of m-class sourcechannel coding is closely tied to UMP coding, and there is a path towards practical implementation of both.…”

“…Second-order coding rate results for the problem of UMP were derived in [5] as a step towards the JSCC dispersion. In [11] the problem of UMP was analyzed via single-shot bounds, as well as dispersion and moderate deviation asymptotic analysis. Additional work on UMP was previously done by BoradeNakiboglu-Zheng [12], Wang-Ingber-Kochman [5], and NazerShkel-Draper [13].…”

“…As such, there is hope for characterizing the third order term of m-class source-channel codes as well. Another asymptotic question of interest is the behavior of mclass source-channel codes in the regime were m is allowed to scale in n. In that set up the more refined results of [11] may prove to be helpful. Finally, much of the normal approximation analysis cited here has been extended to Markov sources and Markov channels [8], [18].…”

The Dispersion of Mismatched Joint Source-Channel Coding for Arbitrary Sources and Additive Channels

“…System model of our NN-JSCC scheme which consists of an encoder f which uses modified minimum distance encoding in(8) and a decoder φ which uses modified nearest neighbor (NN) decoding in(9).…”