arXiv subjects

Adeel Mahmood

Publications and source records attributed to Adeel Mahmood.

8 recordsLinked to original sources

arXiv2026

Lossy Joint Source-Channel Coding over Unknown Channels

We analyze the performance of joint source-channel codes in an unknown-channel framework, where the true channel is unknown but the source distribution is known. We derive achievability bounds for a family of mismatched-design joint source-channel codes constructed for a design channel $Q_{Y|X}$ and operated over a possibly different true channel $P_{Y|X}$. Our one-shot achievability bound allows for standard Borel alphabets for the source, reproduction, channel input and channel output. The subsequent block coding result based on the normal approximation applies to stationary memoryless sources and memoryless, possibly nonstationary channels under regularity and moment conditions. The achievability bound is given in terms of the rate-distortion and rate-dispersion functions, as well as two channel-dependent quantities that we call the mismatched-design rate and mismatched-design rate-dispersion. We use a family of Gibbs posteriors parameterized by a single scalar as decoder-side kernels, and the envelope of the corresponding achievable rates recovers the generalized mutual information. In the stationary matched setting covered by our assumptions, our result recovers the achievability part of Kostina and Verd\'u's 2013 Gaussian approximation result and improves its third-order term. We also formalize a notion of a second-order universal family of source-channel codes under which there is no first- or second-order asymptotic penalty. We then construct two channel-blind families of source-channel codes: one that is second-order universal over a regular class of nonstationary block erasure channels and another that is second-order universal over stationary Gaussian channels. Our code construction uses Poisson functional representations of suitable conditional probability measures to produce the encoder and decoder outputs.

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arXiv2026

Weighted Unequal Error Protection over a Rayleigh Fading Channel

We study a variant of unequal error protection in channel coding, where the message bit string is divided into a finite number of blocks and the maximization objective is a weighted sum of per-block decoding success probabilities. The channel model is quasi-static Rayleigh fading with channel state information available to the receiver but unavailable to the transmitter. We analyze the asymptotic and finite blocklength performance of two achievability schemes, one based on power-domain superposition (PDS) and another based on orthogonal resource allocation (ORA), also known as time-sharing. Upper bounds on the optimal number of blocks to transmit are derived. Algorithms to compute the optimal power and time splits for the two schemes are given. Simplified algorithms to compute locally optimal power and time splits are also given. Our results show that PDS outperforms ORA, but the performance differential is less than 2% in both the asymptotic and finite blocklength regimes (Figures 4 - 6). For both PDS and ORA, numerical results also upper bound the gap between the asymptotic and finite blocklength performance by approximately 10% for n = 1000 and 3% for n = 5000 (Figures 7 - 10).

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arXiv2025

Channel Coding for Gaussian Channels with Multifaceted Power Constraints

Through refined asymptotic analysis based on the normal approximation, we study how higher-order coding performance depends on the mean power as well as on finer statistics of the input power. We introduce a multifaceted power model in which the expectation of an arbitrary (but finite) number of arbitrary functions of the normalized average power is constrained. The framework generalizes existing models, recovering the standard maximal and expected power constraints and the recent mean and variance constraint as special cases. Under certain growth and continuity assumptions on the functions, our main theorem gives an exact characterization of the minimum average error probability for Gaussian channels as a function of the first- and second-order coding rates. The converse proof reduces the code design problem to minimization over a compact (under the Prokhorov metric) set of probability distributions, characterizes the extreme points of this set and invokes the Bauer's maximization principle. Our results for the multifaceted power model serve as more precise benchmarks for practical modulation schemes with multiple amplitude levels, probabilistic shaping and nonuniform constellation geometries.

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arXiv2025

Channel Coding for Gaussian Channels with Mean and Variance Constraints

We consider channel coding for Gaussian channels with the recently introduced mean and variance cost constraints. Through matching converse and achievability bounds, we characterize the optimal first- and second-order performance. The main technical contribution of this paper is an achievability scheme which uses random codewords drawn from a mixture of three uniform distributions on $(n-1)$-spheres of radii $R_1, R_2$ and $R_3$, where $R_i = O(\sqrt{n})$ and $|R_i - R_j| = O(1)$. To analyze such a mixture distribution, we prove a lemma giving a uniform $O(\log n)$ bound, which holds with high probability, on the log ratio of the output distributions $Q_i^{cc}$ and $Q_j^{cc}$, where $Q_i^{cc}$ is induced by a random channel input uniformly distributed on an $(n-1)$-sphere of radius $R_i$. To facilitate the application of the usual central limit theorem, we also give a uniform $O(\log n)$ bound, which holds with high probability, on the log ratio of the output distributions $Q_i^{cc}$ and $Q^*_i$, where $Q_i^*$ is induced by a random channel input with i.i.d. components.

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arXiv2024

Improved Channel Coding Performance Through Cost Variability

Channel coding for discrete memoryless channels (DMCs) with mean and variance cost constraints has been recently introduced. We show that there is an improvement in coding performance due to cost variability, both with and without feedback. We demonstrate this improvement over the traditional almost-sure (per-codeword) cost constraint that prohibits any cost variation above a fixed threshold. Our result simultaneously shows that feedback does not improve the second-order coding rate of simple-dispersion DMCs under the almost-sure cost constraint. This finding parallels similar results for unconstrained simple-dispersion DMCs, additive white Gaussian noise (AWGN) channels and parallel Gaussian channels.

cs.IT↗

arXiv2024

Channel Coding with Mean and Variance Cost Constraints

We consider channel coding for discrete memoryless channels (DMCs) with a novel cost constraint that constrains both the mean and the variance of the cost of the codewords. We show that the maximum (asymptotically) achievable rate under the new cost formulation is equal to the capacity-cost function; in particular, the strong converse holds. We further characterize the optimal second-order coding rate of these cost-constrained codes; in particular, the optimal second-order coding rate is finite. We then show that the second-order coding performance is strictly improved with feedback using a new variation of timid/bold coding, significantly broadening the applicability of timid/bold coding schemes from unconstrained compound-dispersion channels to all cost-constrained channels. Equivalent results on the minimum average probability of error are also given.

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arXiv2022

Minimax Rate-Distortion

We show the existence of variable-rate rate-distortion codes that meet the disortion constraint almost surely and are minimax, i.e., strongly, universal with respect to an unknown source distribution and a distortion measure that is revealed only to the encoder and only at runtime. If we only require minimax universality with respect to the source distribution and not the distortion measure, then we provide an achievable $\tilde{O}(1/\sqrt{n})$ redundancy rate, which we show is optimal. This is in contrast to prior work on universal lossy compression, which provides $O(\log n/n)$ redundancy guarantees for weakly universal codes under various regularity conditions. We show that either eliminating the regularity conditions or upgrading to strong universality while keeping these regularity conditions entails an inevitable increase in the redundancy to $\tilde{O}(1/\sqrt{n})$. Our construction involves random coding with non-i.i.d.\ codewords and a zero-rate uncoded transmission scheme. The proof uses exact asymptotics from large deviations, acceptance-rejection sampling, and the VC dimension of distortion measures.

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arXiv2022

Lossy Compression with Universal Distortion

We consider a novel variant of $d$-semifaithful lossy coding in which the distortion measure is revealed only to the encoder and only at run-time, as well as an extension of it in which the distortion constraint $d$ is also revealed at run-time. Two forms of rate redundancy are used to analyze the performance, and achievability results of both a pointwise and minimax nature are demonstrated. The first coding scheme uses ideas from VC dimension and growth functions, the second uses appropriate quantization of the space of distortion measures, and the third relies on a random coding argument.

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