arXiv subjects

Rajlaxmi Pandey

Publications and source records attributed to Rajlaxmi Pandey.

4 recordsLinked to original sources

arXiv2026

Function-Correcting Codes with Optimal Data Protection for Hamming Code Membership

This paper investigates single-error-correcting function-correcting codes (SEFCCs) for the Hamming code membership function (HCMF), which indicates whether a vector in $\mathbb{F}_2^7$ belongs to the [7,4,3]-Hamming code. Necessary and sufficient conditions for valid parity assignments are established in terms of distance constraints between codewords and their nearest non-codewords. It is shown that the Hamming-distance-3 relations among Hamming codewords induce a bipartite graph, a fundamental geometric property that is exploited to develop a systematic SEFCC construction. By deriving a tight upper bound on the sum of pairwise distances, we prove that the proposed bipartite construction uniquely achieves the maximum sum-distance, the largest possible minimum distance of 2, and the minimum number of distance-2 codeword pairs. Consequently, for the HCMF SEFCC problem, sum-distance maximisation is not merely heuristic-it exactly enforces the optimal distance-spectrum properties relevant to error probability. Simulation results over AWGN channels with soft-decision decoding confirm that the resulting max-sum SEFCCs provide significantly improved data protection and Bit Error Rate (BER) performance compared to arbitrary valid assignments.

cs.IT↗

arXiv2026

Function Correcting Codes for Maximally-Unbalanced Boolean Functions

Function-Correcting Codes (FCCs) enable reliable computation of a function of a $k$-bit message over noisy channels without requiring full message recovery. In this work, we study optimal single-error correcting FCCs (SEFCCs) for maximally-unbalanced Boolean functions, where $k$ denotes the message length and $t$ denotes the error-correction capability. We analyze the structure of optimal SEFCC constructions through their associated codeword distance matrices and identify distinct FCC classes based on this structure. We then examine the impact of these structural differences on error performance by evaluating representative FCCs over the additive white Gaussian noise (AWGN) channel using both soft-decision and hard-decision decoding. The results show that FCCs with different distance-matrix structures can exhibit markedly different Data BER and function error behavior, and that the influence of code structure depends strongly on the decoding strategy.

cs.IT↗

arXiv2025

Hierarchical Coded Caching in High Memory Regime with Coded Placement

We consider a two-layer hierarchical coded caching network where a server with a library of $N$ files is connected to $K_1$ mirrors, each having a cache memory of size $M_1$. Each mirror is further connected to $K_2$ users, each equipped with a dedicated cache of size $M_2$. In this paper, we propose two distinct coded caching schemes based on coded placement, corresponding to two distinct memory pairs, $ (M_1, M_2) $. We show that the proposed schemes outperform the existing schemes at these memory points given by the proposed schemes for smaller values of $K_2$. In setups where mirrors are positioned near each other, avoiding signal interference is crucial. This can be ensured by having all mirrors transmit using orthogonal carrier frequencies. To compare our schemes with existing ones, we used the composite rate metric, which accurately represents the total bandwidth utilized in such setups. The composite rate is given by $\overline{R} = R_1 + K_1 R_2$, where $R_1$ is the rate from the server to the mirrors, and $R_2$ is the rate from the mirrors to the users, with respect to $M_1$ and $M_2$.

cs.IT↗

arXiv2023

Coded Caching for Hierarchical Two-Layer Networks with Coded Placement

We examine a two-layered hierarchical coded caching problem, a configuration addressed in existing research. This involves a server connected to $K_1$ mirrors, each of which serves $K_2$ users. The mirrors and the users are equipped with caches of size $M_1$ and $M_2$, respectively. We propose a hierarchical coded caching scheme with coded placements that outperforms existing schemes. To ensure a fair comparison, we introduce the notion of composite rate, defined as $\overline{R} = R_1 + K_1 R_2$, where $R_1$ is the rate from the server to mirrors and $R_2$ is the rate from mirrors to users. The composite rate has not been discussed before in the literature and is pertinent when mirrors transmit with different carrier frequencies. For the proposed scheme, we show a trade-off between the global memory $\overline{M}=K_1M_1+K_1K_2M_2$ of the system and the composite rate and compare with the existing schemes. Additionally, we conduct this comparative analysis by plotting $R_1$ + $R_2$ against global memory, which is particularly beneficial for systems wherein each mirror can utilize the same carrier frequency, given their significant spatial separation. Additionally, we propose an optimized scheme for the specific case of a single mirror, showing improved performance in this scenario.

cs.IT↗