Niloufar Ahmadypour | Searcharxiv

arXiv2026

Source Coding with Free Bits and the Multi-Way Number Partitioning Problem

We introduce a new variant of variable-length source coding for sending a source over two parallel channels, one of which is costly and the other free. We give a complete solution to this problem. Next, we relate the problem to the number partitioning problem, which is the task of dividing a given list of numbers into a pre-specified number of subsets such that the sum of the numbers in each subset is as nearly equal as possible. We introduce two new objective functions for this problem and show that an adapted version of the Huffman coding algorithm (with a runtime of $\mathcal{O}(n \log n)$ for input size $n$) produces the optimal solution for one objective function, and a nearly optimal solution for the other objective function.

cs.DS↗

arXiv2021

Transmission of a Bit over a Discrete Poisson Channel with Memory

A coding scheme for transmission of a bit maps a given bit to a sequence of channel inputs (called the codeword associated to the transmitted bit). In this paper, we study the problem of designing the best code for a discrete Poisson channel with memory (under peak-power and total-power constraints). The outputs of a discrete Poisson channel with memory are Poisson distributed random variables with a mean comprising of a fixed additive noise and a linear combination of past input symbols. Assuming a maximum-likelihood (ML) decoder, we search for a codebook that has the smallest possible error probability. This problem is challenging because error probability of a code does not have a closed-form analytical expression. For the case of having only a total-power constraint, the optimal code structure is obtained, provided that the blocklength is greater than the memory length of the channel. For the case of having only a peak-power constraint, the optimal code is derived for arbitrary memory and blocklength in the high-power regime. For the case of having both the peak-power and total-power constraints, the optimal code is derived for memoryless Poisson channels when both the total-power and the peak-power bounds are large.

cs.IT↗