Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1310.1712

Partial Sums Computation In Polar Codes Decoding

Guillaume Berhault·Camille Leroux·Christophe Jego·Dominique Dallet
View original source ↗Read source document ↗Export metadata ↓

Abstract

Polar codes are the first error-correcting codes to provably achieve the channel capacity but with infinite codelengths. For finite codelengths the existing decoder architectures are limited in working frequency by the partial sums computation unit. We explain in this paper how the partial sums computation can be seen as a matrix multiplication. Then, an efficient hardware implementation of this product is investigated. It has reduced logic resources and interconnections. Formalized architectures, to compute partial sums and to generate the bits of the generator matrix k^n, are presented. The proposed architecture allows removing the multiplexing resources used to assigned to each processing elements the required partial sums.

Explore related subjects

cs.ARcs.ITmath.IT

Keep this discovery

BibTeXRIS

Guillaume Berhault, Camille Leroux, Christophe Jego, Dominique Dallet. 2015-01-09. Partial Sums Computation In Polar Codes Decoding. https://arxiv.org/abs/1310.1712

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Fengshui: Demystifying Chiplet Ecosystem and Bespoke Neural Network Accelerator Codesign

Modern ML workloads, with stringent latency and energy constraints, are increasingly hard to run efficiently on homogeneous commodity hardware. We argue that operator-level disaggregation--tailoring microarchitecture, batching, and memory hierarchy to each operator--is essential to overcome these limitations, though the resulting highly bespoke accelerators incur prohibitive Non-Recurring Engineering (NRE) costs. Chiplet-based integration amortizes NRE across applications, but choosing which chiplets to build and how to compose them into accelerators is circularly dependent--a chiplet pool's value depends on the constructed accelerators, while accelerator quality is constrained by available chiplets. This paper introduces Fengshui, a chiplet ecosystem and accelerator co-design framework that jointly optimizes chiplet pool composition and bespoke application-specific integrated circuit (BASIC) design. Fengshui constructs BASICs through operator-level disaggregation, co-exploring chiplet and memory heterogeneity, tensor fusion, and pipeline/tensor/expert parallelism with place-and-route validation for physical implementability. With just 8 strategically selected chiplets, encompassing network switches, processing-in-memory units, and accelerators with diverse microarchitectures, Fengshui-generated BASICs achieve 48.5%, 88.1%, 93.0%, and 97.8% reductions in energy, energy-cost product (EC), energy-delay product (EDP), and energy-delay-cost product (EDPC) over homogeneous accelerators, while scoring within 4.1% of unconstrained heterogeneous designs across diverse neural networks. For datacenter MoE and dense LLM serving, Fengshui reduces prefill energy and EC by up to 16.8% and 28.7%, respectively; for edge autonomous vehicle perception, it achieves 12.0% energy and 23.6% EC reductions under real-time latency constraints.

cs.AR↗
arXiv2026

BEACON: A Versatile Accelerator for Computational Pathology Applications

While accelerators for AI have seen great commercial success, it is challenging to replicate that success for other specialized domains due to a number of factors. We make the case that barriers for new accelerators can be lowered by starting with a baseline AI accelerator, and adding minimal logic to support new operators demanded by new specialized domains. This leads to a versatile chip that can be manufactured at high volume and deployed for a range of popular applications. We refer to this as the AI+X approach. This paper explores its potential for the emerging domain of Computational Pathology, which involves analysis of large whole-slide tissue images with a multi-stage pipeline. The pipeline requires support for a number of different kernels and operators - early stages perform segmentation and feature extraction, followed by graph creation with k nearest neighbor (kNN) algorithms, and finally inference with an iterative graph convolutional network (GCN) that alternates between Aggregation and Combination. We show that these stages execute inefficiently on a range of baseline CPU, GPU, AI, and GCN accelerators. That inefficiency is addressed with a combination of software re-structuring and small modifications to a baseline systolic AI accelerator. Many of the above kernels can be mapped to a systolic accelerator by offering a flexible datapath between processing elements and register access mechanisms. We add support for feature aggregation, load balanced execution, Euclidean distance calculation, binning, and counter aggregation. This additional flexibility and logic grows the area of a baseline AI chiplet by 1.1x, but by avoiding the memory wall and offering high parallelism, the proposed accelerator BEACON yields over an order of magnitude higher throughput for Computational Pathology than baseline CPU and GPU platforms.

cs.AR↗
arXiv2026

Bio-inspired Learning and Decision-Making with Probabilistic In-Memory Computing Hardware: Part 2

This report extends our previous work (Part 1), which introduced an energy-based model for learning and decision-making under uncertainty. The model leverages stochastic Langevin dynamics to continuously evolve approximate probability distributions over neuron states and model weights. However, as noted in Part 1 and confirmed through GPU-based implementations, large-scale probabilistic energy-based models of this nature face significant scalability challenges due to excessive execution latency. This latency stems from a fundamental mismatch: massively parallel models with low arithmetic intensity (such as energy-based models) are being executed on processor architectures like GPUs that rely on high-bandwidth memory (HBM) interfaces. The HBM imposes brutally sequential execution constraints on inherently parallelizable models, creating the false impression that such models are unscalable. In reality, it is the GPU architecture itself, with its dependence on HBM interfaces, that is not a scalable processor architecture for this class of AI model. In this report, we demonstrate using a detailed transaction-level model (TLM) of a probabilistic analogue in-memory computing (AIMC) processor that the same energy-based model can execute well over 1000x faster than data-center-grade hardware by eliminating the HBM interface and performing computation directly within on-chip memory.

cs.AR↗