# Enhanced architecture and implementation of spectrum shaping codes

## TL;DR

This paper improves the design of spectral shaping codes used in communication systems by reducing hardware complexity and computational costs.

## Contribution

The paper introduces novel algorithms for parallel scrambling and reduced complexity MASP computations in spectral shaping codes.

## Key findings

- A parallel scrambling algorithm with O(1) time complexity is proposed.
- MASP computations are optimized using a search algorithm and shift operations, reducing complexity to O(1).
- The proposed methods use only 6% of hardware resources on a Spartan6 XC6SLX25 chip.

## Abstract

Spectral shaping codes are modulation codes widely used in communication and data storage systems. This research enhances the algorithms employed in constructing spectral shaping codes for hardware implementation. We present a parallel scrambling calculation with a time complexity of O(1). Second, in the minimum accumulated signal power (MASP) module, the sine-cosine accumulation needs to be determined by remainder with time complexity O(n2). We offer reduced MASP computations for short bit-width data, ROM storage, and addition pipelines. It can remove the remainder operation, reducing accumulated complexity to O(1). In addition, we present a search algorithm to generate segmented lines to replace the square operations in the MASP module. By employing the search algorithm and shift operations, we can reduce the complexity of the square from O(n2) to O(1). The implementation results reveal that the original and proposed MASPs yield nearly identical spectrum nulls. The encoder-decoder of the spectral shaping codes with proposed approaches consumes just 6% of the hardware resources when carried out with a Spartan6 XC6SLX25.