On Redundancy Reduction of Non-Recursive Second-Order Spectral-Null Codes

D. Pelusi

doi:10.1109/access.2019.2934847

Abstract

The code design problem of non-recursive second-Order Spectral Null (2-OSN) codes is to convert balanced information words into 2-OSN words employing the minimum possible redundancy. Let $k$ be the balanced information word length. If $k\in \,\,2 {{I}}{{N}}$ then the 2-OSN coding scheme has length $n=k+r$ , with 2-OSN redundancy $r \in \,\,2 {{I}}{{N}}$ and $n\in \,\,4 {{I}}{{N}}$ . Here, we use a scheme with $r=2 \log k+\Theta (\log \log k)$ . The challenge is to reduce redundancy even further for any given $k$ . The idea is to exploit the degree of freedom to select from more than one possible 2-OSN encoding of a given balanced information word. To reduce redundancy, empirical results suggest that extra information $\delta _{k}=0.5 \log k+\Theta (\log \log k)$ is obtained. Thus, the proposed approach would give a smaller redundancy $r^{\prime }=1.5 \log k+\Theta (\log \log k)$ less than $r=2 \log k+\Theta (\log \log k)$ .

Highlights

The spectral-null codes are an important class of codes applied in recording systems
We propose to convey extra auxiliary data using the freedom of choosing more than one possible balanced encoding of a given 2-OSN information word [28]
The results show that the extra information δk = 0.5 log k + is conveyed from the encoder

Summary

INTRODUCTION

The spectral-null codes are an important class of codes applied in recording systems. Tallini et al [28] designed 2-OSN codes whose scheme is based on the combination between the Knuth’s parallel decoding proposal [2], [13], [14], [21] and the random walk method for second-Order Spectral Null codes [9], [20], [30]. This approach gives a novel non-recursive efficient codes design method which makes the cited codes less redundant than other code designs.

Pelusi

PROPOSED SCHEME

RESULTS AND DISCUSSION

CONCLUSION