# A Construction for Balancing Non-Binary Sequences Based on Gray Code Prefixes

@article{Mambou2017ACF, title={A Construction for Balancing Non-Binary Sequences Based on Gray Code Prefixes}, author={Elie Ngomseu Mambou and Theo G. Swart}, journal={IEEE Transactions on Information Theory}, year={2017}, volume={64}, pages={5961-5969} }

We introduce a new construction for the balancing of non-binary sequences that make use of Gray codes for prefix coding. Our construction provides full encoding and decoding of sequences, including the prefix. This construction is based on a generalization of Knuth’s parallel balancing approach, which can handle very long information sequences. However, the overall sequence—composed of the information sequence, together with the prefix—must be balanced. This is reminiscent of Knuth’s serial…

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## References

SHOWING 1-10 OF 19 REFERENCES

### Encoding and decoding of balanced q-ary sequences using a Gray code prefix

- Computer Science2016 IEEE International Symposium on Information Theory (ISIT)
- 2016

It is shown how non-binary Gray codes can be used to generate prefixes that form a complete balancing system with straightforward and efficient encoding/decoding.

### Very Efficient Balanced Codes

- Computer ScienceIEEE Journal on Selected Areas in Communications
- 2010

A new construction of sets of balanced codewords is presented, which is simple, does not use look-up tables, and is less redundant than Knuth's construction.

### Balanced Codes with Parallel Encoding and Decoding

- Computer ScienceIEEE Trans. Computers
- 1999

A balanced code with k information bits and r check bits is a binary code of length n=k+r and cardinality 2/sup k/ such that the number of 1s in each code word is equal to [n/2]. This paper describes…

### GENERALIZED GRAY CODES WITH APPLICATIONS

- Computer Science
- 1998

It is shown that the Tower of Hanoi problem, in which disks can only be moved to the adjacent pegs, can be solved by enumerating the (3, k)-Gray code, where k is the number of disks to be moved.

### Knuth’s balancing of codewords revisited

- Computer Science2008 IEEE International Symposium on Information Theory
- 2008

This paper presents results of attempts to improve the performance of Knuthpsilas balanced codes, a very simple algorithm for constructing sets of bipolar codewords with equal numbers of dasia1psil as and dasia-1psils, called balanced codes.

### On balanced codes

- Computer ScienceIEEE Trans. Inf. Theory
- 1990

The 2/sup 2/-r-1 construction given by D.E. Knuth is improved and the new codes are shown to be optimal when Knuth's complementation method is used.

### Efficient balancing of q-ary sequences with parallel decoding

- Computer Science2009 IEEE International Symposium on Information Theory
- 2009

It is shown that the new general scheme is as simple as the original binary scheme, which lends itself to parallel decoding of the balanced sequences.

### Prefixless q-ary balanced codes with ECC

- Computer Science2013 IEEE Information Theory Workshop (ITW)
- 2013

A Knuth-like method for balancing q-ary codewords, which is characterized by the absence of a prefix that carries the information of the balancing index, and can be extended to include error correction of single channel errors.

### m-ary Balanced Codes With Parallel Decoding

- Computer ScienceIEEE Trans. Inf. Theory
- 2015

The proposed codes are less redundant than the $m$ -ary balanced codes with parallel decoding found in the literature and yet maintain the same complexity.

### On independent set of Lee distance Gray codes

- Computer ScienceProceedings of IEEE International Symposium on Information Theory
- 1997

In a Gray code C, the set of k/sup n/ vectors over Z/sub k//sup n/ is arranged in a sequence such that two adjacent vectors are at a Lee distance one. It is assumed that the first and the last…