Improving the redundancy of Knuth's balancing scheme for packet transmission systems

A simple scheme was proposed by Knuth to generate binary balanced codewords from any information word. However, this method is limited in the sense that its redundancy is twice that of the full sets of balanced codes. The gap between Knuth's algorithm's redundancy and that of the full sets of balanced codes is significantly considerable. This paper attempts to reduce that gap. Furthermore, many constructions assume that a full balancing can be performed without showing the steps. A full balancing refers to the overall balancing of the encoded information together with the prefix. We propose an efficient way to perform a full balancing scheme that does not make use of lookup tables or enumerative coding.Comment: 11 pages, 4 figures, journal article submitted to Turkish journal of electrical and computer science

Encoding and Decoding of Balanced q-ary sequences using a gray code prefix

Abstract: Balancing sequences over a non-binary alphabet is considered, where the algebraic sum of the components (also known as the weight) is equal to some specific value. Various schemes based on Knuth’s simple binary balancing algorithm have been proposed. However, these have mostly assumed that the prefix describing the balancing point in the algorithm can easily be encoded. In this paper we show how non-binary Gray codes can be used to generate these prefixes. Together with a non-binary balancing algorithm, this forms a complete balancing system with straightforward and efficient encoding/decoding

A construction for balancing non-binary sequences based on gray code prefixes

Abstract: 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 algorithm. The encoding of our construction does not make use of lookup tables, while the decoding process is simple and can be done in parallel

Efficient balancing of q-ary sequences with parallel decoding

Abstract: Balancing of q-ary sequences, using a generalization of Knuth’s efficient parallel balancing scheme, is considered. 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 fast syndrome-based error correction

Abstract: We investigate a Knuth-like scheme for balancing q-ary codewords, which has the virtue that look-up tables for coding and decoding the prefix are avoided by using precoding and error correction techniques. We show how the scheme can be extended to allow for error correction of single channel errors using a fast decoding algorithm that depends on syndromes only, making it considerably faster compared to the prior art exhaustive decoding strategy. A comparison between the new and prior art schemes, both in terms of redundancy and error performance, completes the study

Construction of efficient q-ary balanced codes

Abstract : Abstract—Knuth proposed a simple scheme for balancing codewords, which was later extended for generating q-ary balanced codewords. The redundancy of existing schemes for balancing q-ary sequences is larger than that of the full balanced set which is the minimum achievable redundancy. In this article, we present a simple and efficient method to encode the prefix that results in less redundancy for the construction of q-ary balanced codewords

The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure

Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed by exploiting a concatenated code structure, which invokes iterative decoding. Therefore, in this paper we provide an extensive step-by-step tutorial for designing EXtrinsic Information Transfer (EXIT) chart aided concatenated quantum codes based on the underlying quantum-to-classical isomorphism. These design lessons are then exemplified in the context of our proposed Quantum Irregular Convolutional Code (QIRCC), which constitutes the outer component of a concatenated quantum code. The proposed QIRCC can be dynamically adapted to match any given inner code using EXIT charts, hence achieving a performance close to the hashing bound. It is demonstrated that our QIRCC-based optimized design is capable of operating within 0.4 dB of the noise limit