Maximum-likelihood Decoding Algorithm Research Articles

An improved method to compute lists of binary vectors that optimize a given weight function with application to soft-decision decoding

Many algorithms, tree-searching and decoding algorithms in particular, need to generate some lists of binary vectors by increasing value of a given weight function and without omission. To this end, there are not many alternatives to the Dijkstra and the Viterbi algorithm. In this letter a technique suggested by Battail in 1986 to perform this task is reviewed. Then a new technique is deduced from it, that proves to be more efficient than all the others. As an illustration of its good performance we compare a maximum-likelihood-decoding (MLD) algorithm that can be derived from it, with current state-of-the-art complete MLD algorithms for general binary linear codes.

A new class of linear codes with two-level structure

The binary extended Golay code has a two-level structure, which can be used in the decoding of the code. However, such structure is not limited to the Golay code, in fact, several binary linear codes can be constructed by a projective method which is related to the structure. In this correspondence, the binary (4n, n+2k, ≥min(8, n, 2d)) linear codes are resulted from quaternary (n, k, d) linear block codes. Based on the structure, the efficient maximum likelihood decoding algorithms can be presented correspondingly for the derived codes.

A trellis-based recursive maximum-likelihood decoding algorithm for binary linear block codes

This paper presents an efficient trellis-based maximum-likelihood decoding algorithm for binary linear block codes. This algorithm is recursive in nature and is devised based on the structural properties and optimum sectionalization of a code trellis. The complexity of the proposed decoding algorithm is analyzed. Numerical results show that the proposed decoding algorithm significantly reduces the decoding complexity. A recursive method for finding the optimum sectionalization of a trellis in terms of computational complexity is given.

Reliability-based code-search algorithms for maximum-likelihood decoding of block codes

Efficient code-search maximum-likelihood decoding algorithms, based on reliability information, are presented for binary Linear block codes. The codewords examined are obtained via encoding. The information set utilized for encoding comprises the positions of those columns of a generator matrix G of the code which, for a given received sequence, constitute the most reliable basis for the column space of G. Substantially reduced computational complexity of decoding is achieved by exploiting the ordering of the positions within this information set. The search procedures do not require memory; the codeword to be examined is constructed from the previously examined codeword according to a fixed rule. Consequently, the search algorithms are applicable to codes of relatively large size. They are also conveniently modifiable to achieve efficient nearly optimum decoding of particularly large codes.

Fast Decoding Algorithms for First Order Reed-Muller and Related Codes

Fast decoding algorithms for short codes based on modifications of maximum likelihood decoding algorithms of first order Reed-Muller codes are described. Only additions-subtractions, comparisons and absolute value calculations are used in the algorithms. Soft and hard decisions maximum likelihood decoding algorithms for first order Reed-Muller and the Nordstrom-Robinson codes with low complexity are proposed.

On classes of rate k/(k+1) convolutional codes and their decoding techniques

For the class of rate k/(k+1) convolutional codes, Yamada et al. (1983) proposed an efficient maximum-likelihood decoding algorithm called the YHM algorithm. In order to reduce the complexity of the YHM algorithm, this paper presents two techniques for simplifying the trellis diagram used in the YHM algorithm. We further observe that the proposed techniques effectively reduce the complexity of the YHM algorithm for two classes /spl Xi/ and /spl Xi//sub f/ (which is a subclass of /spl Xi/) of rate k/(k+1) convolutional codes. The construction of codes in these classes is also discussed. It is shown that /spl Xi/ codes with d/sub free/=3,4 can be obtained by simple construction. A code search algorithm for /spl Xi/ codes with d/sub free//spl ges/5 is also introduced. Computer searches are performed to construct good /spl Xi/ and /spl Xi//sub f/ codes. For specified decoding complexities, a number of these new codes give better error performance than previously reported codes.

Maximum likelihood decoding of the Leech lattice

An algorithm for maximum likelihood decoding of the Leech lattice is presented. The algorithm involves projecting the points of the Leech lattice directly onto the codewords of the (6,3,4) quaternary code-the hexacode. Projection on the hexacode induces a partition of the Leech lattice into four cosets of a certain sublattice 24. Such a partition into cosets enables maximum likelihood decoding of the Leech lattice with 3595 real operations in the worst case and only 2955 operations on the average. This is about half the worst case and the average complexity of the best previously known algorithm. >

Notes on fast maximum-likelihood decoding-algorithm of cyclic code onZ-channel

This paper considers the Z-channel, which is known as a channel model for photon communication or semiconductor memory. A new decoding algorithm is proposed and discussed. Recently, studies have been made from various viewpoints on the asymmetrical error-correcting code suited to the Z-channel, which is considered interesting. One of the basic problems in the Z-channel is the performance and the decoding method when the cyclic code with various features is applied, but it has been investigated little. This paper presents first a maximum-likelihood decoding algorithm which is highly efficient for the cyclic code on the Z-channel. It is then shown that by providing a certain threshold for the algorithm, a higher-speed decoding is realized. It is shown also that by setting the threshold above a certain value, the computational complexity can be improved without sacrificing the maximum-likelihood property. Finally, it is demonstrated by numerical calculation that the decoding error probability is improved greatly by the decoding algorithm proposed in this paper, together with a drastic improvement in the computational complexity.

A new transform algorithm for Viterbi decoding

Implementation of the Viterbi decoding algorithm has attracted a great deal of interest in many applications, but the excessive hardware/time consumption caused by the dynamic and backtracking decoding procedures make it difficult to design efficient VLSI circuits for practical applications. A transform algorithm for maximum-likelihood decoding is derived from trellis coding and Viterbi decoding processes. Dynamic trellis search operations are paralleled and well formulated into a set of simple matrix operations referred to as the Viterbi transform (VT). Based on the VT, the excessive memory accesses and complicated data transfer scheme demanded by the trellis search are eliminated. Efficient VLSI array implementations of the VT have been developed. Long constraint length codes can be decoded by combining the processors as the building blocks.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Coset codes. II. Binary lattices and related codes

For pt.I see ibid., vol.34, no.5, p.1123-51 (1988). The family of Barnes-Wall lattices (including D/sub 4/ and E/sub 8/) of lengths N=2/sup n/ and their principal sublattices, which are useful in constructing coset codes, are generated by iteration of a simple construction called the squaring construction. The closely related Reed-Muller codes are generated by the same construction. The principal properties of these codes and lattices are consequences of the general properties of iterated squaring constructions, which also exhibit the interrelationships between codes and lattices of different lengths. An extension called the cubing construction generates good codes and lattices of lengths N=3*2/sup n/, including the Golay code and Leech lattice, with the use of special bases for 8-space. Another related construction generates the Nordstrom-Robinson code and an analogous 16-dimensional nonlattice packing. These constructions are represented by trellis diagrams that display their structure and interrelationships and that lead to efficient maximum-likelihood decoding algorithms. >

A shortened Viterbi decoding algorithm for terminated rate-&amp;lt;tex&amp;gt;1/N&amp;lt;/tex&amp;gt;convolutional codes with hard decisions (Corresp.)

An algorithm for maximum likelihood decoding of terminated rate-1/ <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> convolutional codes with hard decisions is presented which is based upon, but is simpler than, the Viterbi algorithm. The algorithm makes use of an algebraic description of convolutional codes introduced by Massey et al. For reasonable values of the probability of error, the algorithm is shown to produce substantial savings in decoding complexity compared with the Viterbi algorithm.

Correlative level coding and maximum-likelihood decoding

Modems for digital communication often adopt the so-called correlative level coding or the partial-response signaling, which attains a desired spectral shaping by introducing controlled intersymbol interference terms. In this paper, a correlative level encoder is treated as a linear finite-state machine and an application of the maximum-likelihood decoding (MLD) algorithm, which was originally proposed by Viterbi in decoding convolutional codes, is discussed. Asymptotic expressions for the probability of decoding error are obtained for a class of correlative level coding systems, and the results are confirmed by computer simulations. It is shown that a substantial performance gain is attainable by this probabilistic decoding method.