On the Many Faces of Block Codes

Implementation and Application of Automata

Sasidharan

Aggarwal

et al. 2001

Self Cite

Abstract.We have implemented a package that transforms concise algebraic descriptions of linear block codes into finite automata representations, and also generates decoders from such representations. The transformation takes a description of the code in the form of a k × n generator matrix over a field with q elements, representing a finite language containing q k strings, and constructs a minimal automaton for the language from it, employing a well known algorithm. Next, from a decomposition of the minimal automaton into subautomata, it generates an overlayed automaton, and an efficient decoder for the code using a new algorithm. A simulator for the decoder on an additive white Gaussian noise channel is also generated. This simulator can be used to run test cases for specific codes for which an overlayed automaton is available. Experiments on the well known Golay code indicate that the new decoding algorithm is considerably more efficient than the traditional Viterbi algorithm run on the original automaton.

Section: Tailbiting Trellisesmentioning

confidence: 99%

“…An overlayed trellis has been introduced in [6], and we give the definition below. Let C be a linear code over a finite alphabet.…”

Section: Tailbiting Trellises As Overlayed Automatamentioning

confidence: 99%

Section: Definition 4 An Overlayed Proper Trellis Is Said To Exist Fmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Package for the Implementation of Block Codes as Finite Automata

Implementation and Application of Automata

Sasidharan

Aggarwal

et al. 2001

Self Cite

ML decoding of block codes on their tailbiting trellises

Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252)

Kumar²,

Sasidharan³

et al.

-A m a x i m u m likelihood decoding algor i t h m is presented for tailbiting trellises for block codes. The algorithm works in t w o phases. The first phase is a V i t e r b i decoding algorithm on the tailbiting trellis, while the second uses the A* algorithm adapted for application in this context. Results of simulations on tailbiting trellises for some block codes, indicate that t h i s decoding algorithm is quite fast.

On the complexity of exact maximum likelihood decoding on tail-biting trellises

International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.

An algorithm for exact maximum likelihood(ML) decoding on tail-biting trellises is presented, which exhibits very good average case behavior. An approximate variant is proposed, whose simulated performance is observed to be virtually indistinguishable from the exact one at all values of signal to noise ratio, and which effectively performs computations equivalent to at most two rounds on the tail-biting trellis. The approximate algorithm is analyzed, and the conditions under which its output is different from the ML output are deduced. The results of simulations on an AWGN channel for the exact and approximate algorithms on the 16 state tail-biting trellis for the (24,12) Extended Golay Code, and tail-biting trellises for two rate 1/2 convolutional codes with memories of 4 and 6 respectively, are reported. An advantage of our algorithms is that they do not suffer from the effects of limit cycles or the presence of pseudocodewords. I. INTRODUCTIONTail-biting trellises are perhaps the simplest instances of decoding graphs with cycles. A tail-biting trellis has a Tanner graph [31] with a single cycle and usually approximate algorithms are used for decoding, as exact algorithms are believed to be too expensive. These approximate algorithms iterate around the trellis until either convergence is reached, or for a preset number of cycles. To the best of our knowledge, no exact decoding algorithms other than the brute force algorithm have been proposed so far for the general case, though there are several approximate algorithms for maximum-likelihood decoding [28], [22], [34], [33], [7], [20] and exact algorithms for bounded distance decoding [4]. The problem of Maximum A-Posteriori Probability(MAP)decoding is not addressed here. We propose an exact recursive algorithm, which exhibits very good average case behavior. The algorithm exploits the fact that a linear tail-biting trellis can be viewed as a coset decomposition The results in this paper appear in part in ISIT 2001[25] Priti Shankar acknowledges support fron the Scientific Analysis Group, DRDO, Delhi October 30, 2018 DRAFT