New Set of Codes for the Maximum-Likelihood Decoding Problem
نویسنده
چکیده
The maximum-likelihood decoding problem is known to be NP-hard for general linear and Reed-Solomon codes [1, 4]. In this paper, we introduce the notion of A-covered codes, that is, codes that can be decoded through a polynomial time algorithm A whose decoding bound is beyond the covering radius. For these codes, we show that the maximum-likelihood decoding problem is reachable in polynomial time in the code parameters. Focusing on binary BCH codes, we were able to find several examples of A-covered codes, including two codes for which the maximum-likelihood decoding problem can be solved in quasi-quadratic time.
منابع مشابه
A New Treatment of Priority-First Search Maximum-Likelihood Soft-Decision Decoding of Linear Block Codes
In this correspondence we present a new method to convert the maximum-likelihood soft-decision decoding problem for linear block codes into a graph search problem where generalized Dijkstra’s algorithm can still be applied to the decoding procedure. The cost assigned to every branch in the graph is based on a generalization of Wagner rule which is an equivalent form of the maximum-likelihood de...
متن کاملSpherical codes generated by binary partitions of symmetric pointsets
Recently, Ericson and Zinoviev presented a clever, new construction for spherical codes for the Gaussian channel using ideas of code concatenation and set partitioning. This family of new spherical codes is generated from sets of binary codes using equally spaced symmetric pointsets on the real line. The family contains some of the best known spherical codes in terms of minimum distance. Howeve...
متن کاملAdaptive Maximum-Likelihood Decoding Algorithms for Linear Block Codes
This correspondence represents two new soft decision decoding algorithms that promise to reduce complexity and at the same time achieve the maximum likelihood decoding (MLD) performance. The first method is an Adaptive Two-Stage Maximum Likelihood Decoder [1] that first estimates a minimum sufficient set and performs decoding within the smaller set to reduce complexity and at the same time achi...
متن کاملOn-the-Fly Maximum-Likelihood Decoding of Raptor Codes over the Binary Erasure Channel
In this letter, we propose an efficient on-the-fly algorithm for maximum-likelihood decoding of Raptor codes used over the binary erasure channel. It is shown that our proposed decoding algorithm can reduce the actual elapsed decoding time by more than two-thirds with respect to an optimized conventional maximum-likelihood decoding. key words: raptor codes, on-the-fly decoding, maximum-likeliho...
متن کاملComplexity of decoding positive-rate primitive Reed-Solomon codes
It has been proved that the maximum likelihood decoding problem of Reed-Solomon codes is NP-hard. However, the length of the code in the proof is at most polylogarithmic in the size of the alphabet. For the complexity of maximum likelihood decoding of the primitive Reed-Solomon code, whose length is one less than the size of alphabet, the only known result states that it is at least as hard as ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1011.2834 شماره
صفحات -
تاریخ انتشار 2010