A Generalization of the Parallel Error Correcting Codes

Abstract

-This paper generalizes parallel error correcting codes proposed by Alshwede et al. over a type of multiple access channels called a parallel channel. The generalized parallel error correcting codes can handle with more errors compared with the original ones. We show construction methods of independent and non-independent parallel error correcting code and decoding methods. We derive some bounds about the size of respective parallel error correcting code.

Error control codes for parallel channel with correlated errors

“…In this paper, we introduced two channel models of parallel error channels by allowing more distinct error symbols among two consecutive lines than those in [12]. The introduced channel models are a wider class of that by Ahlswede et al [1] and that in [12].…”

“…, e m ) ∈ GF mn (q) is referred to as a type-I (t, u, s)-parallel error. 2 If u = 0, the type-I channel error model corresponds to a channel model assumed in [12]. The case of u = 0 and s = 0 of type-I channel error model is a channel model in [1], where a parallel error (e 1 , e 2 , .…”

“…The channel is called the parallel error channel and error correcting codes for this channel is referred to as parallel error correcting codes. Subsequently, the present authors [12] have generalized parallel channels by allowing at most s random errors such that s ≤ t besides the same errors in all lines. They have showed a code construction that achieves the maximal size of parallel error correcting codes for given code length, t and s. They also have introduced probabilistic model of parallel error channel and analyzed decoding performance [13].…”

“…Then if we take correlation of burst error into account, it may possible to increase the coding rate of an (asymmetric) interleaving code based-on channel coding technique over a parallel channel [12]. However, argument in [12] cannot be directly adopted to an interleaving code because of the naive assumption s ≤ t. Motivated from this reason, this paper presents a further generalization of parallel error channels.…”

“…Then if we take correlation of burst error into account, it may possible to increase the coding rate of an (asymmetric) interleaving code based-on channel coding technique over a parallel channel [12]. However, argument in [12] cannot be directly adopted to an interleaving code because of the naive assumption s ≤ t. Motivated from this reason, this paper presents a further generalization of parallel error channels. The primary concept is to introduce another parameter u along with t and s, and to permit the number of random errors exceeds the value of s. In order to analyze in detail, we separate the set of error symbols into three parts, and we derive a necessary and sufficient condition of the parallel error correcting codes.…”