Parallel error correcting codes

A Generalization of the Parallel Error Correcting Codes

“…We call this pair of errors (e, ) a (t, s)-parallel error. In this paper, we assume t ≥ s. Note that if s = 0, a (t, 0)-parallel error (e, ) satisfies e = and this model is reduced to that assumed in [1]. Therefore, the above model is a generalized version of that in [1] by allowing additional at most s errors in each line of the channel.…”

“…Especially, for a multiple access adder channel, many studies about code constructions have been conducted [2,3,4,5,6]. In contrast to the conventional works, R. Ahlswede et al have considered a new multiple access channel model called a parallel channel and discussed coding schemes for this channel [1] The parallel channel is a bundle of lines through which messages are transmitted parallelly. When messages are transmitted through the channel, highly correlated errors occur in respective lines.…”

“…Although the results of this paper are applicable to a general m senders model for any m ≥ 2, the case of m = 2 is essential and important. Therefore, as discussed in [1], we first focus on the case of m = 2, and then we generalize the results to a general m senders model. This paper is organized as follows: in Sect.…”

“…They have derived necessary and sufficient conditions of code correcting the t-parallel error. They have given code constructions of the optimal parallel error correcting codes with the largest size for given a code length and t. Their work gives a bunch of suggestions, however the channel model in [1] is not sufficient for practical applications.…”

“…Subsequently, we derive necessary and sufficient conditions of parallel error correcting codes whose line codes are dependent each other. We show a code construction that achieves the maximal size for a given code length and t. Then, we consider linear parallel error correcting codes whose line codes are independent and derive a bound of the maximal achievable rate (pair of dimensions of all line codes [1,5]). Although the results of this paper are applicable to a general m senders model for any m ≥ 2, the case of m = 2 is essential and important.…”