Signaling Over Arbitrarily Permuted Parallel Channels

Capacity-Achieving Polar Codes for Arbitrarily Permuted Parallel Channels

“…In this model, each one of the parallel channels corresponds to a possible state of the time-varying channel, and the communication takes place over one of these parallel channels according to the instantaneous state of the time-varying channel. The model of arbitrarily-permuted parallel channels was introduced in [1] where each message is encoded into a number (say S) of code-sequences with a common block length, each one of the S code-sequences is transmitted over a different parallel channel where the assignment of codewords to channels is known to the receiver, and it is modeled by an arbitrary permutation π of the set {1, . .…”

“…Channel coding over arbitrarily-permuted parallel channels was studied in [1] and more recently in [3], where it was assumed that all these parallel channels have an identical input alphabet. In the case where all the parallel channels have the same capacity-achieving input distribution, it was proved in [1,Theorem 1] that the capacity of the system is equal to the sum of the capacities of the parallel channels.…”

“…Channel coding over arbitrarily-permuted parallel channels was studied in [1] and more recently in [3], where it was assumed that all these parallel channels have an identical input alphabet. In the case where all the parallel channels have the same capacity-achieving input distribution, it was proved in [1,Theorem 1] that the capacity of the system is equal to the sum of the capacities of the parallel channels. Furthermore, [1] also addresses the case where the parallel channels have different capacity-achieving input distributions, and it determines the capacity of the system also in this case (see [1,Theorem 2]).…”

“…In the case where all the parallel channels have the same capacity-achieving input distribution, it was proved in [1,Theorem 1] that the capacity of the system is equal to the sum of the capacities of the parallel channels. Furthermore, [1] also addresses the case where the parallel channels have different capacity-achieving input distributions, and it determines the capacity of the system also in this case (see [1,Theorem 2]). This research was supported by the Israel Science Foundation (grant no.…”

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Channel coding over arbitrarily-permuted parallel channels was first studied by Willems et al (2008). This paper introduces capacity-achieving polar coding schemes for arbitrarily-permuted parallel channels where the component channels are memoryless, binary-input and output-symmetric.

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