Achievable rates for channels with deletions and insertions

Abstract

This paper considers a binary channel with deletions and insertions, where each input bit is transformed in one of the following ways: it is deleted with probability d, or an extra bit is added after it with probability i, or it is transmitted unmodified with probability 1 − d − i. A computable lower bound on the capacity of this channel is derived. The transformation of the input sequence by the channel may be viewed in terms of runs as follows: some runs of the input sequence get shorter/longer, some runs get deleted, and some new runs are added. It is difficult for the decoder to synchronize the channel output sequence to the transmitted codeword mainly due to deleted runs and new inserted runs.The main idea is a mutual information decomposition in terms of the rate achieved by a sub-optimal decoder that determines the positions of the deleted and inserted runs in addition to decoding the transmitted codeword. The mutual information between the channel input and output sequences is expressed as the sum of the rate achieved by this decoder and the rate loss due to its sub-optimality. Obtaining computable lower bounds on each of these quantities yields a lower bound on the capacity. The bounds proposed in this paper provide the first characterization of achievable rates for channels with general insertions, and for channels with both deletions and insertions. For the special case of the deletion channel, the proposed bound improves on the previous best lower bound for deletion probabilities up to 0.3.

Fundamental Bounds for Sequence Reconstruction From Nanopore Sequencers

“…Of particular relevance to our results is the work in deletion channels [13] (see also [18] for a survey). As mentioned, the capacity of independent insertion-deletion channels is as yet unknown, though lower bounds have been proven in the form of explicit distributional constructions and coding schemes [26]. There have been efforts aimed at error correction in insertion-deletion channels in the context of communication, storage, and RFID systems [28].…”

Energy-Efficient Communication Over the Unsynchronized Gaussian Diamond Network

“…We refer the reader to [3] and references therein for a survey on this topic up to 2009. Some of the work that has appeared since 2009 is [4], [5], [6], [7], [8].…”

“…where we have used the definition of α = P 2 /(1 + µgP 1 ) in (6). Since δ N → 0 as N → ∞ by (16), we have that the SNR is lower bounded by SNR lb , where SNR lb is given by…”

Sharp Analytical Capacity Upper Bounds for Sticky and Related Channels

“…Tight numerical upper bounds for the elementary duplication channel were already derived in [13]. Furthermore, there is a line of work studying elementary duplications combined with deletions, insertions, and bit flips [16][17][18][19]. For such channels, the behavior of the capacity for small duplication probability is wellunderstood [20].…”