Joint Network and Gelfand-Pinsker Coding for 3-Receiver Gaussian Broadcast Channels with Receiver Message Side Information

The problem of characterizing the capacity region for Gaussian broadcast channels with receiver message side information appears difficult and remains open for N >= 3 receivers. This paper proposes a joint network and Gelfand-Pinsker coding method for 3-receiver cases. Using the method, we establish a unified inner bound on the capacity region of 3-receiver Gaussian broadcast channels under general message side information configuration. The achievability proof of the inner bound uses an idea of joint interference cancelation, where interference is canceled by using both dirty-paper coding at the encoder and successive decoding at some of the decoders. We show that the inner bound is larger than that achieved by state of the art coding schemes. An outer bound is also established and shown to be tight in 46 out of all 64 possible cases.Comment: Author's final version (presented at the 2014 IEEE International Symposium on Information Theory [ISIT 2014]

On Coding over Sliced Information

The interest in channel models in which the data is sent as an unordered set of binary strings has increased lately, due to emerging applications in DNA storage, among others. In this paper we analyze the minimal redundancy of binary codes for this channel under substitution errors, and provide several constructions, some of which are shown to be asymptotically optimal up to constants. The surprising result in this paper is that while the information vector is sliced into a set of unordered strings, the amount of redundant bits that are required to correct errors is order-wise equivalent to the amount required in the classical error correcting paradigm

Two Deletion Correcting Codes from Indicator Vectors

Construction of capacity achieving deletion correcting codes has been a baffling challenge for decades. A recent breakthrough by Brakensiek et al ., alongside novel applications in DNA storage, have reignited the interest in this longstanding open problem. In spite of recent advances, the amount of redundancy in existing codes is still orders of magnitude away from being optimal. In this paper, a novel approach for constructing binary two-deletion correcting codes is proposed. By this approach, parity symbols are computed from indicator vectors (i.e., vectors that indicate the positions of certain patterns) of the encoded message, rather than from the message itself. Most interestingly, the parity symbols and the proof of correctness are a direct generalization of their counterparts in the Varshamov-Tenengolts construction. Our techniques require 7log(n)+o(log(n)) redundant bits to encode an n-bit message, which is closer to optimal than previous constructions. Moreover, the encoding and decoding algorithms have O(n) time complexity

Two Deletion Correcting Codes from Indicator Vectors

Construction of capacity achieving deletion correcting codes has been a baffling challenge for decades. A recent breakthrough by Brakensiek et al., alongside novel applications in DNA storage, have reignited the interest in this longstanding open problem. In spite of recent advances, the amount of redundancy in existing codes is still orders of magnitude away from being optimal. In this paper, a novel approach for constructing binary two-deletion correcting codes is proposed. By this approach, parity symbols are computed from indicator vectors (i.e., vectors that indicate the positions of certain patterns) of the encoded message, rather than from the message itself. Most interestingly, the parity symbols and the proof of correctness are a direct generalization of their counterparts in the Varshamov- Tenengolts construction. Our techniques require 7log(n)+o(log(n) redundant bits to encode an n-bit message, which is near-optimal

Optimal k-Deletion Correcting Codes

Levenshtein introduced the problem of constructing k-deletion correcting codes in 1966, proved that the optimal redundancy of those codes is O(k log N), and proposed an optimal redundancy single-deletion correcting code (using the so-called VT construction). However, the problem of constructing optimal redundancy k-deletion correcting codes remained open. Our key contribution is a solution to this longstanding open problem. We present a k-deletion correcting code that has redundancy 8k log n+ o(log n) and encoding/decoding algorithms of complexity O(n^(2k+1)) for constant k

Robust Indexing for the Sliced Channel: Almost Optimal Codes for Substitutions and Deletions

Encoding data as a set of unordered strings is receiving great attention as it captures one of the basic features of DNA storage systems. However, the challenge of constructing optimal redundancy codes for this channel remained elusive. In this paper, we address this problem and present an order-wise optimal construction of codes that are capable of correcting multiple substitution, deletion, and insertion errors for this channel model. The key ingredient in the code construction is a technique we call robust indexing: simultaneously assigning indices to unordered strings (hence, creating order) and also embedding information in these indices. The encoded indices are resilient to substitution, deletion, and insertion errors, and therefore, so is the entire code

Two Deletion Correcting Codes from Indicator Vectors

Construction of capacity achieving deletion correcting codes has been a baffling challenge for decades. A recent breakthrough by Brakensiek et al ., alongside novel applications in DNA storage, have reignited the interest in this longstanding open problem. In spite of recent advances, the amount of redundancy in existing codes is still orders of magnitude away from being optimal. In this paper, a novel approach for constructing binary two-deletion correcting codes is proposed. By this approach, parity symbols are computed from indicator vectors (i.e., vectors that indicate the positions of certain patterns) of the encoded message, rather than from the message itself. Most interestingly, the parity symbols and the proof of correctness are a direct generalization of their counterparts in the Varshamov-Tenengolts construction. Our techniques require 7log(n)+o(log(n)) redundant bits to encode an n-bit message, which is closer to optimal than previous constructions. Moreover, the encoding and decoding algorithms have O(n) time complexity