Eran Hof

Secrecy-achieving polar-coding

A polar coding scheme is suggested for the binary-input memoryless symmetric and degraded wire-tap channel. The provided scheme achieves the entire rate-equivocation region for the considered model.

Polar coding for reliable communications over parallel channels

A capacity-achieving polar coding scheme is introduced for reliable communications over a set of parallel communication channels. They are assumed to be arbitrarily-permuted memoryless binary-input and output-symmetric (MBIOS) channels, and they form a set of (stochastically) degraded channels. The general case where the parallel channels are not necessarily degraded is addressed in the full paper version [3], though the suggested scheme is not capacity-achieving in the general case.

Performance Bounds for Nonbinary Linear Block Codes Over Memoryless Symmetric Channels

The performance of nonbinary linear block codes is studied in this paper via the derivation of new upper bounds on the block error probability under maximum-likelihood (ML) decoding. The transmission of these codes is assumed to take place over a memoryless and symmetric channel. The new bounds, which are based on the Gallager bounds and their variations, are applied to the Gallager ensembles of nonbinary and regular low-density parity-check (LDPC) codes. These upper bounds are also compared with sphere-packing lower bounds. This study indicates that the new upper bounds are useful for the performance evaluation of coded communication systems which incorporate nonbinary coding techniques.

Performance Bounds for Erasure, List, and Decision Feedback Schemes With Linear Block Codes

A message independence property and some new performance upper bounds are derived in this work for erasure, list, and decision-feedback schemes with linear block codes transmitted over memoryless symmetric channels. Similar to the classical work of Forney, this work is focused on the derivation of some Gallager-type bounds on the achievable tradeoffs for these coding schemes, where the main novelty is the suitability of the bounds for both random and structured linear block codes (or code ensembles). The bounds are applicable to finite-length codes and to the asymptotic case of infinite block length, and they are applied to low-density parity-check code ensembles.

Capacity-Achieving Polar Codes for Arbitrarily Permuted Parallel Channels

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

Performance bounds for erasure, list and feedback schemes with linear block codes

A message independence property and some new performance upper bounds are reported for erasure, list and decision-feedback schemes with linear block codes transmitted over memoryless symmetric channels. Similarly to the classical work of Forney, this work is focused on the derivation of some Gallager-type bounds on the achievable tradeoffs for these coding schemes, where the main novelty is the suitability of the bounds for both random and structured linear block codes (or code ensembles). The bounds are applicable to finite-length codes and to the asymptotic case of infinite block length, and they are applied to low-density parity-check (LDPC) code ensembles.

On the Deterministic-Code Capacity of the Two-User Discrete Memoryless Arbitrarily Varying General Broadcast Channel With Degraded Message Sets

An inner bound on the deterministic-code capacity region of the two-user discrete memoryless arbitrarily varying general broadcast channel (AVGBC) was characterized by Jahn, assuming that the common message capacity is nonzero; however, he did not indicate how one could decide whether the latter capacity is positive. Csiszaacuter and Narayans result for the single-user arbitrarily varying channel (AVC) establishes the missing part in Jahns characterization. Nevertheless, being based on Ahlswedes elimination technique, Jahns characterization is not applicable for symmetrizable channels under state constraint. Here, the various notions of symmetrizability for the two-user broadcast AVC are defined. Sufficient non-symmetrizability condition that renders the common message capacity of the AVGBC positive is identified using an approach different from Jahns. The decoding rules we use establish an achievable region under state and input constraints for the family of degraded message sets codes over the AVGBC

Guessing Attacks on Distributed-Storage Systems

We study the secrecy of a distributed-storage system for passwords. The encoder, Alice, observes a length-n password and describes it using δ s-bit hints, which she stores in different locations. The legitimate receiver, Bob, observes ν of those hints. In one scenario we require that the expected number of guesses it takes Bob to guess the password approach 1 as n tends to infinity, and in the other that the expected size of the shortest list that Bob must form to guarantee that it contain the password approach 1. The eavesdropper, Eve, sees η <; ν hints. Assuming that Alice cannot control which hints Bob and Eve observe, we characterize for each scenario the largest normalized (by n) exponent that we can guarantee for the expected number of guesses it takes Eve to guess the password.

Gallager-type bounds for non-binary linear block codes over memoryless symmetric channels

The performance analysis of non-binary linear block codes is studied under ML decoding where it is assumed that the transmission takes place over memoryless symmetric channels. Gallager-type bounds are derived, and the proposed bounds are exemplified for expurgated regular ensembles of non-binary low-density parity-check (LDPC) codes. These bounds are also compared with classical and recent improved sphere-packing bounds, indicating that these bounding techniques are informative for the performance evaluation of coded communication systems which incorporate non-binary coding techniques.

Secret and private rates on degraded wire-tap channels via polar coding

A secrecy coding scheme is provided for degraded wire-tap channels via the method of channel polarization. It is shown that the entire rate-equivocation region is achievable via the provided scheme. The key element in the provided scheme is the utilization of the noisy bits, which are required to achieve the secrecy constraint, to provided private non-secure rate for the legitimate user.