International Journal of Information and Coding Theory
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International Journal of Information and Coding Theory (3 papers in press)
Third-Party Cyclic Code Reconstruction over Binary Erasure Channel by Arti Yardi Abstract: We consider a setup where Alice is transmitting channel coded messages to\r\nBob and intruder Willie is snooping over this communication. Willie does not know the channel code that Alice is using and wishes to identify it\r\nin order to decode the intercepted messages. This problem is termed as blind reconstruction of channel codes and has possible applications in cognitive radios and military. In this work, we consider the situation when Willie knows that Alice\'s channel code belongs to the family of binary cyclic codes and the underlying communication channel is the binary erasure channel. We further nsider the situation when the location of codeword boundaries, termed as synchronization of the codeword sequence, is also not known. We present an algorithm to identify the parameters of the unknown channel code corresponding to the given data.The key step in our algorithm consists of distinguishing between the two situations when all of the assumed parameters are correct and when either of the parameter is incorrect. As part of analysis, we present a lower bound on probability of correctly distinguishing between these two situations. Keywords: Cyclic codes; Linear block codes; Blind reconstruction of channel codes; Covert communication.
A New Burst Error Correcting method for Reed-Solomon Codes Based on Composite Parity-Check Matrices by Song Chol Pak Abstract: This paper presents the construction method of composite parity-check (CPC) matrices and a new burst error correcting method for (n, k) Reed-Solomon (RS) codes based on CPC matrices. The proposed method is capable of finding burst error locations by only locations of symbol 0s of syndromes computed by CPC? matrices and evaluating the corresponding error magnitudes using CPC matrices. rnThe simulation results show that the proposed method can correct burst errors for the codes with the rate less than about 0.75 with lower complexity and correct burst errors of length up to n-k-1 and burst erasures of length up to n-k.rn Keywords: Burst error; Composite Parity-check (CPC) matrix; Longest zero span; Reed-Solomon (RS) codes.
Optimisation of information processes using non-extensive entropies without parameters by Jesús Fuentes, Octavio Obregón Abstract: As a non-extensive statistical mechanics application, a possible path to generalised information theory is discussed by introducing a family of non-extensive entropies dependent solely on probability: H ± D (P). In this scheme, two regimes of probabilities are possible; while the low-probability region exactly coincides with standard information theory, the high-probability regime offers further optimisation in certain information approaches. In this work, we explore two fundamental processes. Firstly, we propose generalisations to Shannons coding theorems by modifying the ordinary Kraft inequality. This modification will ensure the codes to be uniquely decipherable in the framework of entropies H ±D (P). Secondly, we calculate the channel capacity of a binary symmetric channel (BSC) and a binary erasure channel (BEC). Our results suggest an improvement in data compression and transmission with respect to the standard formulation. Keywords: data compression; coding theorems; non-extensive entropies. DOI: 10.1504/IJICOT.2021.10041896