The Perfect Binary One-Error-Correcting Codes of Length 15: Part II--Properties

A complete classification of the perfect binary one-error-correcting codes of length 15 as well as their extensions of length 16 was recently carried out in [P. R. J. \"Osterg{\aa}rd and O. Pottonen, "The perfect binary one-error-correcting codes of length 15: Part I--Classification," IEEE Trans. Inform. Theory vol. 55, pp. 4657--4660, 2009]. In the current accompanying work, the classified codes are studied in great detail, and their main properties are tabulated. The results include the fact that 33 of the 80 Steiner triple systems of order 15 occur in such codes. Further understanding is gained on full-rank codes via switching, as it turns out that all but two full-rank codes can be obtained through a series of such transformations from the Hamming code. Other topics studied include (non)systematic codes, embedded one-error-correcting codes, and defining sets of codes. A classification of certain mixed perfect codes is also obtained.Comment: v2: fixed two errors (extension of nonsystematic codes, table of coordinates fixed by symmetries of codes), added and extended many other result

Coding with Scrambling, Concatenation, and HARQ for the AWGN Wire-Tap Channel: A Security Gap Analysis

This study examines the use of nonsystematic channel codes to obtain secure transmissions over the additive white Gaussian noise (AWGN) wire-tap channel. Unlike the previous approaches, we propose to implement nonsystematic coded transmission by scrambling the information bits, and characterize the bit error rate of scrambled transmissions through theoretical arguments and numerical simulations. We have focused on some examples of Bose-Chaudhuri-Hocquenghem (BCH) and low-density parity-check (LDPC) codes to estimate the security gap, which we have used as a measure of physical layer security, in addition to the bit error rate. Based on a number of numerical examples, we found that such a transmission technique can outperform alternative solutions. In fact, when an eavesdropper (Eve) has a worse channel than the authorized user (Bob), the security gap required to reach a given level of security is very small. The amount of degradation of Eve's channel with respect to Bob's that is needed to achieve sufficient security can be further reduced by implementing scrambling and descrambling operations on blocks of frames, rather than on single frames. While Eve's channel has a quality equal to or better than that of Bob's channel, we have shown that the use of a hybrid automatic repeat-request (HARQ) protocol with authentication still allows achieving a sufficient level of security. Finally, the secrecy performance of some practical schemes has also been measured in terms of the equivocation rate about the message at the eavesdropper and compared with that of ideal codes.Comment: 29 pages, 10 figure

Embedding in a perfect code

A binary 1-error-correcting code can always be embedded in a 1-perfect code of some larger lengthComment: Eng: 5pp, Rus: 5pp. V3: revised, a survey added; the accepted version; Russian translation adde

Development of rate-compatible structured LDPC CODEC algorithms and hardware IP

Issued as final reportSamsung Advanced Institute of Technolog

Coding for Cryptographic Security Enhancement using Stopping Sets

In this paper we discuss the ability of channel codes to enhance cryptographic secrecy. Toward that end, we present the secrecy metric of degrees of freedom in an attacker's knowledge of the cryptogram, which is similar to equivocation. Using this notion of secrecy, we show how a specific practical channel coding system can be used to hide information about the ciphertext, thus increasing the difficulty of cryptographic attacks. The system setup is the wiretap channel model where transmitted data traverse through independent packet erasure channels with public feedback for authenticated ARQ (Automatic Repeat reQuest). The code design relies on puncturing nonsystematic low-density parity-check codes with the intent of inflicting an eavesdropper with stopping sets in the decoder. Furthermore, the design amplifies errors when stopping sets occur such that a receiver must guess all the channel-erased bits correctly to avoid an expected error rate of one half in the ciphertext. We extend previous results on the coding scheme by giving design criteria that reduces the effectiveness of a maximum-likelihood attack to that of a message-passing attack. We further extend security analysis to models with multiple receivers and collaborative attackers. Cryptographic security is enhanced in all these cases by exploiting properties of the physical-layer. The enhancement is accurately presented as a function of the degrees of freedom in the eavesdropper's knowledge of the ciphertext, and is even shown to be present when eavesdroppers have better channel quality than legitimate receivers.Comment: 13 pages, 8 figure

A study of digital holographic filters generation. Phase 2: Digital data communication system, volume 1

An empirical study of the performance of the Viterbi decoders in bursty channels was carried out and an improved algebraic decoder for nonsystematic codes was developed. The hybrid algorithm was simulated for the (2,1), k = 7 code on a computer using 20 channels having various error statistics, ranging from pure random error to pure bursty channels. The hybrid system outperformed both the algebraic and the Viterbi decoders in every case, except the 1% random error channel where the Viterbi decoder had one bit less decoding error