Blind Reconciliation

Information reconciliation is a crucial procedure in the classical post-processing of quantum key distribution (QKD). Poor reconciliation efficiency, revealing more information than strictly needed, may compromise the maximum attainable distance, while poor performance of the algorithm limits the practical throughput in a QKD device. Historically, reconciliation has been mainly done using close to minimal information disclosure but heavily interactive procedures, like Cascade, or using less efficient but also less interactive -just one message is exchanged- procedures, like the ones based in low-density parity-check (LDPC) codes. The price to pay in the LDPC case is that good efficiency is only attained for very long codes and in a very narrow range centered around the quantum bit error rate (QBER) that the code was designed to reconcile, thus forcing to have several codes if a broad range of QBER needs to be catered for. Real world implementations of these methods are thus very demanding, either on computational or communication resources or both, to the extent that the last generation of GHz clocked QKD systems are finding a bottleneck in the classical part. In order to produce compact, high performance and reliable QKD systems it would be highly desirable to remove these problems. Here we analyse the use of short-length LDPC codes in the information reconciliation context using a low interactivity, blind, protocol that avoids an a priori error rate estimation. We demonstrate that 2x10^3 bits length LDPC codes are suitable for blind reconciliation. Such codes are of high interest in practice, since they can be used for hardware implementations with very high throughput.Comment: 22 pages, 8 figure

Optimized puncturing distributions for irregular non-binary LDPC codes

In this paper we design non-uniform bit-wise puncturing distributions for irregular non-binary LDPC (NB-LDPC) codes. The puncturing distributions are optimized by minimizing the decoding threshold of the punctured LDPC code, the threshold being computed with a Monte-Carlo implementation of Density Evolution. First, we show that Density Evolution computed with Monte-Carlo simulations provides accurate (very close) and precise (small variance) estimates of NB-LDPC code ensemble thresholds. Based on the proposed method, we analyze several puncturing distributions for regular and semi-regular codes, obtained either by clustering punctured bits, or spreading them over the symbol-nodes of the Tanner graph. Finally, optimized puncturing distributions for non-binary LDPC codes with small maximum degree are presented, which exhibit a gap between 0.2 and 0.5 dB to the channel capacity, for punctured rates varying from 0.5 to 0.9.Comment: 6 pages, ISITA1

Multiplicatively Repeated Non-Binary LDPC Codes

We propose non-binary LDPC codes concatenated with multiplicative repetition codes. By multiplicatively repeating the (2,3)-regular non-binary LDPC mother code of rate 1/3, we construct rate-compatible codes of lower rates 1/6, 1/9, 1/12,... Surprisingly, such simple low-rate non-binary LDPC codes outperform the best low-rate binary LDPC codes so far. Moreover, we propose the decoding algorithm for the proposed codes, which can be decoded with almost the same computational complexity as that of the mother code.Comment: To appear in IEEE Transactions on Information Theor

Untainted Puncturing for Irregular Low-Density Parity-Check Codes

Puncturing is a well-known coding technique widely used for constructing rate-compatible codes. In this paper, we consider the problem of puncturing low-density parity-check codes and propose a new algorithm for intentional puncturing. The algorithm is based on the puncturing of untainted symbols, i.e. nodes with no punctured symbols within their neighboring set. It is shown that the algorithm proposed here performs better than previous proposals for a range of coding rates and short proportions of punctured symbols.Comment: 4 pages, 3 figure

Bilayer Protograph Codes for Half-Duplex Relay Channels

Despite encouraging advances in the design of relay codes, several important challenges remain. Many of the existing LDPC relay codes are tightly optimized for fixed channel conditions and not easily adapted without extensive re-optimization of the code. Some have high encoding complexity and some need long block lengths to approach capacity. This paper presents a high-performance protograph-based LDPC coding scheme for the half-duplex relay channel that addresses simultaneously several important issues: structured coding that permits easy design, low encoding complexity, embedded structure for convenient adaptation to various channel conditions, and performance close to capacity with a reasonable block length. The application of the coding structure to multi-relay networks is demonstrated. Finally, a simple new methodology for evaluating the end-to-end error performance of relay coding systems is developed and used to highlight the performance of the proposed codes.Comment: Accepted in IEEE Trans. Wireless Com

Design of rate-compatible structured LDPC codes for hybrid ARQ applications

In this paper, families of rate-compatible protograph-based LDPC codes that are suitable for incremental-redundancy hybrid ARQ applications are constructed. A systematic technique to construct low-rate base codes from a higher rate code is presented. The base codes are designed to be robust against erasures while having a good performance on error channels. A progressive node puncturing algorithm is devised to construct a family of higher rate codes from the base code. The performance of this puncturing algorithm is compared to other puncturing schemes. Using the techniques in this paper, one can construct a rate-compatible family of codes with rates ranging from 0.1 to 0.9 that are within 1 dB from the channel capacity and have good error floors