Shogo Usami

Gradient descent bit flipping algorithms for decoding LDPC codes

A novel class of bit-flipping (BF) algorithms for decoding low-density parity-check (LDPC) codes is presented. The proposed algorithms, which are called gradient descent bit flipping (GDBF) algorithms, can be regarded as simplified gradient descent algorithms. Based on gradient descent formulation, the proposed algorithms are naturally derived from a simple nonlinear objective function.

Superadditivity in capacity of quantum channel for q-ary linearly dependent real symmetric-state signals

An analytical expression for the mutual information is derived for q-ary pseudo-cyclic codes. We compute mutual information for 3- and 5-ary linearly dependent signals. It is shown that higher quantum gain can be achieved by 3-ary codes and 50 percent of full quantum gain is achieved even for the codeword length n=16.

The multiple coding gain with two criteria in an attenuated quantum channel

Recently, the capacity of an attenuated quantum channel which is a model of a long distance optical fiber channel was derived. This capacity is in principle achieved by a continuous modulation and a random coding. However, a continuous modulation and a random coding are not practical. Therefore, we need discussion about capacity used for more practical modulation and coding. In this paper, we show characteristics of both information and error probability criteria for an attenuated channel using M-ary PSK modulation and pseudo-cyclic codes.

On attainment of the capacity of broadband quantum channel by wavelength division multiplexing

Recently, the exact solution of the capacity of an attenuated quantum channel which is a model of a long distance optical fiber channel was derived [V. Giovannetti, et al., Phys. Rev. Lett. 90, 027902, (2004)]. In particular, the capacity of a broadband quantum channel, which is the ultimate limit of quantum communications, was shown. In this paper, we consider wavelength division multiplexing in order to attain the capacity of a broadband quantum channel.

Modified Algorithm on Maximum Detected Bit Flipping Decoding for High Dimensional Parity-Check Code

We have researched high dimensional parity-check (HDPC) codes that give good performance over a channel that has a very high error rate. HDPC code has a little coding overhead because of its simple structure. It has hard-in, maximum detected bit flipping (MDBF) decoding that has reasonable decoding performance and computational cost. In this paper, we propose a modified algorithm for MDBF decoding and compare the proposed MDBF decoding with conventional hard-in decoding.

Consideration on two dimensional constraint codes with honeycomb structure

In this paper, we defined the new two-dimensional constraint named the honeycomb constraint, and we evaluated the capacity bounds for the first-order honeycomb constraint. As a result, we were able to achieve the more precise capacity bounds by considering special matrix. Moreover, we applied the single-state block coding for the first-order honeycomb constraints, therefore we obtained the coding rates near the capacity.

‘Pure’ Square‐Root Measurement and its Optimality for Mixed‐State Signals

The optimum quantum measurements that minimize the error probability for mixed‐state signals are considered. The square‐root measurement (SRM) is known to be the optimal measurement for many pure‐state signals, e.g., symmetric states, linear codes, etc. However, when the states are mixed, the SRM is no longer guaranteed to be optimal even if the states are symmetric. Here, we define the ‘pure’ square‐root measurement (pure‐SRM) which is the SRM for pure states and its optimality for mixed states. It is shown that the pure‐SRM is satisfied the necessary and sufficient conditions of the quantum Bayes strategy when the signals are mixed by transmission errors, and therefore the pure‐SRM is the optimal measurement.

Construction of Quantum Error Correcting Code for Specific Position Errors

Quantum error correcting codes for specific position errors, which are a different type from ordinary quantum error correcting codes, are proposed. The quantum Hamming bound is modified to apply to such codes. Furthermore, an example of the code which breaks the modified quantum Hamming bound is shown.

On IP based access protocol for high-speed wireless LAN

Next-generation wireless LAN and mobile communications might be constructed upon IP based radio networks. A deep and fast fading of high-frequency high-speed radio transmission with a longer path will be inevitable and give rise to severe erroneous channels. It causes frame synchronization loss and address misreading of the IP packet. New schemes are requested for the protocol and physical layer of such IEEE 802.11s to improve degradation in reception probability or throughput of the packet. The proposed new schemes are three fold. First is the introduction of an error correcting code (ECC) into the physical layer of the packet header and to the payload frame. A new ECC and new scheme for the robust packet synchronization are proposed. The second proposal is the adoption of GPS data to discriminate mobiles accessible to the access point (AP). The distance is the prime parameter to estimate RF signal quality. Third is enhancement of busy or idle messages by introducing the marked packet upon the handshaking and termination modes to cover the hidden terminal problem. Furthermore, a single-carrier transceiver is discussed as one candidate for future applications, basing on the controlled access distance and fading. The transceiver is promising from the respects of simple circuit configuration and constant envelope modulation with low power consumption. The developed torus knot code (TKC) is robust and high-speed for the decoding, and considered as the outer code for the 8-PSK TCM with inner code of a rate 2/3 convolution code.

Superadditivity in Capacity of Quantum Channel by Classical Pseudo-Cyclic Codes

Analytical solution of mutual information by square-root measurement for binary linear code is given. Applying the solution, we show properties of superadditivity in capacity by BCH codes with codeword length 15 and 31. Furthermore, we refer to codes almost achieving the quantum channel capacity.