Lower Bounds on the Minimum Pseudodistance for Linear Codes with $q$-ary PSK Modulation over AWGN

Index Coded PSK Modulation

In this paper we consider noisy index coding problem over AWGN channel. We give an algorithm to map the index coded bits to appropriate sized PSK symbols such that for the given index code, in general, the receiver with large amount of side information will gain in probability of error performance compared to the ones with lesser amount, depending upon the index code used. We call this the \textbf{PSK side information coding gain}. Also, we show that receivers with large amount of side information obtain this coding gain in addition to the bandwidth gain whereas receivers with lesser amount of…

Non Binary Polar Codes with Equidistant Transform for Transmission over the AWGN Channel

Finding fast polarizing transforms is an important problem as polar codes suffer from slow finitelength performance. This paper considers non binary polar codes for transmission over the AWGN channel and designs polarizing transforms with better distance characteristics using a simple procedure for signal sets. The main idea of the paper is to define Equidistant Polarizing Transforms and show that they achieve the best distance spectrum bound. We provides an example of such transform for q = 5. In this case PSK-type signal set is used. Finally, we show performance gains and some comparison wit…

Noisy Index Coding with PSK and QAM

Noisy index coding problems over AWGN channel are considered. For a given index coding problem and a chosen scalar linear index code of length $N$, we propose to transmit the $N$ index coded bits as a single signal from a $2^N$- PSK constellation. By transmitting the index coded bits in this way, there is an $N/2$ - fold reduction in the bandwidth consumed. Also, receivers with side information satisfying certain conditions get coding gain relative to a receiver with no side information. This coding gain is due to proper utilization of their side information and hence is called "PSK side infor…

Codeword-Independent Performance of Nonbinary Linear Codes Under Linear-Programming and Sum-Product Decoding

A coded modulation system is considered in which nonbinary coded symbols are mapped directly to nonbinary modulation signals. It is proved that if the modulator-channel combination satisfies a particular symmetry condition, the codeword error rate performance is independent of the transmitted codeword. It is shown that this result holds for both linear-programming decoders and sum-product decoders. In particular, this provides a natural modulation mapping for nonbinary codes mapped to PSK constellations for transmission over memoryless channels such as AWGN channels or flat fading channels wit…

PSK调制索引编码中带边信息接收机的最优两步译码

An Optimal Two-Step Decoding at Receivers with Side Information in PSK-Modulated Index Coding

本文研究了无优先级接收机在PSK调制索引编码中的两步译码问题，推导了边信息有噪时消息比特的错误估计概率表达式，并揭示了多级调制下最小化传输数不再等价于最小化错误概率，译码策略选择标准随边信息信噪比变化。

Linear-Programming Decoding of Nonbinary Linear Codes

A framework for linear-programming (LP) decoding of nonbinary linear codes over rings is developed. This framework facilitates linear-programming based reception for coded modulation systems which use direct modulation mapping of coded symbols. It is proved that the resulting LP decoder has the 'maximum-likelihood certificate' property. It is also shown that the decoder output is the lowest cost pseudocodeword. Equivalence between pseudocodewords of the linear program and pseudocodewords of graph covers is proved. It is also proved that if the modulator-channel combination satisfies a particul…

New Accurate Approximation for Average Error Probability Under $κ-μ$ Shadowed Fading Channel

This paper proposes new accurate approximations for average error probability (AEP) of a communication system employing either $M$-phase-shift keying (PSK) or differential quaternary PSK with Gray coding (GC-DQPSK) modulation schemes over $κ-μ$ shadowed fading channel. Firstly, new accurate approximations of error probability (EP) of both modulation schemes are derived over additive white Gaussian noise (AWGN) channel. Leveraging the trapezoidal integral method, a tight approximate expression of symbol error probability for $M$-PSK modulation is presented, while new upper and lower bounds for …

Pseudocodeword weights for non-binary LDPC codes

Pseudocodewords of q-ary LDPC codes are examined and the weight of a pseudocodeword on the q-ary symmetric channel is defined. The weight definition of a pseudocodeword on the AWGN channel is also extended to two-dimensional q-ary modulation such as q-PAM and q-PSK. The tree-based lower bounds on the minimum pseudocodeword weight are shown to also hold for q-ary LDPC codes on these channels.

Linear-programming Decoding of Non-binary Linear Codes

We develop a framework for linear-programming (LP) decoding of non-binary linear codes over rings. We prove that the resulting LP decoder has the `maximum likelihood certificate' property, and we show that the decoder output is the lowest cost pseudocodeword. Equivalence between pseudocodewords of the linear program and pseudocodewords of graph covers is proved. LP decoding performance is illustrated for the (11,6,5) ternary Golay code with ternary PSK modulation over AWGN, and in this case it is shown that the LP decoder performance is comparable to codeword-error-rate-optimum hard-decision b…

Efficient Multi-Dimensional Mapping Using QAM Constellations for BICM-ID

Bit-interleaved coded modulation with iterative decoding (BICM-ID) offers very good error performance over additive white Gaussian noise (AWGN) and fading channels if it uses a wisely designed signal mapping. Further, error performance of BICM-ID can significantly be improved by employing multi-dimensional (MD) modulation. However, suitable MD mappings are obtained by computer search techniques except for MD modulations that use smaller constellation e.g., binary phase shift keying (BPSK), quadrature phase shift keying (QPSK) and $8$-ary phase shift keying ($8$-PSK) as basic modulation. The al…

基于张量的调制：从编码角度出发

Tensor-Based Modulation on the Unit Circle: A Coding Perspective

本文提出了一种基于张量的调制方法，通过非二元线性分组码和M-PSK调制，构建了几何上均匀的信号空间码，并展示了其在多用户通信中的鲁棒性和抗干扰能力。