迭代硬判决解码的BCH码块马尔可夫叠加传输提升系统性能

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本文主要探讨了具有迭代硬判决解码的块马尔可夫叠加传输(BlockMarkov Superposition Transmission, BMST)在BCH码(Bose-Chaudhuri-Hocquenghem Codes)中的应用，即BMST-BCH编码。相比于其他类型的BMST编码，BMST-BCH编码的一个关键优势在于它能够在保持较低错误率地板的同时，只需求两个编码记忆单元，这对于减少延迟和降低实现复杂性至关重要。这种编码方法特别注重效率，因为它降低了对连续存储的需求，这对于实时通信系统来说是个显著优点。为了进一步简化实现，作者提出了一种硬决策滑动窗口解码算法。在这个算法中，仅处理二进制和/或缺失（即擦除）信息，并在节点间交换这些简单的数据形式。这有助于简化节点间的通信和处理流程，减少了中间步骤所需的计算量。评估BMST-BCH编码性能的方法也是本文的重要部分。作者开发了一种快速的仿真方法，结合使用 genie-aided lower bound (一种利用理想情况下的性能界限进行分析的技术)和密度演化分析，这两种工具能够提供对编码性能的精确估计，而无需进行大量的实际运行测试。通过这种方式，研究人员可以快速优化编码参数，提高系统的可靠性并减小设计周期。这篇研究论文旨在解决在通信系统中高效利用BCH码的问题，通过改进的编码策略和优化的解码算法，提高了系统的性能指标，对于实际通信系统的实时性和效率提升具有重要意义。这项工作对于那些关注低延迟、低成本以及高效纠错能力的无线通信和数据传输应用具有实用价值。

Block Markov Superposition Transmission of BCH

Codes with Iterative Hard-decision Decoding

Nina Lin

, Suihua Cai

, and Xiao Ma

2,3

School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou 510006, China

School of Data and Computer Science, Sun Yat-sen University, Guangzhou 510006, China

Guangdong Key Laboratory of Information Security Technology, Sun Yat-sen University, Guangzhou 510006, China

Email: linnina@mail2.sysu.edu.cn, caish5@mail2.sysu.edu.cn, maxiao@mail.sysu.edu.cn

Abstract—This paper is concerned with block Markov super-

position transmission of BCH (BMST-BCH) codes. Compared

with other BMST codes, BMST-BCH codes can achieve a lower

error ﬂoor with an encoding memory of two, which is critical to

reduce both delay and implementation complexity. To further re-

duce the implementation complexity, we propose a hard-decision

sliding-window decoding algorithm, in which only binary and/or

erasure messages are processed and exchanged between nodes. A

fast simulation approach is proposed, with the help of the genie-

aided lower bound and the density evolution analysis, to evaluate

the performance of BMST-BCH codes at the BER of 10

−15

BMST-BCH codes are constructed with overheads ranging from

15% to 25%, exhibiting performances comparable to staircase

codes with similar latencies. The proposed construction is more

ﬂexible to trade off latency against performance, and may

ﬁnd applications in optical transport networks as an attractive

candidate.

I. INTRODUCTION

In optical communication systems, Bose-Chaudhuri-

Hocquenghem (BCH) codes are often taken as the component

codes to construct forward error correction (FEC) codes with

high rates to achieve very low error probabilities [1]. For

example, with an overhead (OH) of 6.7%, the BCH-BCH

product code with erasures-and-errors decoding is capable of

achieving a net coding gain (NCG) of 9.24 dB at the output bit

error rate (BER) of 10

−15

, as seen from Fig. I.37 in the ITU-T

G.975.1 standard [2]. With a similar overhead, a staircase

code (an elegant extension from a block BCH-BCH product

code to its convolutional counterpart) was proposed in [3]

to achieve an NCG of 9.41 dB at the same BER. Another

attractive advantage is their low-complexity hard-decision

decoding (HDD), which is commonly believed to be the most

feasible decoding to implement for the next-generation 100

Gb/s applications [4]. However, in addition to the inﬂexibility

with respect to varying frame sizes and overheads, the

construction of staircase codes usually requires a large

amount of calculation for searching good code parameters

either by the extensive software simulations [5] or by density

evolution (DE) analysis [6].

In this paper, we present a new type of convolutional

BCH codes, where short BCH codes are embedded into the

block Markov superposition transmission (BMST) system [7],

resulting in BMST-BCH codes. The construction is ﬂexible

in the sense that any given overhead can be attained with

adjustable frame sizes while keeping the basic hardware un-

changed [8]. Meanwhile, the decoding can be implemented as

a hard-decision sliding-window decoding (SWD) algorithm,

where only binary and/or erasure messages are processed and

passed over a normal graph. To analyze the performance at

an extreme low target BER, a fast simulation approach is

proposed for the component BCH code. This approach allows

us to calculate efﬁciently both the genie-aided lower bound

and the DE threshold, which coincide with each other in the

error-ﬂoor region. Then the genie-aided lower bound, whose

calculation is much simpler than the DE analysis, is taken as

a criterion for code optimization.

Numerical results shows that the performance of BMST-

BCH codes is well predicted by the proposed DE threshold

and genie-aided lower bound. It is shown that BMST-BCH

codes can achieve performances comparable to staircase codes

at the BER of 10

−15

. More distinguishedly, the performance

of BMST-BCH codes can be easily tailored by adjusting the

encoding/decoding delay while keeping unchanged the basic

hardware components of the encoder and decoder.

II. E

NCODING AND DECODING OF BMST-BCH SYSTEM

A. Channel Model

In this paper, we consider binary phase-shift keying (BP-

SK) signalling over additive white Gaussian noise (AWGN)

channels with hard decisions. The channel can be reduced to

binary symmetric erasure channels (BSEC) with input alphabet

= {0, 1} and output alphabet {0, 1,e}, where the symbol e

represents the bit erasure. Such a channel can be characterized

by a probability vector (p

), where p

is the probability

of a bit being correctly transmitted, p

is the probability of

bit error and p

is the probability of bit erasure. Obviously, a

binary symmetric channel (BSC) is a special case with p

=0.

B. Encoding of BMST-BCH System

Let BCH [n, k, d

min

] be a binary systematic BCH code,

where n is the code length, k is the code dimension and

min

is the designed distance. By deﬁnition, the code rate is

R 

, and the overhead is calculated as

n−k

. An erasures-

and-errors decoder is assumed to correct both erasures and

errors. In the case when the number i of occurrences of

errors and the number j of occurrences of erasures satisfy

2i + j<d

min

, the erasures-and-errors decoder outputs the

2017 IEEE International Symposium on Information Theory (ISIT)

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